# Tag Archives: Cosmology

## Black Holes* as a possible source of Universal Dark Energy

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.

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.

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.

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/pdfObservational 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”

## 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:

1. MOND – Modified Newtonian Dynamics, from Milgrom
2. Emergent gravity, from Verlinde
3. 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.

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/

## Dark Energy Survey First Results: Canonical Cosmology Supported

The Dark Energy Survey (DES) first year results, and a series of papers, were released on August 4, 2017. This is a massive international collaboration with over 60 institutions represented and 200 authors on the paper summarizing initial results. Over 5 years the Dark Energy Survey team plans to survey some 300 million galaxies.

The instrument is the 570-megapixel Dark Energy Camera installed on the Cerro Tololo Inter-American Observatory 4-meter Blanco Telescope.

Image: DECam imager with CCDs (blue) in place. Credit: darkenergysurvey.org

Over 26 million source galaxy measurements from far, far away are included in these initial results. Typical distances are several billion light-years, up to 9 billion light-years. Also included is a sample of 650,000 luminous red galaxies, lenses for the gravitational lensing, and typically these are foreground elliptical galaxies. These are at redshifts < 0.9 corresponding to up to 7 billion light-years.

They use 3 main methods to make cosmological measurements with the sample:

1. The correlations of galaxy positions (galaxy-galaxy clustering)

2. The gravitational lensing of the large sample of background galaxies by the smaller foreground population (cosmic shear)

3. The gravitational lensing of the luminous red galaxies (galaxy-galaxy lensing)

Combining these three methods provides greater interpretive power, and is very effective in eliminating nuisance parameters and systematic errors. The signals being teased out from the large samples are at only the one to ten parts in a thousand level.

They determine 7 cosmological parameters including the overall mass density (including dark matter), the baryon mass density, the neutrino mass density, the Hubble constant, and the equation of state parameter for dark energy. They also determine the spectral index and characteristic amplitude of density fluctuations.

Their results indicate Ωm of 0.28 to a few percent, indicating that the universe is 28% dark matter and 72% dark energy. They find a dark energy equation of state w = – 0.80 but with error bars such that the result is consistent with either a cosmological constant interpretation of w = -1 or a somewhat softer equation of state.

They compare the DES results with those from the Planck satellite for the cosmic microwave background and find they are statistically significant with each other and with the Λ-Cold Dark MatterΛ model (Λ, or Lambda, stands for the cosmological constant). They also compare to other galaxy correlation measurements known as BAO for Baryon Acoustic Oscillations (very large scale galaxy structure reflecting the characteristic scale of sound waves in the pre-cosmic microwave background plasma) and to Type 1a supernovae data.

This broad agreement with Planck results is a significant finding since the cosmic microwave background is at very early times, redshift z = 1100 and their galaxy sample is at more recent times, after the first five billion years had elapsed, with z < 1.4 and more typically when the universe was roughly ten billion years old.

Upon combining with Planck, BAO, and the supernovae data the best fit is Ωm of 0.30 with an error of less than 0.01, the most precise determination to date. Of this, about 0.25 is ascribed to dark matter and 0.05 to ordinary matter (baryons). And the implied dark energy fraction is 0.70.

Furthermore, the combined result for the equation of state parameter is precisely w = -1.00 with only one percent uncertainty.

The figure below is Figure 9 from the DES paper. The figure indicates, in the leftmost column the measures and error bars for the amplitude of primordial density fluctuations, in the center column the fraction of mass-energy density in matter, and in the right column the equation of state parameter w.

The DES year one results for all 3 methods are shown in the first row. The Planck plus BAO plus supernovae combined results are shown in the last row. And the middle row, the fifth row, shows all of the experiments combined, statistically. Note the values of 0.3 and – 1.0 for Ωm and w, respectively, and the extremely small error bars associated with these.

This represents continued strong support for the canonical Λ-Cold Dark Matter cosmology, with unvarying dark energy described by a cosmological constant.

They did not evaluate modifications to general relativity such as Emergent Gravity or MOND with respect to their data, but suggest they will evaluate such a possibility in the future.

References

https://arxiv.org/abs/1708.01530, “Dark Energy Survey Year 1 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing”, 2017, T. Abbott et al.

https://en.wikipedia.org/wiki/Weak_gravitational_lensing, Wikipedia article on weak gravitational lensing discusses galaxy-galaxy lensing and cosmic shear

## The Curiously Tangential Dwarf Galaxies

There are some 50 or so satellite galaxies around the Milky Way, the most famous of which are the Magellanic Clouds. Somewhat incredibly, half of these have been discovered within the last 2 years, since they are small, faint, and have low surface brightness. The image below shows only the well known ‘classical’ satellites. The satellites are categorized primarily as dwarf spheroidals, and most are low in gas content.

Image credit: Wikipedia, Richard Powell, Creative Commons Attribution-Share Alike 2.5 Generic

“Satellite galaxies that orbit from 1,000 ly (310 pc) of the edge of the disc of the Milky Way Galaxy to the edge of the dark matter halo of the Milky Way at 980×103 ly (300 kpc) from the center of the galaxy, are generally depleted in hydrogen gas compared to those that orbit more distantly. The reason is the dense hot gas halo of the Milky Way, which strips cold gas from the satellites. Satellites beyond that region still retain copious quantities of gas.

In a recent paper “The tangential velocity excess of the Milky Way satellites“, Marius Cautun and Carlos Frenk find that a sample of satellites (drawn from those known for more than a few years) deviates from the predictions of the canonical Λ – Cold Dark Matter (ΛCDMcosmology. (Λ refers to the cosmological constant, or dark energy).

“We estimate the systemic orbital kinematics of the Milky Way classical satellites and compare them with predictions from the Λ cold dark matter (ΛCDM) model derived from a semi-analytical galaxy formation model applied to high resolution cosmological N-body simulations. We find that the Galactic satellite system is atypical of ΛCDM systems. The subset of 10 Galactic satellites with proper motion measurements has a velocity anisotropy, β = −2.2 ± 0.4, that lies in the 2.9% tail of the ΛCDM distribution. Individually, the Milky Way satellites have radial velocities that are lower than expected for their proper motions, with 9 out of the 10 having at most 20% of their orbital kinetic energy invested in radial motion. Such extreme values are expected in only 1.5% of ΛCDM satellites systems. This tangential motion excess is unrelated to the existence of a Galactic ‘disc of satellites’. We present theoretical predictions for larger satellite samples that may become available as more proper motion measurements are obtained.”

Radial velocities are easy, we get those from redshifts. Tangential velocities are much tougher, but can be obtained from relatively nearby objects by measuring their proper motions. That is, how much do their apparent positions change on the sky after many years have passed. It’s all the more tough when your object is not a point object, but a fuzzy galaxy!

For a ‘random’ distribution of velocities in accordance with ΛCDM cosmology, one would expect the two components of tangential velocity to be each roughly equal on average to the radial component, and thus 2/3 of the kinetic energy would be tangential and 1/3 would be radial. But rather than 33% of the kinetic energy being in radial motion, they find that the Galactic satellites have only about 1/2 that amount in radial, and over 80% of their kinetic energy in tangential motion.

Formally, they find a negative velocity anistropy, β, which as it is defined in practice, should be around zero for a ΛCDM distribution. They find that β differs from zero by 5 standard deviations.

One possible explanation is that the dwarf galaxies are mainly at their perigee or apogee points of their orbits. But why should this be the case? Another explanation: “alternatively indicate that the Galactic satellites have orbits that are, on average, closer to circular than is typical in ΛCDM. This would mean that MW halo mass estimates based on satellite orbits (e.g. Barber et al. 2014) are biased low.” Perhaps the Milky Way halo mass estimate is too low. Or, they also posit, without elaborating, do the excess tangential motions “indicate new physics in the dark sector”?

So one speculation is that the tangential motions are reflective of emergent gravity class of theories, for which dark matter is not required, but for which the gravitational force changes (strengthens) at low accelerations, of order $c \cdot H$, where H is the Hubble parameter, and the value works out to be around 2 centimeters per second per year. And it does this in a way that ‘spoofs’ the existence and gravitational affect of dark matter. This is also what is argued for in Modified Newtonian Dynamics, which is an empirical observation about galaxy light curves.

In the next article of this series we will look at Erik Verlinde’s emergent gravity proposal, which he has just enhanced, and will attempt to explain it as best we can. If you want to prepare yourself for this challenging adventure, first read his 2011 paper, “On the Origin of Gravity and the Laws of Newton”.

## Dark Sector Experiments

A dark energy experiment was recently searching for a so-called scalar “chameleon field”. Chameleon particles could be an explanation for dark energy. They would have to make the field strength vanishingly small when they are in regions of significant matter density, coupling to matter more weakly than does gravity. But in low-density regions, say between the galaxies, the chameleon particle would exert a long range force.

Chameleons can decay to photons, so that provides a way to detect them, if they actually exist.

Chameleon particles were originally suggested by Justin Khoury of the University of Pennsylvania and another physicist around 2003. Now Khoury and Holger Muller and collaborators at UC Berkeley have performed an experiment which pushed millions of cesium atoms toward an aluminum sphere in a vacuum chamber. By changing the orientation in which the experiment is performed, the researchers can correct for the effects of gravity and compare the putative chameleon field strength to gravity.

If there were a chameleon field, then the cesium atoms should accelerate at different rates depending on the orientation, but no difference was found. The level of precision of this experiment is such that only chameleons that interact very strongly with matter have been ruled out. The team is looking to increase the precision of the experiment by additional orders of magnitude.

For now the simplest explanation for dark energy is the cosmological constant (or energy of the vacuum) as Einstein proposed almost 100 years ago.

The Large Underground Xenon experiment to detect dark matter (CC BY 3.0)

“Dark radiation” has been hypothesized for some time by some physicists. In this scenario there would be a “dark electromagnetic” force and dark matter particles could annihilate into dark photons or other dark sector particles when two dark matter particles collide with one another. This would happen infrequently, since dark matter is much more diffusely distributed than ordinary matter.

Ordinary matter clumps since it undergoes frictional and ordinary radiation processes, emitting photons. This allows it to cool it off and to become more dense under mutual gravitational forces. Dark matter rarely decays or interacts, and does not interact electromagnetically, thus no friction or ordinary radiation occurs. Essentially dark matter helps ordinary matter clump together initially since it dominates on the large scales, but on small scales ordinary matter will be dominant in certain regions. Thus the density of dark matter in the solar system is very low.

Earthbound dark matter detectors have focused on direct interaction of dark matter with atomic nuclei for the signal. John Cherry and co-authors have suggested that dark matter may not interact directly, but rather it first annihilates to light particles, which then scatter on the atomic nuclei used as targets in the direct detection experiments.

So in this scenario dark matter particles annihilate when they encounter each other, producing dark radiation, and then the dark radiation can be detected by currently existing direct detection experiments. If this is the main channel for detection, then much lower mass dark matter particles can be observed, down to of order 10 MeV (million electron-Volts), whereas current direct detection is focused on masses of several GeV (billion electron-Volts) to 100 GeV or more. (The proton rest mass is about 1 GeV)

A Nobel Prize awaits, most likely, the first unambiguous direct detection of either dark matter, or dark energy, if it is even possible.

References

https://en.wikipedia.org/wiki/Chameleon_particle – Chameleon particle

http://scitechdaily.com/physicists-work-on-new-approach-to-detect-dark-matter/ – article on detecting dark matter generated dark radiation

http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.231303 – Cherry et al. paper in Physical Review Letters

## Planck 2015 Constraints on Dark Energy and Inflation

The European Space Agency’s Planck satellite gathered data for over 4 years, and a series of 28 papers releasing the results and evaluating constraints on cosmological models have been recently released. In general, the Planck mission’s complete results confirm the canonical cosmological model, known as Lambda Cold Dark Matter, or ΛCDM. In approximate percentage terms the Planck 2015 results indicate 69% dark energy, 26% dark matter, and 5% ordinary matter as the mass-energy components of the universe (see this earlier blog:

Dark Energy

We know that dark energy is the dominant force in the universe, comprising 69% of the total energy content. And it exerts a negative pressure causing the expansion to continuously speed up. The universe is not only expanding, but the expansion is even accelerating! What dark energy is we do not know, but the simplest explanation is that it is the energy of empty space, of the vacuum. Significant departures from this simple model are not supported by observations.

The dark energy equation of state is the relation between the pressure exerted by dark energy and its energy density. Planck satellite measurements are able to constrain the dark energy equation of state significantly. Consistent with earlier measurements of this parameter, which is usually denoted as w, the Planck Consortium has determined that w = -1 to within 4 or 5 percent (95% confidence).

According to the Planck Consortium, “By combining the Planck TT+lowP+lensing data with other astrophysical data, including the JLA supernovae, the equation of state for dark energy is constrained to w = −1.006 ± 0.045 and is therefore compatible with a cosmological constant, assumed in the base ΛCDM cosmology.”

A value of -1 for w corresponds to a simple Cosmological constant model with a single parameter Λ  that is the present-day energy density of empty space, the vacuum. The Λ value measured to be 0.69 is normalized to the critical mass-energy density. Since the vacuum is permeated by various fields, its energy density is non-zero. (The critical mass-energy density is that which results in a topologically flat space-time for the universe; it is the equivalent of 5.2 proton masses per cubic meter.)

Such a model has a negative pressure, which leads to the accelerated expansion that has been observed for the universe; this acceleration was first discovered in 1998 by two teams using certain supernova as standard candle distance indicators, and measuring their luminosity as a function of redshift distance.

Modified gravity

The phrase modified gravity refers to models that depart from general relativity. To date, general relativity has passed every test thrown at it, on scales from the Earth to the universe as a whole. The Planck Consortium has also explored a number of modified gravity models with extensions to general relativity. They are able to tighten the restrictions on such models, and find that overall there is no need for modifications to general relativity to explain the data from the Planck satellite.

Primordial density fluctuations

The Planck data are consistent with a model of primordial density fluctuations that is close to, but not precisely, scale invariant. These are the fluctuations which gave rise to overdensities in dark matter and ordinary matter that eventually collapsed to form galaxies and the observed large scale structure of the universe.

The concept is that the spectrum of density fluctuations is a simple power law of the form

P(k) ∝ k**(ns−1),

where k is the wave number (the inverse of the wavelength scale). The Planck observations are well fit by such a power law assumption. The measured spectral index of the perturbations has a slight tilt away from 1, with the existence of the tilt being valid to more than 5 standard deviations of accuracy.

ns = 0.9677 ± 0.0060

The existence and amount of this tilt in the spectral index has implications for inflationary models.

Inflation

The Planck Consortium authors have evaluated a wide range of potential inflationary models against the data products, including the following categories:

• Power law
• Hilltop
• Natural
• D-brane
• Exponential
• Spontaneously broken supersymmetry
• Alpha attractors
• Non-minimally coupled

Figure 12 from Planck 2015 results XX Constraints on Inflation. The Planck 2015 data constraints are shown with the red and blue contours. Steeper models with  V ~ φ³ or V ~ φ² appear ruled out, whereas R² inflation looks quite attractive.

Their results appear to rule out some of these, although many models remain consistent with the data. Power law models with indices greater or equal to 2 appear to be ruled out. Simple slow roll models such as R² inflation, which is actually the first inflationary model proposed 35 years ago, appears more favored than others. Brane inflation and exponential inflation are also good fits to the data. Again, many other models still remain statistically consistent with the data.

Simple models with a few parameters characterizing the inflation suffice:

“Firstly, under the assumption that the inflaton* potential is smooth over the observable range, we showed that the simplest parametric forms (involving only three free parameters including the amplitude V (φ∗ ), no deviation from slow roll, and nearly power-law primordial spectra) are sufficient to explain the data. No high-order derivatives or deviations from slow roll are required.”

* The inflaton is the name cosmologists give to the inflation field

“Among the models considered using this approach, the R2 inflationary model proposed by Starobinsky (1980) is the most preferred. Due to its high tensor- to-scalar ratio, the quadratic model is now strongly disfavoured with respect to R² inflation for Planck TT+lowP in combination with BAO data. By combining with the BKP likelihood, this trend is confirmed, and natural inflation is also disfavoured.”

Isocurvature and tensor components

They also evaluate whether the cosmological perturbations are purely adiabatic, or include an additional isocurvature component as well. They find that an isocurvature component would be small, less than 2% of the overall perturbation strength. A single scalar inflaton field with adiabatic perturbations is sufficient to explain the Planck data.

They find that the tensor-to-scalar ratio is less than 9%, which again rules out or constrains certain models of inflation.

Summary

The simplest LambdaCDM model continues to be quite robust, with the dark energy taking the form of a simple cosmological constant. It’s interesting that one of the oldest and simplest models for inflation, characterized by a power law relating the potential to the inflaton amplitude, and dating from 35 years ago, is favored by the latest Planck results. A value for the power law index of less than 2 is favored. All things being equal, Occam’s razor should lead us to prefer this sort of simple model for the universe’s early history. Models with slow-roll evolution throughout the inflationary epoch appear to be sufficient.

The universe started simply, but has become highly structured and complex through various evolutionary processes.

References

Planck Consortium 2015 papers are at http://www.cosmos.esa.int/web/planck/publications – This site links to the 28 papers for the 2015 results, as well as earlier publications. Especially relevant are these – XIII Cosmological parameters, XIV Dark energy and modified gravity, and XX Constraints on inflation.

## Dark Matter Bridge Discovered

A team of astronomers claims to have detected an enormous bridge or filament of dark matter, with a mass estimated to be of order 100 trillion solar masses, and connecting two clusters of galaxies. The two clusters, known as Abell 222 and Abell 223, are about 2.8 billion light-years away and separated from one another by 400 million light-years. Each cluster has around 150 galaxies; actually one of the pair is itself a double cluster.

Clusters of galaxies are gravitationally bound collections of hundreds to a thousand or more galaxies. Often a cluster will be found in the vicinity of other clusters to which it is also gravitationally bound. The universe as a whole is gravitationally unbound – the matter, including the dark matter – is insufficient to stop the continued expansion, which is driven to acceleration in fact, by dark energy.

Figure: Subaru telescope optical photo with mass density shown in blue and statistical significance contours superimposed. In the filament area found near the center of the image, the contours indicate four standard deviations of significance in the detection of dark matter. The cluster Abell 222 is in the south, and Abell 223 is the double cluster in the north of the image. The distance between the two clusters is about 14 arc-minutes, or about ½ the apparent size of the Moon.

Dark matter was originally called “missing matter”, and was first posited by Fritz Zwicky (http://en.wikipedia.org/wiki/Fritz_Zwicky) in the 1930s because of his studies of the kinematics of galaxies and galaxy clusters. He measured the velocities of galaxies moving around inside a cluster and found they were significantly greater than expected from the amount of ordinary matter seen in the galaxies themselves. This implied there was more matter than seen in galaxies because the velocities of the galaxies would be determined by the total gravitational field in a cluster, and the questions have been where is, and what is, the “missing matter” inferred by the gravitational effects. X-ray emission has been detected from most clusters of galaxies, and this is due to an additional component of matter outside of galaxies, namely hot gas between galaxies. But it is still insufficient to explain the total mass of clusters as revealed by both the galaxy velocities and the temperature of the hot gas itself, since both are a reflection of the gravitational field in the cluster.

Dark matter is ubiquitous, found on all scales and is generally less clumped than ordinary matter, so it is not surprising that significant dark matter would be found between two associated galaxy clusters. In fact the researchers in this study point out that “It is a firm prediction of the concordance Cold Dark Matter cosmological model that galaxy clusters live at the intersection of large-scale structure filaments.”

The technique used to map the dark matter is gravitational lensing, which is a result of general relativity. The gravitational lensing effect is well established; it has been seen in many clusters of galaxies to date. In gravitational lensing, light is deflected away from a straight-line path by matter in its vicinity.

In this case the gravitational field of the dark matter filament and the galaxy clusters deflect light passing nearby. The image of a background galaxy located behind the cluster will be distorted as the light moves through or nearby the foreground cluster. The amount of distortion depends on the mass of the cluster (or dark matter bridge) and how near the line of sight passes to the cluster center.

There is also a well-detected bridge of ordinary matter in the form of hot X-ray emitting gas connecting the two clusters and in the same location as the newly discovered dark matter bridge.  The scientists used observations from the XMM-Newton satellite to map the X-ray emission from the two clusters Abell 222 and Abell 223 and the hot gas bridge connecting them. Because of the strong gravitational fields of galaxy clusters, the gas interior to galaxy clusters (but exterior to individual galaxies within the cluster) is heated to very high temperatures by frictional processes, resulting in thermal X-ray emission from the clusters.

The research team, led by Jörg Dietrich at the University of Michigan, then performed a gravitational lensing analysis, focusing on the location of the bridge as determined from the X-ray observations. The gravitational lensing work is based on optical observations obtained from the Subaru telescope (operated by the Japanese government, but located on the Big Island of Hawaii) to map the total matter density profile around and between the two clusters. This method detects the sum of dark matter and ordinary matter.

They analyzed the detailed orientations and shapes of over forty thousand background galaxies observable behind the two clusters and the bridge. This work allowed them to determine the contours of the dark matter distribution. They state a 98% confidence in the existence of a bridge or filament dominated by dark matter.

The amount of dark matter is shown to be much larger than that of ordinary matter, representing over 90% of the total in the filament region, so the gravitational lensing effects are primarily due to the dark matter. Less than 9% of the mass in the filament is in the form of hot gas (ordinary matter). The estimated total mass in the filament is about 1/3 of the mass of either of the galaxy clusters, each of which is also dominated by dark matter.

Observations of galaxy distributions show that galaxies are found in groups, clusters, and filaments connecting regions of galaxy concentration. Cosmological simulations of the evolution of the universe on supercomputers indicate that the distribution of dark matter should have a filamentary structure as well. So although the result is in many ways not surprising, it represents the first detection of such a structure to date.

References:

http://ns.umich.edu/new/releases/20623-dark-matter-scaffolding-of-universe-detected-for-the-first-time – press release from the University of Michigan

http://www.gizmag.com/dark-matter-filaments-found/23281/ “Dark matter filaments detected for the first time”

J. Dietrich et al. 2012 http://arxiv.org/abs/1207.0809 “A filament of dark matter between two clusters of galaxies”

## Foreword, by Rich Brueckner

“Through our eyes, the universe is perceiving itself. Through our ears, the universe is listening to its harmonies. We are the witnesses through which the universe becomes conscious of its glory, of its magnificence.”

— Alan Watts

We all know of the Big Bang, how our universe came to be in a massive explosion, seemingly starting from nothingness. And for those who study cosmology, further understanding requires us to define the dark energies that somehow endowed our world with order.

Now, we haven’t observed dark energy, dark matter, and the secrets of dark gravity directly, but we do see their effects. As we learn in this book, without them, the universe would not have formed in a way that could have spawned intelligent life.

As a writer, I am intrigued by these dark energies because they imply a backstory–phenomena that happened first that led to this outcome. So in this way, dark energies seem to me to be metaphors of science. Like the stories of Genesis and Adam and Eve, what they really represent is a deeper truth.

In this book, Dr. Perrenod does a wonderful job of explaining the origins of the universe in way that is accessible to the layman. When you want to understand how the universe came to be, you ask an astrophysicist. But when you really want to know why, I think you have to start by asking yourself some questions. Try a thought experiment.

Put yourself in the place of a Universal Mind before the Big Bang. If you really wanted to understand yourself, you would need to have something intelligent outside of yourself that could experience that which is you. Not to get metaphysical here, but if we were at the scene of a crime, what I’d be suggesting here is motive.

Thanks to modern physics and cosmology, we no longer live in a universe where dark forces lurk far beyond our capacity for comprehension. I believe that, through the works of Stephen Perrenod and others, we will come to that knowing. But even as we look out to the stars, I think it begins with understanding that not only are we within the universe, but the universe is within us.

Rich Brueckner is President of insideHPC.com

## Dark Matter, Dark Energy, Dark Gravity

Enabling a Universe that Supports Intelligent Life

Author: Stephen Perrenod

An e-book now available through:

We are immersed in a sea of light emanating from ordinary matter that is floating, as it were, on an ocean of dark matter. The dark matter itself floats on the dark energy of the particle vacuum that in turn is in embedded within the scaffolding of space-time – which is shaped by the dark gravity effects from all matter and energy.

• Dedication
• Foreword (by Rich Brueckner)
• Preface and Acknowledgements
1. Scale of the Universe
2. The Big Bang Model
3. Inflation
4. Dark Matter
5. Dark Energy
6. Dark Gravity
7. Future of the Universe
• Glossary
• References, Suggested Reading and Viewing