Dark Matter, Dark Energy, Dark Gravity

Previously I have written about the possibility of primordial black holes as the explanation for dark matter, and on the observational constraints around such a possibility.

But maybe it is dark energy, not dark matter, that black holes explain. More precisely, it would be dark energy stars (or gravatars, or GEODEs) that are observationally similar to black holes.

Dark energy

Dark energy is named thusly because it has negative pressure. There is something known as an equation of state that relates pressure to energy density. For normal matter, or for dark matter, the coefficient of the relationship, w, is zero or slightly positive, and for radiation it is 1/3.

If it is non-zero and positive then the fluid component loses energy as the universe expands, and for radiation, this means there is a cosmological redshift. The redshift is in proportion to the universe’s linear scale factor, which can be written as the inverse of the cosmological redshift plus one, by normalizing it to the present-day scale. The cosmological redshift is a measure of the epoch as well, currently z = 0, and the higher the redshift the farther we look back into the past, into the earlier years of the universe. Light emitted at frequency ν is shifted to lower frequency (longer wavelength) ν’ = ν / (1 + z).

Since 1998, we have known that we live in a universe dominated by dark energy (and its associated dark pressure, or negative pressure). The associated dark pressure outweighs dark energy by a factor of 3 because it appears 3 times, once for each spatial component in Einstein’s stress-energy tensor equations of general relativity.

Thus dark energy contributes a negative gravity, or expansion acceleration, and we observe that our universe has been accelerating in its expansion for the past 4 or 5 billion years, since dark energy now provides over 2/3 of the universal energy balance. Dark matter and ordinary matter together amount to just less than 1/3 of the average rest-mass energy density.

If w is less than -1/3 for some pervasive cosmological component, then you have dark energy behavior for that component, and in our universe today over the past several billion years, measurements show w = -1 or very close to it. This is the cosmological constant case where dark energy’s negative pressure has the same magnitude but the opposite sign of the positive dark energy density. More precisely, the dark pressure is the negative of the energy density times the speed of light squared.

Non-singular black holes

There has been consideration for decades of other types of black holes that would not have a singularity at the center. In standard solutions of general relativity black holes have a central singular point or flat zone, depending on whether their angular momentum is zero or positive.

For example a collapsing neutron star overwhelms all pressure support from neutron degeneracy pressure once its mass exceeds the TOV limit at about 2.7 solar masses (depending on angular momentum), and forms a black hole that is often presumed to collapse to a singularity.

But when considering quantum gravity, and quantum physics generally, then there should be some very exotic behavior at the center, we just don’t know what. Vacuum energy is one possibility.

For decades various proposals have been made for alternatives to a singularity, but the problem has been observationally intractable. A Soviet cosmologist Gliner, who was born just 100 years ago in Kyiv, and who only passed away in 2021, proposed the basis for dark energy stars and a dark energy driven cosmology framework in 1965 (in English translation, 1966).

E. Gliner, early 1970s in St. Petersburg, courtesy Gliner family

He defended his Ph.D. thesis in general relativity including dark energy as a component of the stress-energy tensor in 1972. Gliner emigrated to the US in 1980.

The essential idea is that the equation of state for compressed matter changes to that of a material (or “stuff”) with a fully negative pressure, w = -1 and thus that black hole collapse would naturally result in dark energy cores, creating dark energy stars or gravatars rather than traditional black holes. The cores could be surrounded with an intermediate transition zone and a skin or shell of normal matter (Beltracchi and Gondolo 2019). The dark energy cores would have negative pressure.

Standard black hole solution is incomplete

Normally black hole physics is attacked with Kerr (non-zero angular momentum) or Schwarzschild (zero angular momentum) solutions. But these are incomplete, in that they assume empty surroundings. There is no matching of the solution to the overall background which is a cosmological solution. The universe tracks an isotropic and homogeneous (on the largest scales) Lambda-cold dark matter (ΛCDM) solution of the equations of general relativity. Since dark energy now dominates, it is approaching a de Sitter exponential runaway, whereas traditional black hole solutions with singularities are quite the opposite, known as anti-de Sitter.

We have no general solution for black hole equations including the backdrop of an expanding universe. The local Kerr solution for rotating black holes that is widely used ignores the far field. Really one should match the two solution regimes, but there has been no analytical solution that does that; black hole computations are very difficult in general, even ignoring the far field.

In 2019, Croker and Weiner of the University of Hawaii found a way to match a model of dark energy cores to the standard ΛCDM cosmology, and demonstrate that for w = -1 that dark energy stars (black holes with dark energy cores) would have masses that grow in proportion to the cube of the universe’s linear scale factora, starting immediately from their initial formation at high redshifts. In effect they are forced to grow their masses and expand (with their radius proportional to mass as for a black hole) by all of the other dark energy stars in the universe acting in a collective fashion. They call this effect, cosmological coupling of the dark energy star gravity to the long-range and long-term cosmological gravitational field.

This can be considered a blueshift for mass, as distinguished from the energy or frequency redshift we see with radiation in the cosmos.

Their approach potentially addresses several problems: (1) an excess of larger galaxies and their supermassive black holes seen very early on in the recent James Webb Space Telescope data, (2) more intermediate mass black holes than expected, as confirmed from gravitational wave observations of black hole mergers, (see Coker, Zevin et al. 2021 for a possible explanation via cosmological coupling), and (3) possibly a natural explanation for all or a substantial portion of the dark energy in the universe, which has been assumed to be highly diffuse rather than composed primarily of a very large number of point sources.

Inside dark energy stars, the dark energy density would be many, many orders of magnitude higher than it is in the universe at large. But as we will see below, it might be enough to explain all of the dark energy budget of the ΛCDM cosmology.

M87* supermassive black hole (or dark energy star) imaged in polarized radio waves by the Event Horizon Telescope collaboration; signals are combined from a global collection of radio telescopes via aperture synthesis techniques. European Southern Observatory, licensed under a Creative Commons Attribution 4.0 International License

A revolutionary proposal

Here’s where it gets weird. A number of researchers have investigated the coupling of a black hole’s interior to an external expanding universe. In this case there is no singularity but instead a vacuum energy solution interior to the (growing) compact stellar remnant.

And one of the most favored possibilities is that the coupling causes the mass for all black holes to grow in proportion to the universe’s characteristic linear size a cubed, just as if it were a cosmological constant form of dark energy. This type of “stuff” retains equal energy density throughout all of space even as the space expands, as a result of its negative pressure with equation of state parameter w = -1.

Just this February a very interesting pair of papers has been published in The Astrophysical Journal (the most prestigious American journal for such work) by a team of astronomers from 9 countries (US, UK, Canada, Japan, Netherlands, Germany, Denmark, Portugal, and Cyprus), led by the University of Hawaii team mentioned above.

They have used observations of a large number of supermassive black holes and their companion galaxies out to redshift 2.5 (when the universe was less than 3 billion years of age) to argue that there is observable cosmologicalcouplingbetween the cosmological gravitational field at large and the SMBH masses, where they suppose those masses are dominated by dark energy cores.

Figure 1 from Farrah, Croker, et al. shows their measured cosmological coupling parameter k based on 3 catalogs (5 samples using different emission lines) of supermassive black holes contained in elliptical galaxies at high redshifts, 0.7 < z < 2.5. If k =3, that corresponds to the cosmological constant case with equation of state parameter w = -1.

Their argument is that the black hole* (or *dark energy star) masses have grown much faster than could be explained by the usual mechanism of accretion of nearby matter and mergers.

In Figure 1 from their second paper of the pair (Farrah, Croker, et al. 2023), they present their measurements of the strength of cosmological coupling for five different galaxy surveys (three sets of galaxies but two sets were surveyed at two frequencies each). They observed strong increases in the measured SMBH masses from redshifts close to z =1 and extending above z = 2. They derive a coupling strength parameter k that measures the power law index of how fast the black hole masses grow with redshift.

Their reformulation of the black hole model to include the far field yields cosmological coupling of the dark energy cores. The mass of the dark energy core, coupled to the overall cosmological solution, results in a mass increase M ~ a^k , a power law of index k, depending on the equation of state for the dark energy. Here a is the cosmological linear scale factor of the universal expansion and is also equal to 1/(1+z) where z is the redshift at which a galaxy and its SMBH are observed. (The scale factor a is normalized to 1 presently, such that z = 0 now and is positive in the past).

And they are claiming that their sample of several hundred galaxies and supermassive black holes indicates k = 3, on average, more or less. So between z = 1 and z = 0, over the past 8 billion years, they interpret their observations as an 8-fold growth in black hole masses. And they say this is consistent with M growing by a^3 as the universe’s linear scale has doubled (a was 1/2 at z = 1). This implies they are measuring a different class of black holes than we normally think of, those don’t increase in mass other than by accretion and mergers. Normal black holes would yield k > 0 but not by much, based on expected accretion and mergers. The k = 0 case they state is excluded by their observations with over 99.9% confidence.

The set of upper graphs in Figure 1 is for the various surveys, and the large lower graph combines all of the surveys as a single data set. They find a near-Gaussian distribution, and k is centered near 3, with an uncertainty close to 1. There is a 2/3 chance that the value lies between 2.33 and 3.85, based on their total sample of over 400 active galaxy nuclei.

And they also suggest this effect would be for all dark energy dominated “black holes”, including stellar class and intermediate BHs, not just SMBHs. So they claim fast evolution in all dark energy star masses, in proportion to the volume growth of the expanding universe, and consistent with dark energy cores having an equation of state just like the observed cosmological constant.

Now it gets really interesting.

We already know that the dark energy density of the universe, unlike the ever-thinning mater and radiation density, is more or less constant in absolute terms. That is the cosmological constant, due to vacuumenergy, interpretation of dark energy for which the pressure is negative and causes acceleration of the universe’s expansion. Each additional volume of the growth has its own associated vacuum energy (around 4 proton masses’ worth of rest energy per cubic meter). This is the universe’s biggest free lunch since its original creation.

The authors focus on dark energy starts created during the earliest bursts of star formation. These are the so-called Pop III stars, never observed because all or mostly all have reached end of life long ago. When galaxy and star formation starts as early as about 200 million years after the Big Bang, there is only hydrogen and helium for atomic matter. Heavier elements must be made in those first Pop III stars. As a result of their composition, the first stars with zero ‘metallacity’ have higher stellar masses; high mass stars are the ones that evolve most rapidly and they quickly end up as white dwarfs, or more to the point here, black holes or neutron stars in supernovae events. Or, they end their lives as dark energy stars.

The number of these compact post supernova remnant stars will decrease in density in inverse proportion to the increasing volume of the expanding universe. But the masses of all those that are dark energy stars would increase as the cube of the scale factor, in proportion to the increasing volume.

And the net effect would be just right to create a cosmological constant form of dark energy as the total contribution of billions upon billions of dark energy stars. And dark energy would be growing as a background field from very early on. Regular matter and dark matter thin out with time, but this cohort would have roughly constant energy density once most of the first early rounds of star formation completed, perhaps by redshift z = 8, well within the first billion years. Consequently, dark energy cores, collectively, would dominate the universe within the last 4 or 5 billion years or so, as the ordinary and dark matter density fell off. And now its dominance keeps growing with time.

But is there enough dark energy in cores?

But is it enough? How much dark energy is captured in these dark energy stars, and can it explain the dominant 69% of the universe’s energy balance that is inferred from observations of distant supernovae, and from other methods?

The dark energy cores are presumably formed from the infall and extreme compression of ordinary matter, from baryons captured into the progenitors of these black hole like stars and being compressed to such a high degree that they are converted into a rather uniform dark energy fluid. And that dark energy fluid has the unusual property of negative pressure that prevents further compression to a singularity.

It is possible they could consume some dark matter, but ordinary matter clumps much more easily since it can radiate away energy via radiation, which dark matter does not do. Any dark matter consumption would only build their case here, but we know the overall dark matter ratio of 5:1 versus ordinary matter has not changed much since the cosmic microwave background emission after the first 380,000 years.

We know from cosmic microwave background measurements and other observations, that the ordinary matter or baryon budget of the universe is just about 4.9%, we’ll call it 5% in round numbers. The rest is 69% dark energy, and 26% dark matter.

So the question is, how much of the 5% must be locked up in dark energy stars to explain the 69% dark energy dominance that we currently see?

Remember that with dark energy stars the mass grows as the volume of the universe grows, that is in proportion to (1 + z)3. Now dark energy stars will be formed at different cosmological redshifts, but let’s just ask what fraction of baryons would we need to convert, assuming all are formed at the same epoch. This will give us a rough feel for the range of when and of how much.

Table 1 looks at some possibilities. It asks what fraction of baryons need to collapse into dark energy cores, and we see that the range is from only about 0.2% to 1% of baryons are required. Those baryons are just 5% of the mass-energy of the universe, and only 1% or less of those are needed, because the mass expansion factors range from about 1000 to about 10,000 — 3 to 4 orders of magnitude, depending on when the dark energy stars form.

Table 1. The first column has the redshift (epoch) of dark energy star formation. In actuality it will happen over a broad range of redshifts, but the earliest stars and galaxies seem to have formed from around 200 to 500 million years after the Big Bang started. The second column has the mass expansion factor (1+z)3; the DE star’s gravitational mass grows by that factor from the formation z until now. The third column is the age of the universe at DE star formation. The fourth column tells us what fraction of all baryons need to be incorporated into dark energy cores in those stars (they could be somewhat more massive than that). The fifth column is the lower bound on their current mass if they never experience a merger or accretion of other matter. All in all it looks as if less than 1% of baryons convert to dark energy cores.

The fifth column shows the current mass of a minimal 3 solar mass dark energy star at present, noting that 3 solar masses is the lightest known black hole. There may be lighter dark energy stars, but not very much lighter than that, perhaps a little less than 2 solar masses. And the number density should be highest at the low end according to everything we know about star formation.

Now to some degree these are underestimates for the final mass, as shown in the fifth column, since there will be mergers and accretion of other matter into these stars, and of the two effects, the mergers are more important, but they support the general argument. If a dark energy star merges with a neutron star, or other type of black hole, the dark energy core gains in relative terms. So all of this is a plausibility argument that says if the formation is of dark energy stars of a few solar masses in the epoch from 200 to 500 million years after the Big Bang, that less than 1% of all baryons are needed. And it says that the final masses are well into the intermediate range of thousands or tens of thousands of solar masses, and yet they can hide out in galaxies or between galaxies with hundreds of billions of solar masses, only contributing a few percent to the total mass.

Dark energy star cosmology

Dark energy star cosmology needs to agree with the known set of cosmological observations. It has to provide all or a significant fraction of the total dark energy budget in order to be useful. It appears from simple arguments that it can meet the budget by conversion of a small percentage of the baryons in the universe to dark energy stars.

It should exhibit an equation of state w = -1 or nearly so, and it appears to do that. It should not contribute too much mass to upset our galaxy mass estimates. It does that and it does not appear to explain dark matter in any direct way.

Dark energy stars collectively could potentially fill that role. In the model described above it is their collective effects that are being modeled as a dark energy background field that in turn drives dark energy star cores to higher masses over time. Dark energy (as a global field) feeds on itself (the dark energy cores)!

There are some differences with the normal ΛCDM cosmology assumption of a highly uniform dark energy background, not one composed of a very large number of point sources. In particular the ΛCDM cosmology has the dark energy background there from the very beginning, but it is not significant until,the universe has expanded sufficiently.

With the dark energy star case it has to be built up, one dark energy core at a time. So the dark energy effects do not begin until redshifts less than say z = 20 to 30 and most of it may be built up by z = 8 to 10, within the first billion years.

In the dark energy star case we will have accretion of nearby matter including stars, and mergers with neutron stars, other dark energy stars, and other black hole types.

A merger with a neutron star or non dark energy star only increases the mass in dark energy cores; it is positive evolution in the aggregate dark energy core component. A merger of two dark energy stars will lose some of the collective mass in conversion to gravitational radiation, and is a negative contribution toward the overall dark energy budget.

One way to distinguish between the two cosmological models is to push our measurement of the strength of dark energy as far back as we can and look for variations. Another is to identify as many individual intermediate scale black holes / dark energy stars as we can from gravitational wave surveys and from detailed studies of globular clusters and dwarf galaxies.

What about dark matter?

Dark matter’s ratio to ordinary matter at the time of the cosmic microwave background emission is measured to be 5:1 and currently in galaxies and their rotation curves and in clusters of galaxies in their intracluster medium it is also seen to be around 5:1 on average. Since the dark energy cores in the Croker et al. proposal are created hundreds of millions of years after the cosmic microwave background era, then these dark energy stars can not be a major contribution to dark matter per se.

The pair of papers just published by the team doesn’t really discuss dark matter implications. But a previous paper by Croker, Runburg and Farrah (2020) explored the interaction between the dark energy bulk behavior of the global population of dark energy stars with cold dark matter and found little or no affect.

Their process converts a rather small percentage of baryons (or even some dark matter particles) into dark energy and its negative pressure. Such material couples differently to the gravitational field than dark matter, which like ordinary matter is approximately dust-like with an equation of state parameter w = 0.

In the 2020 paper they find that GEODEs or dark energy stars can be spread out even more than dark matter that dominates galaxy halos, or the intracluster medium in rich clusters of galaxies.

Prizes ahead?

This concept of cosmological coupling is one of the most interesting areas of observational and theoretical cosmology in this century. If this work by Croker and collaborators is confirmed the team will be winning prizes in astrophysics and cosmology, since it could be a real breakthrough in both our understanding of the nature of dark energy and our understanding of black hole physics.

In any case, Dark Energy Star already has its own song.

Glossary

Black Hole: A dense collection of matter that collapses inside a small radius, and in theory, to a singularity, and which has sufficiently strong gravity that nothing, not even light, is able to escape. Black holes are characterized by three numbers: mass, angular momentum, and charge.

Cosmological constant: Einstein added this term, Λ, on the left hand side of the equations of general relativity, in a search for a static universe solution. It corresponds to an equation of state parameter w = -1. If the term is moved to the right hand side it becomes a dark energy source term in the stress-energy tensor.

Cosmological coupling: The coupling of local properties to the overall cosmological model. For example, photons redshift to lower energies with the expansion of the universe. It is argued that dark energy stellar cores would collectively couple to the overall Friedmann cosmology that matches the bulk parameters of the universe. In this case it would be a ‘blueshift’ style increase in mass in proportion to the growing volume of the universe, or perhaps more slowly.

Dark Energy: Usually attributed to energy of the vacuum, dark energy has a negative pressure in proportion to its energy density. It was confirmed by Nobel prize winning teams that dark energy is the dominant component of the universe’s mass-energy balance, some 69% of the critical value, and is driving an accelerated expansion with an equation of state w = -1 to within small errors.

Dark Energy Star: A highly compact object that should look like a black hole externally but has no singularity at its core. Instead it has a core of dark energy. If one integrates over all dark energy stars, it may add up to a portion or all of the universe’s dark energy budget. It should have a crust of ‘normal’ matter with anisotropic stress at the boundary with the core, or an intermediate transition zone with varying equation of state between the crust and the core.

Dark Matter: An unknown substance thought to reside in galactic halos, with 5 times as much matter density on average as ordinary matter. Dark matter does not interact electromagnetically and is typically considered to be particulate in nature, although primordial mini black holes have been suggested as one possible explanation.

Equation of state: The relationship between pressure and energy density, P = w * ρ * c^2 where P is pressure and can be negative, and ρ the energy density is positive. If w < -1/3 there is dark pressure, if w = -1 it is the simplest cosmological constant form. Dark matter or a collection of stars or galaxies can be modeled as w ~ 0.

GEODEs: GEneric Objects of Dark Energy, dark energy stars. Formation is thought to occur from Pop III stars, the first stellar generation, at epochs 30 > z > 8.

Gravastar: A stellar model that has a dark energy core and a very thin outer shell. With normal matter added there is anisotropic stress at the boundary to maintain pressure continuity from the core to the shell.

Non-singular black holes: A black hole like object with no singularity.

Primordial black holes: Black holes that may have formed in the very early universe, within the first second. Primordial dark energy stars in large numbers would be problematic, because they would grow in mass by (1 + z)^3 where z >> 1000.

Vacuum energy: The irreducible energy of the vacuum state. The vacuum state is not empty, it is pervaded by fields and virtual particles that pop in and out of existence on very short time scales.

References

https://scitechdaily.com/cosmological-coupling-new-evidence-points-to-black-holes-as-source-of-dark-energy/ – Popular article about the research from University of Hawaii lead authors and collaborators

https://www.phys.hawaii.edu/~kcroker/ – Kevin Croker’s web site at University of Hawaii

Beltracchi, P. and Gondolo, P. 2019, https://arxiv.org/abs/1810.12400 “Formation of Dark Energy Stars”

Croker, K.S. and Weiner J.L. 2019, https://dor.org/10.3847/1538-4357/ab32da “Implications of Symmetry and Pressure in Friedmann Cosmology. I. Formalism”

Croker, K.S., Nishimura, K.A., and Farrah D., 2020 https://arxiv.org/pdf/1904.03781.pdf, “Implications of Symmetry and Pressure in Friedmann Cosmology. II. Stellar Remnant Black Hole Mass Function”

Croker, K.S., Runburg, J., and Farrah D., 2020 https://doi.org/10.3847/1538-4357/abad2f “Implications of Symmetry and Pressure in Friedmann Cosmology. III. Point Sources of Dark Energy that tend toward Uniformity”

Croker, K.S., Zevin, M.J., Farrah, D., Nishimura, K.A., and Tarle, G. 2021, “Cosmologically coupled compact objects: a single parameter model for LIGO-Virgo mass and redshift distributions” https://arxiv.org/pdf/2109.08146.pdf

Farrah, D., Croker, K.S. et al. 2023 February, https://iopscience.iop.org/article/10.3847/2041-8213/acb704/pdf “Observational Evidence for Cosmological Coupling of Black Holes and its Implications for an Astrophysical Source of Dark Energy” (appeared in Ap.J. Letters 20 February, 2023)

Farrah, D., Petty S., Croker K.S. et al. 2023 February, https://doi.org/10.3847/1538-4357/acac2e “A Preferential Growth Channel for Supermassive Black Holes in Elliptical Galaxies at z <~ 2”

Ghezzi, C.R. 2011, https://arxiv.org/pdf/0908.0779.pdf “Anisotropic dark energy stars”

Gliner, E.B. 1965, Algebraic Properties of the Energy-momentum Tensor and Vacuum-like States of Matter. ZhTF 49, 542–548. English transl.: Sov. Phys. JETP 1966, 22, 378.

Harikane, Y., Ouchi, M., et al. arXiv:2208.01612v3, “A Comprehensive Study on Galaxies at z ~ 9 – 16 Found in the Early JWST Data: UV Luminosity Functions and Cosmic Star-Formation History at the Pre-Reionization Epoch”

Perrenod, S.C. 2017, “Dark Energy and the Cosmological Constant” https://darkmatterdarkenergy.com/2017/07/13/dark-energy-and-the-comological-constant/

Whalen, D.J., Even, W. et al.2013, doi:10.1088/004-637X/778/1/17, “Supermassive Population III Supernovae and the Birth of the first Quasars”

Yakovlev, D. and Kaminker, A. 2023, https://arxiv.org/pdf/2301.13150.pdf “Nearly Forgotten Cosmological Concept of E.B. Gliner”

1 Comment | tags: black holes, cosmological constant, cosmological coupling, Cosmology, Dark energy, dark energy stars, supermassive black holes | posted in Big Bang & Inflation, black holes, Dark Energy, Early Universe

March 10, 2020

Hexaquark Dark Matter: Bosons, but not WIMPy at all

By darkmatterdarkenergy

Dibaryons

Imagine you smash a proton and neutron together. What do you get? Typically you get a deuteron which is the nucleus of deuterium, heavy hydrogen. Deuterium has one electron in its neutral atomic state. And it has two baryons, the proton and neutron, so it is known as a dibaryon.

Now as you have heard, protons and neutrons are really quark triplets, held together by gluons in bound configurations. A proton has two up quarks (electric charge +2/3) and a down quark (charge -1/3) for a net charge of +1 and a neutron has two down quarks and an up quark for a net charge of 0.

These are the two lightest quarks and protons and neutrons are by far the dominant components in the ordinary matter in the universe, mostly as hydrogen and helium.

Quarks, protons, and neutrons are all fermions, particles with half-integer spins (1/2, 3/2, -1/2, etc.).

The other main class of particles is called bosons, and that class includes photons, gluons, the W and Z of the weak interaction, and the never directly observed graviton. They all have integer spins (typically 1, but 0 for the Higgs boson, and 2 for the graviton).

Figure 1: The Standard Model major particles: quarks (purple), leptons (green), force carrier bosons (orange), Higgs boson (yellow) with mass, charge, spin indicated.

Six quarks in a Bag

Suppose you collided a proton and neutron together, each with three quarks, and you ended up with a single six quark particle that was stable. It would be a more exotic type of dibaryon. It would have three up quarks, three down quarks, and it would not be a fermion. It would be a boson, with integer spin, spin 0 or 1, in this case. It would be six quarks in a bag, a bound state held together by gluons.

sixquarksinabag

Figure 2. Six quarks in a bag, a hexaquark

Hexaquark2380

Figure 3. The d* resonance at 2.38 GeV, observed at the Cooler Synchrotron in Julich, Germany

Such a particle has been discovered in the past decade, and is named the d* hexaquark. It is seen as the resonance in Figure 3 above, found in proton-neutron collisions, and has a mass of 2.38 GeV (for reference the proton mass is 0.935 GeV and the neutron mass is 0.938 GeV). It decays to a deuteron and two pions, either neutral as shown in the figure, or charged pions.

It is also possible to produce a d* by irradiating a deuteron with a gamma ray.

The d* was already predicted by the famed mathematician and physicist Freeman Dyson in 1964, working with his collaborator Xuong. Their mass estimate was quite close at 2.35 GeV, using a simple quark model.

Dyson just passed away recently; you may have heard of his Dyson sphere concept. The idea is that an advanced civilization would build a sphere of solid material surrounding its star in order to hold an extremely large population and absorb virtually all of the star’s energy. Larry Niven modified this to a ring in his 1970 sci-fi novel Ringworld.

Hexaquark dark matter

Azizi, Ageav, and Sundu have recently suggested a hexaquark of the form uuddss, that is, two up, two down, and two strange quarks. Their mass estimate is around 1.2 GeV, half that of the d* composed of only up and down quarks. It is expected to be stable with long lifetime.

And also recently, Bashkanov and Watts at the University of York have made a nice proposal that d* could be the dark matter particle. The d* particle is itself unstable, but they propose that stable condensates with many d* particles could form. Their paper, “A New Possibility for Light-Quark Dark Matter” is here:

https://iopscience.iop.org/article/10.1088/1361-6471/ab67e8/pdf

The d* has one great advantage over the other proposed particles, it has actually been discovered! The d* has a good sized mass for a dark matter candidate, at about 2.5 times the mass of the proton.

The authors find that the d* could form lengthy chains or spherical condensates with thousands to millions of d* particles. Unlike individual d* particles, the condensates could be stable ‘super atoms’ lasting for billions of years.

However to make this work the binding energy would have to exceed the difference between the 2.38 GeV d* mass and the deuteron mass of 2.014mGeV, thus would have to be greater than about 0.4 GeV.

The d* would be produced thermally when the universe was at temperatures in the range from 1 to 3 trillion Kelvins. The condensates would need to form quickly before individual d* particles of short lifetimes decayed away.

The favored candidates for dark matter have been WIMPs, supersymmetric particles. But no supersymmetric particle has ever been detected at the Large Hadron Collider or elsewhere, which is incredibly disappointing for many particle physicists. The other main candidates have been the axion and sterile neutrino, both quite low in mass. These have never been directly detected either; they remain hypothetical.

The d* particle is a boson, and the authors’ theoretical approach is that in the early universe as it cooled, both baryons and dibaryonic matter froze out. The baryons ended up, after the cosmic nucleosynthesis phase as protons, deuterium dibaryons, and helium nuclei (alpha particles, that are composed essentially of two deuterons), the main constituents of ordinary matter.

What would happen to d* under the early conditions of the Big Bang? Bosons like to clump together, into something called Bose-Einstein condensates. Yes, that Einstein. And that Boson. Bose-Einstein statistics were developed in the 1920s and govern the statistics of bosons (integer spin particles), and differ from that of fermions.

To confirm this model would require astronomical observations or cosmic ray observations. Decays of d* particles could result in gamma ray production with energies up to 0.5 GeV. Their decay products might also be seen as upward moving cosmic rays, in Earth-bound cosmic ray experiments. These would be seen coming up through the Earth, unlike normal cosmic rays that cannot penetrate so much ordinary matter, and the decay events would result in gamma rays, nucleons and deuterons, as well as pions as the decay products.

Additional reference: http://www.sci-news.com/physics/dark-matter-particle-d-star-hexaquark-08188.html

4 Comments | tags: baryons, Bose-Einstein condensates, Dark matter, dibaryons, hexaquarks, WIMPs | posted in Big Bang & Inflation, Dark Matter, Early Universe

November 11, 2019

Dark Catastrophe, a few Trillion Years away?

By darkmatterdarkenergy

The Equation of State for Dark Energy

The canonical cosmological model, known as ΛCDM, has all matter including CDM (cold dark matter), at approximately 30% of critical density. And it has dark energy, denoted by Λ, at 70%. While the cosmological constant form of dark energy, first included in the equations of general relativity by Einstein himself, has a positive energy, its pressure is negative.

The negative pressure associated with dark energy, not the positive dark energy density itself, is what causes the universe’s expansion to accelerate.

The form of dark energy introduced by Einstein does not vary as the universe expands, and the pressure, although of opposite sign, is directly proportional to the dark energy density. The two are related by the formula

P = – ρ c²

where P is the pressure and ρ the energy density, while c is the speed of light.

More generally one can relate the pressure to the energy density as an equation of state with the parameter w:

P = – w ρ c²

And in the cosmological constant form, w = -1 and is unvarying over the billions of years of cosmological time.

Does Dark Energy vary over long timescales?

String theory (also known as membrane theory) indicates that dark energy should evolve over time.

The present day dark energy may be the same field that was originally much much stronger and drove a very brief period of inflation, before decaying to the current low value of about 6 GeV (proton rest masses) per cubic meter.

There are searches for variation in the equation of state parameter w; they are currently inconclusive.

How much variance could there be?

In string theory, the dark energy potential gradient with respect to the field strength yields a parameter c of order unity. For differing values of c, the equation of state parameter w varies with the age of the universe, more so as c is larger.

When we talk about cosmological timescales, it is convenient to speak in terms of the cosmological redshift, where z = 0 is the present and z > 0 is looking back with a larger z indicating a larger lookback time. If the parameter c were zero then the value of w would be -1 at all redshifts (z = 0 is the current epoch and z = 1 is when the universe only about 6 billion years old, almost 8 billion years ago).

WvsC

This Figure 3 from an article referenced below by Cumrun Vafa of Harvard shows the expected variance with redshift z for the equation of state parameter w. The observationally allowed region is shaded gray. The colored lines represent different values of the parameter c from string theory (not the speed of light). APS/Alan Stonebraker

Observational evidence constraining w is gathered from the cosmic microwave background, from supernovae of Type Ia, and from the large scale galaxy distribution. That evidence from all three methods in combination restricts one to the lower part of the diagram, shaded gray, thus w could be -1 or somewhat less. There are four colored curves, labelled by their value of the string theory parameter c, and it appears that c > 0.65 could be ruled out by observations.

Hubble Constant tension: String theory explaining?

It’s not the constant tension of the Hubble constant. Rather it is the tension, or disagreement between the cosmic microwave background observational value of the Hubble constant, at around 67 kilometers/sec/Megaparsec and the value from supernovae observations, which yield 73 kilometers/sec. And the respective error bars on each measurement are small enough that the difference may be real.

The cosmic microwave background observations imply a universe about a billion years older, and also better fit with the ages of the oldest stars.

It turns out a varying dark energy with redshift as described above could help to explain much of the discrepancy although perhaps not all of it.

Better observations of the early universe’s imprint on the large scale distribution of galaxies from ground-based optical telescope surveys and from the Euclid satellite’s high redshift gravitational lensing and spectroscopic redshift measurements in the next decade will help determine whether dark energy is constant or not. This could help to disprove string theory or enhance the likelihood that string theory has explanatory power in physics.

Tests of string theory have been very elusive since we cannot reach the extremely high energies required with our Earth-based particle accelerators. Cosmological tests may be our best hope, small effects from string theory might be detectable as they build up over large distances.

And this could help us to understand if the “swampland conjecture” of string theory is likely, predicting an end to the universe within the next few trillion years as the dark energy field tunnels to an even lower energy state or all matter converts into a “tower of light states” meaning much less massive particles than the protons and neutrons of which we are composed.

Reference

“Cosmic Predictions from the String Swampland”, Cumrun Vafa, 2019. Physics 12, 115, physics.aps.org

1 Comment | tags: Dark energy, Dark matter, hubble constant, inflation, string theory | posted in Dark Energy

April 3, 2019

Modified Gravity

By darkmatterdarkenergy

We don’t Need no Stinkin’ Dark Matter

Extra Acceleration

You’ve heard of dark matter, right? Some sort of exotic particle that lurks in the outskirts of galaxies.

Maybe you know the story of elusive dark matter. The first apparent home for dark matter was in clusters of galaxies, as Fritz Zwicky postulated for the Coma Cluster in the 1930s, due to the excessive galaxy random motions that he measured.

There have been eight decades of discovery and measurement of the gravitational anomalies that dark matter is said to cause, and eight decades of notable failure to directly find any very faint ordinary matter, black holes, or exotic particle matter in sufficient quantities to explain the magnitude of the observed anomalies.

If dark matter is actually real and composed of particles or primordial black holes then there is five times as much mass per unit volume on average in that form as there is in the form of ordinary matter. Ordinary matter is principally in the form of protons and neutrons, primarily as hydrogen and helium atoms and ions.

Why do we call it dark? It gives off no light. Ordinary matter gives off light, it radiates. What else gives off no light? A gravitational field stronger than predicted by existing laws.

Gravitational anomalies are seen in the outer regions of galaxies by examining galaxy rotation curves, which flatten out unexpectedly with distance from the galactic center. They are seen in galaxy groups and clusters from measuring galaxy velocity dispersions, from X-ray observations of intracluster gas, and from gravitational lensing measurements. A dark matter component is also deduced at the cosmic scale from the power spectrum of the cosmic microwave background spatial variations.

The excessive velocities due to extra acceleration are either caused by dark matter or by some departure of gravity over and above the predictions of general relativity.

Actually at high accelerations general relativity is the required model but at low accelerations Newtonian dynamics is an accurate approximation. The discrepancies arise only at very low accelerations. These excess velocities, X-ray emission, and lensing are observed only at very low accelerations, so we are basically talking about an alternative of extra gravity which is over and above the 1/r² law for Newtonian dynamics.

Alternatives to General Relativity and Newtonian Dynamics

There are multiple proposed laws for modifying gravity at very low accelerations. To match observations the effect should start to kick in for accelerations less than c * H, where H is the Hubble expansion parameter and its inverse is nearly equal to the present age of the universe.

That is only around 1 part in 14 million expressed in units of centimeters per second per second. This is not something typically measurable in Earth-bound laboratories; scientists have trouble pinning down the value of the gravitational constant G to within 1 part in 10,000.

This is a rather profound coincidence, suggesting that there is something fundamental at play in the nature of gravity itself, not necessarily a rather arbitrary creation of exotic dark matter particle in the very early universe. It suggests instead that there is an additional component of gravity tied in some way to the age and state of our universe.

Do you think of general relativity as the last word on gravity? From an Occam’s razor point of view it is actually simpler to think about modifying the laws of gravity in very low acceleration environments, than to postulate an exotic never-seen-in-the-lab dark matter particle. And we already know that general relativity is incomplete, since it is not a quantum theory.

The emergent gravity concept neatly solves the quantum issue by saying gravity is not fundamental in the way that electromagnetism and the nuclear forces are. Rather it is described as an emergent property of a system due to quantum entanglement of fields and particles. In this view, the fabric of space also arises from this entanglement. Gravity is a statistical property of the system, the entropy (in thermodynamic terms) of entanglement at each point.

Dark Energy

Now we have a necessary aside on dark energy. Do you know that dark energy is on firmer standing now than dark matter? And do you know that dark energy is just described by additional energy and pressure components in the stress-energy tensor, fully described within general relativity?

We know that dark energy dominates over dark matter in the canonical cosmological model (Lambda-Cold Dark Matter) for the universe. The canonical model has about 2/3 dark energy and the solution for the universe’s expansion approximates a de Sitter model in general relativity with an exponential ‘runaway’ expansion.

Dark Gravity

As we discuss this no dark matter alternative, we refer to it as dark gravity, or dark acceleration. Regardless of the nature of dark matter and dark gravity, the combination of ordinary gravity and dark gravity is still insufficient to halt the expansion of the universe. In this view, the dark gravity is due to ordinary matter, there is just more of it (gravity) than we expect, again only for the very low c * H or lower acceleration environments.

Some of the proposed laws for modified gravity are:

MOND – Modified Newtonian Dynamics, from Milgrom
Emergent gravity, from Verlinde
Metric skew tensor gravity (MSTG), from Moffat (and also the more recent variant scalar-tensor-vector gravity (STVG), sometimes called MOG (Modified gravity)

Think of the dark gravity as an additional term in the equations, beyond the gravity we are familiar with. Each of the models adds an additional term to Newtonian gravity, that only becomes significant for accelerations less than c*H. The details vary between the proposed alternatives. All do a good job of matching galaxy rotation curves for spiral galaxies and the Tully-Fisher relation that can be used for analyzing elliptical galaxies.

Things are trickier in clusters of galaxies, which are observed for galaxy velocity dispersions, X-ray emission of intracluster gas, and gravitational lensing. The MOND model appears to come up short by a factor of about two in explaining the total dark gravity implied.

Emergent gravity and modified gravity theories including MSTG claim to be able to match the observations in clusters.

Clusters of Galaxies

Most galaxies are found in groups and clusters.

Clusters and groups form from the collapse of overdense regions of hydrogen and helium gas in the early universe. Collapsing under its own gravity, such a region will heat up via frictional processes and cooler sub-regions will collapse further to form galaxies within the cluster.

Rich clusters have hundreds, even thousands of galaxies, and their gravitational potential is so high that the gas is heated to millions of degrees via friction and shock waves and gives off X-rays. The X-ray emission from clusters has been actively studied since the 1970s, via satellite experiments.

What is found is that most matter is in the form of intracluster gas, not galaxies. Some of this is left over primordial gas that never formed galaxies and some is gas that was once in a galaxy but expelled via energetic processes, especially supernovae.

Observations indicate that around 90% of (ordinary) matter is in the form of intracluster gas, and only around 10% within the galaxies in the form of stars or interstellar gas and dust. Thus modeling the mass profile of a cluster is best done by looking at how the X-ray emission falls off as one moves away from the center of a cluster.

In their 2005 paper, Brownstein and Moffat compiled X-ray emission profiles and fit gas mass profiles with radius and temperature profiles for 106 galaxy clusters. They aggregated data from a sample of 106 clusters and find that an MSTG model can reproduce the X-ray emission with a mass profile that does not require dark matter.

The figure below shows the average profile of cumulative mass interior to a given radius. The mass is in units of solar masses and runs into the hundreds of trillions. The average radius extends to over 1000 Kiloparsecs or over 1 Megaparsec (a parsec is 3.26 light-years).

The bottom line is that emergent gravity and MSTG both claim to have explanatory power without any dark matter for observations of galaxy rotation curves, gravitation lensing in clusters (Brower et al. 2016), and cluster mass profiles deduced from the X-ray emission from hot gas.

galaxyclustermasseswodm.fig2

Figure 2 from J.R. Brownstein⋆ and J.W. Moffat (2005), “Galaxy Cluster Masses without Non-Baryonic Dark Matter”. Shown is cumulative mass required as a function of radius. The red curve is the average of X-ray observations from a sample of 106 clusters. The black curve is the authors’ model assuming MSTG, a good match. The cyan curve is the MOND model, the blue curve is a Newtonian model, and both require dark matter. The point is that the authors can match observations with much less matter and there is no need to postulate additional exotic dark matter.

What we would very much like to see is a better explanation of the cosmic microwave background density perturbation spectrum for the cosmic scale, for either of these dark gravity models. The STVG variant of MSTG claims to address those observations as well, without the need for dark matter.

In future posts we may look at that issue and also the so called ‘silver bullet’ that dark matter proponents often promote, the Bullet Cluster, that consists of two galaxy clusters colliding and a claimed separation of dark matter and gas.

References

Brower, M. et al. 2016, “First test of Verlinde’s theory of Emergent Gravity using Weak Gravitational Lensing Measurements” https://arxiv.org/abs/1612.03034v2

Brownstein, J. and Moffat, J. 2005, “Galaxy Cluster Masses without Non-baryonic Dark Matter”, https://arxiv.org/abs/astro-ph/0507222

Perrenod, S. 1977 “The Evolution of Cluster X-ray Sources” http://adsabs.harvard.edu/abs/1978ApJ…226..566P, thesis.

https://darkmatterdarkenergy.com/2018/09/19/matter-and-energy-tell-spacetime-how-to-be-dark-gravity/

https://darkmatterdarkenergy.com/2016/12/30/emergent-gravity-verlindes-proposal/

https://darkmatterdarkenergy.com/2016/12/09/modified-newtonian-dynamics-is-there-something-to-it/

3 Comments | tags: clusters of galaxies, Cosmology, Dark matter, emergent gravity, general relativity, gravitational lensing, metric skew tensor gravity, MOND, scalar-tensor gravity, X-ray clusters | posted in Dark Matter, Gravity

February 7, 2019

Does Dark Energy Vary with Time?

By Stephen Perrenod

Einstein introduced the concept of dark energy 100 years ago.

The Concordance Lambda-Cold Dark Matter cosmology appears to fit observations of the cosmic microwave background and other cosmological observations including surveys of large-scale galaxy grouping exceedingly well.

In this model, Lambda is shorthand for the dark energy in the universe. It was introduced as the greek letter Λ into the equations of general relativity, by Albert Einstein, as an unvarying cosmological constant.

Measurements of Λ indicate that dark energy accounts for about 70% of the total energy content of the universe. The remainder is found in dark matter and ordinary matter, and about 5/6 of that is in the form of dark matter.

Alternative models of gravity, with extra gravity in very low acceleration environments, may replace apparent dark matter with this extra gravity, perhaps due to interaction between dark energy and ordinary matter.

The key point about dark energy is that while it has a positive energy, it rather strangely has a negative pressure. In the tensor equations of general relativity the pressure terms act as a negative gravity, driving an accelerated expansion of the universe.

In fact our universe is headed toward a state of doubling in scale in each dimension every 11 or 12 billion years. In the next trillion years we are looking at 80 or 90 such repeated doublings.

That assumes that dark energy is constant per volume over time, with a value equivalent to two proton – antiproton pair annihilations per cubic meter (4 GeV / m³).

But is it?

The Dark Energy Survey results seem to say so. This experiment looked at 26 million galaxies for the clustering patterns, and also gravitational lensing (Einstein taught us that mass bends light paths).

They determined the parameter w for dark energy and found it to be consistent with -1.0 as expected for the cosmological constant model of unvarying dark energy. See this blog for details:

https://darkmatterdarkenergy.com/2017/08/10/dark-energy-survey-first-results-canonical-cosmology-supported/

The pressure – energy density relation is:

$P = w \cdot \rho \cdot c^2$

The parameter w elucidates the relation between the energy density given by ρ and the pressure P. This is called the equation of state. Matter and radiation have w >= 0. In order to have dark energy with a negative pressure dominating, then w should be < -1/3. And w = -1 gives us the cosmological constant form.

EquationofState Image credit: www.scholarpedia.org

Cosmologists seek to determine w, and whether it varies over time scales of billions of years.

The Concordance model is not very well tested at high redshifts with z > 1 (corresponding to epochs of the universe less than half the current age) other than with the cosmic microwave background data. Recently two Italian researchers, Risaliti and Lusso have examined datasets of high-redshift quasars to investigate whether the Concordance model fits.

Typically supernovae are employed for the redshift-distance relation, and cosmological models are tested against the observed relationship, known as the Hubble diagram. The authors use X-ray and ultraviolet fluxes of quasars to extend the diagram to high redshifts (greater distances, earlier epochs), and calibrate observed quasar luminosities with the supernovae data sets.

Their analysis drew from a sample of 1600 quasars with redshifts up to 5 and including a new sample of 30 high redshift z ~ 3 quasars, observed with the European XMM-Newton satellite.

They claim a 4 standard deviation variance for z > 2, a reasonably high significance.

Models with a varying w include quintessence models, with time-varying scalar fields. If w decreases below -1, it is known as phantom energy. Their results are suggestive of a value of w < -1, corresponding to a dark or phantom energy increasing with time.

For convenience cosmologists introduce a second parameter for possible evolution in w, writing as:

w = w0 + wa*(1-a) ,where a, the scale factor equals 1/(1+z) and a = 1 for present day.

darkenergyvaries.fig4

The best fit results for their analysis are with w0 = -1.4 and wa ~ 1, but these results have large errors, as shown in Figure 4 above, from their paper. Their results are within the red (2 standard deviation, or σ) and orange (3σ) contours. The outer 3σ contours almost touch the cosmological constant point that has w0 = -1 and wa = 0.

These are intriguing results that require further investigation. They are antithetical to quintessence models, and apparently in tension with a simple cosmological constant.

The researchers plan on further analysis in future work by including Baryon Acoustic Oscillation (large scale galaxy clustering) measurements at z > 2.

References

https://darkmatterdarkenergy.com/2017/08/10/dark-energy-survey-first-results-canonical-cosmology-supported/ – Results from Dark Energy Survey of galaxies

Risaliti, G. and Lusso, E. 2018 Cosmological constraints from the Hubble diagram of quasars at high redshifts https://arxiv.org/abs/1811.02590

1 Comment | tags: cosmological constant, Dark energy, phantom energy, quintessence, vacuum energy, XMM-Newton | posted in Dark Energy, Early Universe

January 27, 2019

Mini Black Holes as Dark Matter?

By darkmatterdarkenergy

Ancient Voyager Satellite Says No for the Smallest Possible

Hawking Radiation

Black holes can come in all sizes from about a billion tons up to billions of solar masses.

Because isolated black holes are difficult to detect, especially smaller mass ones, they have long been considered as candidates for dark matter, invoked to explain the extra gravitational accelerations measured at the outskirts of galaxies.

Stephen Hawking showed that black holes radiate low energy particles very slowly due to quantum thermodynamic effects. So the very lowest mass black holes evaporate away due to Hawking radiation during the life of the universe.

Voyager Satellites

The Voyager satellites were launched in 1977 and NASA has determined that Voyager 1 crossed the heliopause in 2012. This is the boundary for the solar wind, which holds back a large portion of galactic cosmic rays. Voyager 2 crossed the heliopause last year.

Forty-two years after launch, and having toured Jupiter, Saturn, Uranus, and Neptune, these remarkable satellites are still returning valuable data about the outer reaches of the Solar System.

What is the connection between black holes, dark matter, and Voyager 1?

In the early universe, large numbers of so-called primordial black holes (PBHs) of various sizes may have formed. The question arises, could these be the primary component of dark matter?

Primordial Black Holes as Dark Matter Candidates

The detection of gravitational waves from half a dozen mergers of black holes of intermediate mass has given new energy to this idea. Also, there is the continued failure to detect exotic particle candidates for dark matter in Earth-bound laboratory experiments.

A team of Japanese astronomers, searching for microlensing effects with stars in the Andromeda galaxy, have ruled out small black holes in the range of $10^{20}$ grams up to about 3 times the Earth’s mass. https://darkmatterdarkenergy.com/2017/12/07/primordial-black-holes-and-dark-matter has more detail.

Constraints from other lensing experiments (MACHO, EROS) and the cosmic microwave background appear to rule out more massive primordial black holes as the explanation for most dark matter.

What about the tiniest allowable black holes, from about $4 \cdot 10^{14}$ gm (smaller ones have evaporated already) up to $10^{20}$ gm?

Voyager 1 Constraints

With a recent analysis researchers at the Laboratoire de Physique Theorique et Hautes Energies (LPTHE) show that the Voyager 1 satellite now rules out primordial black holes with masses below $10^{17}$ gm as well, as the source of most dark matter. And it is because of the Hawking radiation that we do not detect.

Although Hawking radiation has never been detected, it is on very firm theoretical grounds that it should exist. Everything, including strange objects like black holes, has a quantum nature.

Smaller black holes radiate at higher temperatures and have shorter lifetimes. The Hawking radiation temperature is

$T = 1.1 GeV / (m/10^{13} gm)$

Thus for an $m = 10^{16}$ gm black hole the Hawking temperature is about 1 MeV. (GeV or giga electron-Volt is a billion eV and around the rest mass energy of a proton, and an MeV or mega electron-Volt is a million eV and about twice the rest mass energy of an electron.)

Since these temperatures are in the MeV range, only very light particles such as neutrinos, electrons, and positrons would be emitted by the PBHs.

Figure 1 from the Boudaud and Cirelli paper shows the observed combined electron and positron cosmic ray flux from Voyager 1 in the energy range from 3 MeV to 50 MeV. It also shows results in the 1 to 10 GeV range from the Alpha Magnetic Spectrometer 2 experiment on the International Space Station (located well inside the heliopause). Two different models of how the energetic particles propagate through the galaxy are used.

Smallest possible Black Holes ruled out

PBHs with $10^{15}$ or $10^{16}$ grams are clearly ruled out; they would inject far too many energetic electron and positron cosmic rays into the interstellar medium that Voyager 1 has entered.

The authors state that no more than 0.1% of dark matter can be due to PBHs of mass less than $10^{16}$ grams (10 billion tons).

In Figure 1, a monotonic mass distribution was assumed (PBHs all have the same mass). They also consider various log-normal mass distributions and similar constraints on the allowable PBH mass were found.

What about at $10^{17}$ grams and above? Most mass regions are ruled out.

The mass region above $5 \cdot 10^{17}$ grams and up to about $10^{20}$ grams has been excluded as a primary source of dark matter from PBHs by a 2012* result from Barnacka, Glicenstein, and Moderski. They searched for gravitational lensing effects upon gamma ray burst sources due to intervening black holes.

So vast ranges of possible PBH masses are ruled out. However the mass region from $3 \cdot 10^{16}$ up to $5 \cdot 10^{17}$ grams remains a possibility as a dark matter hideout for PBHs.

*The same year that Voyager 1 crossed the heliopause, coincidentally

References

Boudaud, M. And Cirelli, M. 2019 “Voyager 1 electrons and positrons further constrain primordial black holes as dark matter” https://arxiv.org/abs/1807.03075

https://darkmatterdarkenergy.com/2017/12/07/primordial-black-holes-and-dark-matter/

Barnacka, A., Glicenstein, J.-F., Moderski, R. 2012 “New constraints on primordial black holes abundance from femtolensing of gamma-ray bursts” http://arxiv.org/abs/1204.2056

Leave a comment | tags: black holes, cosmic microwave background, Dark matter, gravitational lensing, primordial black holes, very early universe, Voyager satellite | posted in Dark Matter, primordial black holes

September 19, 2018

Matter and Energy Tell Spacetime How to Be: Dark Gravity

By Stephen Perrenod

Is gravity fundamental or emergent? Electromagnetism is one example of a fundamental force. Thermodynamics is an example of emergent, statistical behavior.

Newton saw gravity as a mysterious force acting at a distance between two objects, obeying the well-known inverse square law, and occurring in a spacetime that was inflexible, and had a single frame of reference.

Einstein looked into the nature of space and time and realized they are flexible. Yet general relativity is still a classical theory, without quantum behavior. And it presupposes a continuous fabric for space.

As John Wheeler said, “spacetime tells matter how to move; matter tells spacetime how to curve”. Now Wheeler full well knew that not just matter, but also energy, curves spacetime.

A modest suggestion: invert Wheeler’s sentence. And then generalize it. Matter, and energy, tells spacetime how to be.

Which is more fundamental? Matter or spacetime?

Quantum theories of gravity seek to couple the known quantum fields with gravity, and it is expected that at the extremely small Planck scales, time and space both lose their continuous nature.

In physics, space and time are typically assumed as continuous backdrops.

But what if space is not fundamental at all? What if time is not fundamental? It is not difficult to conceive of time as merely an ordering of events. But space and time are to some extent interchangeable, as Einstein showed with special relativity.

So what about space? Is it just us placing rulers between objects, between masses?

Particle physicists are increasingly coming to the view that space, and time, are emergent. Not fundamental.

If emergent, from what? The concept is that particles, and quantum fields, for that matter, are entangled with one another. Their microscopic quantum states are correlated. The phenomenon of quantum entanglement has been studied in the laboratory and is well proven.

Chinese scientists have even, just last year, demonstrated quantum entanglement of photons over a satellite uplink with a total path exceeding 1200 kilometers.

Quantum entanglement thus becomes the thread Nature uses to stitch together the fabric of space. And as the degree of quantum entanglement changes the local curvature of the fabric changes. As the curvature changes, matter follows different paths. And that is gravity in action.

Newton’s laws are an approximation of general relativity for the case of small accelerations. But if space is not a continuous fabric and results from quantum entanglement, then for very small accelerations (in a sub-Newtonian range) both Newton dynamics and general relativity may be incomplete.

The connection between gravity and thermodynamics has been around for four decades, through research on black holes, and from string theory. Jacob Bekenstein and Stephen Hawking determined that a black hole possesses entropy proportional to its area divided by the gravitational constant G. This area law entropy approach can be used to derive general relativity as Ted Jacobson did in 1995.

But it may be that the supposed area law component is insufficient; according to Erik Verlinde’s new emergent gravity hypothesis, there is also a volume law component for entropy, that must be considered due to dark energy and when accelerations are very low.

We have had hints about this incomplete description of gravity in the velocity measurements made at the outskirts of galaxies during the past eight decades. Higher velocities than expected are seen, reflecting higher acceleration of stars and gas than Newton (or Einstein) would predict. We can call this dark gravity.

Now this dark gravity could be due to dark matter. Or it could just be modified gravity, with extra gravity over what we expected.

It has been understood since the work of Mordehai Milgrom in the 1980s that the excess velocities that are observed are better correlated with extra acceleration than with distance from the galactic center.

Stacey McGaugh and collaborators have demonstrated a very tight correlation between the observed accelerations and the expected Newtonian acceleration, as I discussed in a prior blog here. The extra acceleration kicks in below a few times $10^{-10}$ meters per second per second (m/s²).

This is suspiciously close to the speed of light divided by the age of the universe! Which is about $7 \cdot 10^{-10}$ m/s².

Why should that be? The mass/energy density (both mass and energy contribute to gravity) of the universe is dominated today by dark energy.

The canonical cosmological model has 70% dark energy, 25% dark matter, and 5% ordinary matter. In fact if there is no dark matter, just dark gravity, or dark acceleration, then it could be more like a 95% and 5% split between dark energy and (ordinary) matter components.

A homogeneous universe composed only of dark energy in general relativity is known as a de Sitter (dS) universe. Our universe is, at present, basically a dS universe ‘salted’ with matter.

Then one needs to ask how does gravity behave in dark energy influenced domains? Now unlike ordinary matter, dark energy is highly uniformly distributed on the largest scales. It is driving an accelerated expansion of the universe (the fabric of spacetime!) and dragging the ordinary matter along with it.

But where the density of ordinary matter is high, dark energy is evacuated. An ironic thought, since dark energy is considered to be vacuum energy. But where there is lots of matter, the vacuum is pushed aside.

That general concept was what Erik Verlinde used to derive an extra acceleration formula in 2016. He modeled an emergent, entropic gravity due to ordinary matter and also due to the interplay between dark energy and ordinary matter. He modeled the dark energy as responding like an elastic medium when it is displaced within the vicinity of matter. Using this analogy with elasticity, he derived an extra acceleration as proportional to the square root of the product of the usual Newtonian acceleration and a term related to the speed of light divided by the universe’s age. This leads to a 1/r force law for the extra component since Newtonian acceleration goes as 1/r².

$g _D = sqrt {(a_0 \cdot g_B / 6 )}$

Verlinde’s dark gravity depends on the square root of the product of a characteristic acceleration a0 and ordinary Newtonian (baryonic) gravity, gB

The idea is that the elastic, dark energy medium, relaxes over a cosmological timescales. Matter displaces energy and entropy from this medium, and there is a back reaction of the dark energy on matter that is expressed as a volume law entropy. Verlinde is able to show that this interplay between the matter and dark energy leads precisely to the characteristic acceleration is $a_0 / 6 = c \cdot H / 6$ , where H is the Hubble expansion parameter and is equal to one over the age of the universe for a dS universe. This turns out be the right value of just over $10^{-10}$ m/s² that matches observations.

In our solar system, and indeed in the central regions of galaxies, we see gravity as the interplay of ordinary matter and other ordinary matter. We are not used to this other dance.

Domains of gravity

Acceleration	Domain	Gravity vis-a-vis Newtonian formula	Examples
High (GM/R ~ c²)	Einstein, general relativity	Higher	Black holes, neutron stars
Normal	Newtonian dynamics	1/r²	Solar system, Sun orbit in Milky Way
Very low (< c/ age of U.)	Dark Gravity	Higher, additional 1/r term	Outer edges of galaxies, dwarf galaxies, clusters of galaxies

The table above summarizes three domains for gravity: general relativity, Newtonian, and dark gravity, the latter arising at very low accelerations. We are always calculating gravity incorrectly! Usually, such as in our solar system, it matters not at all. For example at the Earth’s surface gravity is 11 orders of magnitude greater than the very low acceleration domain where the extra term kicks in.

Recently, Alexander Peach, a Teaching Fellow in physics at Durham University, has taken a different angle based on Verlinde’s original, and much simpler, exposition of his emergent gravity theory in his 2010 paper. He derives an equivalent result to Verlinde’s in a way which I believe is easier to understand. He assumes that holography (the assumption that all of the entropy can be calculated as area law entropy on a spherical screen surrounding the mass) breaks down at a certain length scale. To mimic the effect of dark energy in Verlinde’s new hypothesis, Peach adds a volume law contribution to entropy which competes with the holographic area law at this certain length scale. And he ends up with the same result, an extra 1/r entropic force that should be added for correctness in very low acceleration domains.

Peach.fig2.jpeg

In figure 2 (above) from Peach’s paper he discusses a test particle located beyond a critical radius $r_c$ for which volume law entropy must also be considered. Well within $r_c$ (shown in b) the dark energy is fully displaced by the attracting mass located at the origin and the area law entropy calculation is accurate (indicated by the shaded surface). Beyond $r_c$ the dark energy effect is important, the holographic screen approximation breaks down, and the volume entropy must be included in the contribution to the emergent gravitational force (shown in c). It is this volume entropy that provides an additional 1/r term for the gravitational force.

Peach makes the assumption that the bulk and boundary systems are in thermal equilibrium. The bulk is the source of volume entropy. In his thought experiment he models a single bit of information corresponding to the test particle being one Compton wavelength away from the screen, just as Verlinde initially did in his description of emergent Newtonian gravity in 2010. The Compton wavelength is equal to the wavelength a photon would have if its energy were equal to the rest mass energy of the test particle. It quantifies the limitation in measuring the position of a particle.

Then the change in boundary (screen) entropy can be related to the small displacement of the particle. Assuming thermal equilibrium and equipartition within each system and adopting the first law of thermodynamics, the extra entropic force can be determined as equal to the Newtonian formula, but replacing one of the r terms in the denominator by $r_c$ .

To understand $r_c$ , for a given system, it is the radius at which the extra gravity is equal to the Newtonian calculation, in other words, gravity is just twice as strong as would be expected at that location. In turn, this traces back to the fact that, by definition, it is the length scale beyond which the volume law term overwhelms the holographic area law.

It is thus the distance at which the Newtonian gravity alone drops to about $1.2 \cdot 10^{-10}$ m/s², i.e. $c \cdot H / 6$ , for a given system.

So Peach and Verlinde use two different methods but with consistent assumptions to model a dark gravity term which follows a 1/r force law. And this kicks in at around $10^{-10}$ m/s².

The ingredients introduced by Peach’s setup may be sufficient to derive a covariant theory, which would entail a modified version of general relativity that introduces new fields, which could have novel interactions with ordinary matter. This could add more detail to the story of covariant emergent gravity already considered by Hossenfelder (2017), and allow for further phenomenological testing of emergent dark gravity. Currently, it is not clear what the extra degrees of freedom in the covariant version of Peach’s model should look like. It may be that Verlinde’s introduction of elastic variables is the only sensible option, or it could be one of several consistent choices.

With Peach’s work, physicists have taken another step in understanding and modeling dark gravity in a fashion that obviates the need for dark matter to explain our universe

We close with another of John Wheeler’s sayings:

“The only thing harder to understand than a law of statistical origin would be a law that is not of statistical origin, for then there would be no way for it—or its progenitor principles—to come into being. On the other hand, when we view each of the laws of physics—and no laws are more magnificent in scope or better tested—as at bottom statistical in character, then we are at last able to forego the idea of a law that endures from everlasting to everlasting. “

It is a pleasure to thank Alexander Peach for his comments on, and contributions to, this article.

References:

https://darkmatterdarkenergy.com/2018/08/02/dark-acceleration-the-acceleration-discrepancy/ blog “Dark Acceleration: The Acceleration Discrepancy”

https://arxiv.org/abs/gr-qc/9504004 “Thermodynamics of Spacetime: The Einstein Equation of State” 1995, Ted Jacobson

https://darkmatterdarkenergy.com/2017/07/13/dark-energy-and-the-comological-constant/ blog “Dark Energy and the Cosmological Constant”

https://darkmatterdarkenergy.com/2016/12/30/emergent-gravity-verlindes-proposal/ blog “Emergent Gravity: Verlinde’s Proposal”

https://arxiv.org/pdf/1806.10195.pdf “Emergent Dark Gravity from (Non) Holographic Screens” 2018, Alexander Peach

https://arxiv.org/pdf/1703.01415.pdf “A Covariant Version of Verlinde’s Emergent Gravity” Sabine Hossenfelder

1 Comment | tags: Dark energy, dark gravity, Dark matter, Einstein, emergent gravity, MOND, Newton, Wheeler | posted in Dark Energy, Dark Matter, Gravity

August 2, 2018

Dark Acceleration: The Acceleration Discrepancy

By Stephen Perrenod

Are Newton and Einstein both wrong?

Maybe Dark Matter has been going by the wrong name all along, ever since the cantankerous Swiss astronomer Fritz Zwicky coined the name, when his observations of the Coma cluster of galaxies showed the velocities were very much higher than expected.

He assumed Newton’s laws, and indeed general relativity, are correct. And that has been the canonical assumption ever since.

“Dark matter” has been studied on the scale of individual galaxies, clusters of galaxies, and the universe as a whole. The measurements of rotation velocity of spiral galaxies decades ago set the tone.

But the effects have been seen in the velocity dispersions of elliptical galaxies, in clusters of galaxies, and indeed in the cosmic microwave background temperature fluctuations.

What effects? Well for galaxies, whether for rotation or for dispersions within elliptical galaxies, what is actually observed is extra acceleration.

We all know F = ma, force equals mass times acceleration, for Newtonian dynamics.

In the case of galaxy rotation curves, the outer regions of the galaxies rotate faster than expected, where the expectation is set by the profile of visible matter and the modeling of the relationship between stellar luminosity and masses.

What is actually measured is the rotational (centripetal) observed acceleration of outer regions as being higher than expected, sometimes very much so.

But is m the problem? Is there missing ‘dark matter’? Or is ‘a’ the problem; does the Newtonian formula fail for the outer regions, or more specifically in environments where the acceleration is very low, less than about one ten billionth of a meter per second per second (less than 1 Angstrom per second per second)?

Now general relativity is not the explanation for the discrepancy, because we see departures from Newtonian behavior towards general relativistic formulae when acceleration is quite high, not when it is very low. So if Newton is wrong at very low accelerations, so is Einstein.

It turns out that the extra acceleration is best correlated not with the distance from the galaxy center, but with the amplitude of the expected Newtonian acceleration. When the expected acceleration is very low, the observed acceleration has the biggest discrepancy, always in the direction of more acceleration than expected.

fig3.radialacceleration

Figure 3 from Lelli et al. 2016 “One Law to Rule Them All” This shows the observed gravitational acceleration on the y-axis (log scale) displayed vs. the expected Newtonian acceleration on the x-axis. Over 2000 data points drawn from 153 galaxy rotation curves would lie on the dotted line if there were no extra acceleration. There is very clear extra acceleration and it is correlated to the Newtonian acceleration, with a larger proportional effect at lower accelerations. At these very low accelerations the observed values are about an order of magnitude above the Newtonian value.

From an Occam’s razor point of view it is actually simpler to think about modifying the laws of gravity in very low acceleration environments. It is only in these actual astrophysical laboratories that we are able to test how gravity behaves at very low accelerations.

Explanations such as emergent gravity and other modified Newtonian dynamics approaches need serious theoretical and experimental investigation. They have been playing a distant second fiddle to expensive dark matter searches for WIMPs and axions, which keep coming up short even as the experiments become more and more sensitive.

References

F. Lelli, S. McGaugh, J. Schombert, M. Pawlowski, 2016 “One Law to Rule Them All: The Radial Acceleration Relation of Galaxies” https://arxiv.org/pdf/1610.08981.pdf

Blog on Verlinde’s Emergent Gravity https://darkmatterdarkenergy.com/2016/12/30/emergent-gravity-verlindes-proposal/

1 Comment | posted in Uncategorized

June 26, 2018

WIMPZillas: The Biggest WIMPs

By Stephen Perrenod

In the search for direct detection of dark matter, the experimental focus has been on WIMPS – weakly interacting massive particles. Large crystal detectors are placed deep underground to avoid contamination from cosmic rays and other stray particles.

WIMPs are often hypothesized to arise as supersymmetric partners of Standard Model particles. However, there are also WIMP candidates that arise due to non-supersymmetric extensions to the Standard Model.

The idea is that the least massive supersymmetric particle would be stable, and neutral. The (hypothetical) neutralino is the most often cited candidate.

The search technique is essentially to look for direct recoil of dark matter particles onto ordinary atomic nuclei.

The only problem is that we keep not seeing WIMPs. Not in the dark matter searches, not at the Large Hadron Collider whose main achievement has been the detection of the Higgs boson at mass 125 GeV. The mass of the Higgs is somewhat on the heavy side, and constrains the likelihood of supersymmetry being a correct Standard Model extension.

The figure below shows WIMP interaction with ordinary nuclear matter cross-section limits from a range of experiments spanning from 1 to 1000 GeV masses for WIMP candidates. Typical supersymmetric (SUSY) models are disfavored by these results at higher masses above 40 GeV or so as the observational limits are well down into the yellow shaded regions.

WIMPLimits

Perhaps the problem is that the WIMPs are much heavier than where the experiments have been searching. Most of the direction detection experiments are sensitive to candidate masses in the range from around 1 GeV to 1000 GeV (1 GeV or giga-electronVolt is about 6% greater than the rest mass energy of a proton). The 10 to 100 GeV range has been the most thoroughly searched region and multiple experiments place very strong constraints on interaction cross-sections with normal matter.

WIMPzillas is the moniker given to the most massive WIMPs, with masses from a billion GeV up to potentially as large as the GUT (grand Unified Theory) scale of $10^{16} GeV$ .

The more general term is Superheavy Dark Matter, and this is proposed as a possibility for unexplained ultra high energy cosmic rays (UHECR). The WIMPzillas may decay to highly energetic gamma rays, or other particles, and these would be detected as the UHECR.

UHECR have energies greater than a billion GeV ( $10^9 GeV$ ) and the most massive event ever seen (the so-called Oh My God Particle) was detected at $3 \cdot 10^{11} GeV$ . It had energy equivalent to a baseball with velocity of 94 kilometers per hour. Or 40 million times the energy of particles in the Large Hadron Collider.

It has taken decades of searching at multiple cosmic ray arrays to detect particles at or near that energy.

Most UHECR appear to be spatially correlated with external galaxy sources, in particular with nearby Active Galactic Nuclei that are powered by supermassive black holes accelerating material near, but outside of, their event horizons.

However, they are not expected to be able to produce cosmic rays with energies above around $10^{11} GeV$ , thus the WIMPzilla possibility. Again WIMPzillas could span the range from $10^9 GeV$ up to $10^{16} GeV$ .

In a paper published last year, Kolb and Long calculated the production of WIMPzillas from Higgs boson pairs in the early universe. These Higgs pairs would have very high kinetic energies, much beyond their rest mass.

This production would occur during the “Reheating” period after inflation, as the inflaton (scalar energy field) dumped its energy into particles and radiation of the plasma.

There is another production mechanism, a gravitational mechanism, as the universe transitions from the accelerated expansion phase during cosmological inflation into the matter dominated (and then radiation-dominated) phases.

Thermal production from the Higgs portal, according to their results, is the dominant source of WIMPzillas for masses above $10^{14} GeV$ . It may also be the dominant source for masses less than about $10^{11} GeV$ .

They based their assumptions on chaotic inflation with quadratic inflation potential, followed by a typical model for reheating, but do not expect that their conclusions would be changed strongly with different inflation models.

It will take decades to discriminate between Big Bang-produced WIMPzilla style cosmic rays and those from extragalactic sources, since many more $10^{11} GeV$ and above UHECRs should be detected to build statistics on these rare events.

But it is possible that WIMPzillas have already been seen.

The density is tiny. The current dark matter density in the Solar neighborhood is measured at 0.4 Gev per cc. Thus in a cubic meter there would be the equivalent of 400,000 proton masses.

But if the WIMPzillas are at energies $10^{11} Gev$ and above (100 billion GeV), a cubic kilometer would only contain 4000 particles at a given time. Not easy to catch.

References

http://cdms.berkeley.edu/publications.html – SuperCDMS experiment led by UC Berkeley

http://pdg.lbl.gov/2017/reviews/rpp2017-rev-dark-matter.pdf – Dark matter review chapter from Lawrence Berkeley Lab (Figure above is from this review article).

http://home.physics.ucla.edu/~arisaka/home3/Particle/Cosmic_Rays/ – Ultra high energy cosmic rays

https://arxiv.org/pdf/1708.04293.pdf – E. Kolb and A. Long, 2017 “Superheavy Dark Matter through Higgs Portal Operators”

2 Comments | tags: cosmic rays, Dark matter, GUT, LHC, WIMPs, WIMPZillas | posted in Dark Matter

March 4, 2018

Dark Ages, Dark Matter

By Stephen Perrenod

Cosmologists call the first couple of hundred million years of the universe’s history the Dark Ages. This is the period until the first stars formed. The Cosmic Dawn is the name given to the epoch during which these first stars formed.

Now there has been a stunning detection of the 21 centimeter line from neutral hydrogen gas in that era. Because the first stars are beginning to form, their radiation induces the hyperfine transition for electrons in the ground state orbitals of hydrogen. This radiation undergoes a cosmological expansion of around a factor of 18 since the era of the Cosmic Dawn. By the time it reaches us, instead of being at the laboratory frequency of 1420 MHz, it is at around 78 MHz.

This is a difficult frequency at which to observe, since the region of spectrum is between the TV and FM bands in the U.S. and instrumentation itself is a source of radio noise. Very remote, radio quiet, sites are necessary to minimize interference from terrestrial sources, and the signal must be picked out from a much stronger cosmic background.

Image credit: CSIRO-Australia and EDGES collaboration, MIT and Arizona State University. EDGES is funded by the National Science Foundation.

This detection was made in Western Australia with a radio detector known as EDGES, that is sensitive in the 50 to 100 MHz range. It is surprisingly small, roughly the size of a large desk. The EDGES program is a collaboration between MIT and Arizona State University.

The researchers detected an absorption feature beginning at 78 MHz, corresponding to a redshift of 17.2 (1420/78 = 18.2 = 1 + z, where z is redshift) and for the canonical cosmological model it corresponds to an age of the universe of 180 million years.

The absorption feature is much stronger than expected from models, implying a lower gas temperature than expected.

At that redshift the cosmic microwave background temperature is at 50 Kelvins (at the present era it is only 2.7 Kelvins). The neutral hydrogen feature is seen in absorption against the warmer cosmic microwave background, and is much cooler (both its ‘spin’ and ‘kinetic’ temperatures).

This neutral hydrogen appears to be at only 3 Kelvins. Existing models had the expectation that it would be at around 7 Kelvins or even higher. (A Kelvin degree equals a Celsius degree, but has its zero point at absolute zero rather than water’s freezing temperature).

In a companion paper, it has been proposed that interactions with dark matter kept the hydrogen gas cooler than expected. This would require an interaction cross section between dark matter and ordinary matter (non- gravitational interaction, perhaps due to the weak force) and low velocities and low masses for dark matter particles. The mass should be only a few GeV (a proton rest mass is .94 GeV). Most WIMP searches in Earth-based labs have been above 10 GeV.

These results need to be confirmed by other experiments. And the dark matter explanation is speculative. But the door has been opened for Cosmic Dawn observations of neutral hydrogen as a new way to hunt for dark matter.

References:

“A Surprising Chill before the Cosmic Dawn” https://www.nature.com/articles/d41586-018-02310-9

EDGES science: http://loco.lab.asu.edu/edges/edges-science/

EDGES array and program: https://www.haystack.mit.edu/ast/arrays/Edges/

R. Barkana 2018, “Possible Interactions between Baryons and Dark Matter Particles Revealed by the First Stars” http://www.nature.com/articles/nature25791

1 Comment | tags: cosmic dawn, dark ages, Dark matter, early universe, EDGES, radio astronomy | posted in Dark Matter, Early Universe