# Tag Archives: inflation

## Dark Catastrophe, a few Trillion Years away?

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).

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

## Axions, Inflation and Baryogenesis: It’s a SMASH (pi)

Searches for direct detection of dark matter have focused primarily on WIMPs (weakly interacting massive particles) and more precisely on LSPs (the lightest supersymmetric particle). These are hypothetical particles such as neutralinos that are least massive members of the hypothesized family of supersymmetric partner particles.

But supersymmetry may be dead. There have been no supersymmetric particles detected at the Large Hadron Collider at CERN as of yet, leading many to say that this is a crisis in physics.

At the same time as CERN has not been finding evidence for supersymmetry, WIMP dark matter searches have been coming up empty as well. These searches keep increasing in sensitivity with larger and better detectors and the parameter space for supersymmetric WIMPs is becoming increasingly constrained. Enthusiasm unabated, the WIMP dark matter searchers continue to refine their experiments.

LUX dark matter detector in a mine in Lead, South Dakota is not yet detecting WIMPs. Credit: Matt Kapust/ Sanford Underground Research Facility

What if there is no supersymmetry? Supersymmetry adds a huge number of particles to the particle zoo. Is there a simpler explanation for dark matter?

Alternative candidates under consideration for dark matter, including sterile neutrinos, axions, and primordial black holes, and are now getting more attention.

From a prior blog I wrote about axions as dark matter candidates:

Axions do not require the existence of supersymmetry. They have a strong theoretical basis in the Standard Model as an outgrowth of the necessity to have charge conjugation plus parity conserved in the strong nuclear force (quantum chromodynamics of quarks, gluons). This conservation property is known as CP-invariance. (While CP-invariance holds for the strong force, the weak force is CP violating).

In addition to the dark matter problem, there are two more outstanding problems at the intersection of cosmology and particle physics. These are baryogenesis, the mechanism by which matter won out over antimatter (as a result of CP violation of Charge and Parity), and inflation. A period of inflation very early on in the universe’s history is necessary to explain the high degree of homogeneity (uniformity) we see on large scales and the near flatness of the universe’s topology. The cosmic microwave background is at a uniform temperature of 2.73 Kelvins to better than one part in a hundred thousand across the sky, and yet, without inflation, those different regions could never have been in causal contact.

A team of European physicists have proposed a model SMASH that does not require supersymmetry and instead adds a few particles to the Standard Model zoo, one of which is the axion and is already highly motivated from observed CP violation. SMASH (Standard Model Axion Seesaw Higgs portal inflation) also adds three right-handed heavy neutrinos (the three known light neutrinos are all left-handed). And it adds a complex singlet scalar field which is the primary driver of inflation although the Higgs field can play a role as well.

The SMASH model is of interest for new physics at around 10^11 GeV or 100 billion times the rest mass of the proton. For comparison, the Planck scale is near 10^19 GeV and the LHC is exploring up to around 10^4 GeV (the proton rest mass is just under 1 GeV and in this context GeV is short hand for GeV divided by the speed of light squared).

Figure 1 from Ballesteros G. et al. 2016. The colored contours represent observational limits from the Planck satellite and other sources regarding the tensor-to-scalar power ratio of primordial density fluctuations (r, y-axis) and the spectral index of these fluctuations (ns, x-axis). These constraints on primordial density fluctuations in turn constrain the inflation models. The dashed lines ξ = 1, .1, .01, .001 represent a key parameter in the assumed slow-roll inflation potential function. The near vertical lines labelled 50, 60, 70, 80 indicate the number N of e-folds to the end of inflation, i.e. the universe inflates by a factor of e^N in each of 3 spatial dimensions during the inflation phase.

So with a single model, with a few extensions to the Standard Model, including heavy right-handed (sterile) neutrinos, an inflation field, and an axion, the dark matter, baryogenesis and inflation issues are all addressed. There is no need for supersymmetry in the SMASH model and the axion and heavy neutrinos are already well motivated from particle physics considerations and should be detectable at low energies. Baryogenesis in the SMASH model is a result of decay of the massive right-handed neutrinos.

Now the mass of the axion is extremely low, of order 50 to 200 μeV (millionths of an eV) in their model (by comparison, neutrino mass limits are of order 1 eV), and detection is a difficult undertaking.

There is currently only one active terrestrial axion experiment for direct detection, ADMX. It has its primary detection region at lower masses than the SMASH model is suggesting, and has placed interesting limits in the 1 to 10 μeV range. It is expected to push its range up to around 30 μeV in a couple of years. But other experiments such as MADMAX and ORPHEUS are coming on line in the next few years that will explore the region around 100 μeV, which is more interesting for the SMASH model.

Not sure why the researchers didn’t call this the SMASHpie model (Standard Model Axion Seesaw Higgs portal inflation), because it’s a pie in the face to Supersymmetry!

It would be wonderfully economical to explain baryogenesis, inflation, and dark matter with a handful of new particles, and to finally detect dark matter particles directly.

Reference

“Unifying inflation with the axion, dark matter, baryogenesis and the seesaw mechanism” Ballesteros G., Redondo J., Ringwald A., and Tamarit C. 2016  https://arxiv.org/abs/1608.05414

## 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.

## Planck Mission Full Results Confirm Canonical Cosmology Model

Dark Matter, Dark Energy values refined

The Planck satellite, launched by the European Space Agency, made observations of the cosmic microwave background (CMB) for a little over 4 years, beginning in August, 2009 until October, 2013.

Preliminary results based on only the data obtained over the first year and a quarter of operation, and released in 2013, established high confidence in the canonical cosmological model. This ΛCDM (Lambda-Cold Dark Matter) model is of a topologically flat universe, initiated in an inflationary Big Bang some 13.8 billion years ago and dominated by dark energy (the　Λ component), and secondarily by cold dark matter (CDM). Ordinary matter, of which stars, planets and human beings are composed, is the third most important component from a mass-energy standpoint. The amount of dark energy is over twice the mass-energy equivalent of all matter combined, and the dark matter is well in excess of the ordinary matter component.

This general model had been well-established by the Wilkinson Microwave Anisotropy Probe (WMAP), but the Planck results have provided much greater sensitivity and confidence in the results.

Now a series of 28 papers have been released by the Planck Consortium detailing results from the entire mission, with over three times as much data gathered. The first paper in the series, Planck 2015 Results I, provides an overview of these results. Papers XIII and XIV detail the cosmological parameters measured and the findings on dark energy, while several additional papers examine potential departures from a canonical cosmological model and constraints on inflationary models.

In particular they find that:

Ωb*h²  = .02226 to within 1%.

In this expression Ωb is the baryon (basically ordinary matter) mass-energy fraction (fraction of total-mass energy in ordinary matter) and h =　H0/100. H0 is the Hubble constant which measures the expansion rate of the universe, and indirectly, its age. The best value for H0 is 67.8 kilometers/sec/Megaparsec  (millions of parsecs, where 1 parsec = 3.26 light-years). H0 has an uncertainty of about 1.3% (two standard deviations). In this case h = .678 and the expression above becomes:

Ωb = .048, with uncertainty around 3% of its value. Thus, just under 5% of the mass-energy density in the universe is in ordinary matter.

The cold matter density is measured to be:

Ωc*h²  = .1186 with uncertainty less than 2% and with the h value substituted we have Ωc = .258 with similar uncertainty.

Since the radiation density in the universe is known to be very low, the remainder of the mass-energy fraction is from dark energy,

Ωe = 1 – .048 – .258 = .694

So in approximate percentage terms the Planck 2015 results indicate 69% dark energy, 26% dark matter, and 5% ordinary matter as the mass-energy balance of the universe. These results are essentially the same as the ratios found from the preliminary results reported in 2013. It is to be emphasized that these are present-day values of the constituents. The components evolve differently as the universe expands. Dark energy is manifested with its current energy density in every new unit of volume as the universe continues to expand, while the average dark matter and ordinary matter densities decrease inversely as the volume grows. This implies that in the past, dark energy was less important, but it will dominate more and more as the universe continues to expand.

Why is dark energy produced as the universe expands? The simplest explanation is that it is the irreducible quantum energy of empty space, of the vacuum. Empty space – space with no particles whatsoever – still has fields (scalar fields, in particular) permeating it, and these fields have a minimum energy. It also has ‘virtual’ particles popping in and out of existence very briefly. This is the cosmological constant (Λ) model for the dark energy.

This is the ultimate free lunch in nature. The dark energy works as a negative gravity; it enters into the equations of general relativity as a negative pressure which causes space to expand. And as space expands, more dark energy is created! A wonderful self-reinforcing process is in place. Since the dark energy dominates over matter, the expansion of the universe is accelerating, and has been for the last 5 billion years or so. Why wonderful? Because it adds billions upon billions of years of life to our universe.

The Planck Consortium also find the universe is topologically flat to a very high degree, with an upper limit of 1/2 of 1% deviation from flatness at large scales. This is an impressive observational result.

One of the most interesting results is Planck’s ability to constrain inflationary models. While a massive inflation almost certainly happened during the first billionth of a trillionth of a trillionth of a second as the Universe began, as indicated by the very uniformity of the CMB signal, there are many possible models of the inflationary field’s energy potential.

We’ll take a look at this in a future blog entry.

## BICEP2 Apparently Detects Quantum Nature of Gravity and Supports Inflationary Big Bang

Can a single experiment do all of the following?

1. Provide significant confirmation of the inflationary version of the Big Bang model (and help constrain which model of inflation is correct)
2. Confirm the existence of gravitational waves
3. Support the quantum nature of gravity (at very high energies)
4. Provide the first direct insight into the highest energy levels imagined by physicists – 10^16 GeV (10,000 trillion GeV) – 12 orders of magnitude beyond the LHC

Apparently it can! BICEP2 is a radio telescope experiment located at the South Pole, taking advantage of the very cold, dry air at that remote location for greater sensitivity. It is focused on measuring polarization of the cosmic microwave background radiation that is a remnant of the hot Big Bang of the early universe. (BICEP is an abbreviation of Background Imaging of Cosmic Extragalactic Polarization; this is the second version of the experiment).

The results announced by the BICEP2 team on March 17 at the Harvard-Smithsonian Center for Astrophysics, if they have been correctly interpreted, are the most important in cosmology in the 21st century to date. They are of such enormous significance that a Nobel Prize in Physics is highly likely, if the results and interpretation are confirmed.

We infer from a number of previous observations that there was likely an inflationary period very early on in the universes’s history. We are talking very, very, early – in the first billionth of a trillionth of a trillionth of a second. See this earlier post of mine here: https://darkmatterdarkenergy.com/2011/03/22/inflation/ This new result from BICEP2 is very supportive of inflationary Big Bang models, and that includes very simple models for inflation.

What is the observation? It is B-mode polarization in the cosmic microwave background radiation. The cosmic microwave background (CMB) is the thermal radiation left over from a time when the universe became transparent, at age 380,000 years, almost 14 billion years ago. There are two polarization modes for alignment of CMB radiation, the E-mode and the B-mode. The B-mode measures the amount of “curliness” in the alignment of CMB microwave photons (as you can easily see in the image below).

There are two known causes of B-mode polarization for the CMB. The first, also detected by the BICEP2 experiment, is due to intervening clusters of galaxies along the line of sight. These clusters bend the light paths due to their immense masses, in accordance with general relativity. These effects are seen at smaller spatial scales. At larger spatial scales, we have the more significant effect, whereby the gravitational waves generated during the inflation epoch imprint the polarization.

You can easily see the curly B-mode polarization with a quick glance at BICEP2’s results. (bicepkeck.org)

What is being seen in today’s CMB is due to this second and more profound cause, which is nothing less than quantum fluctuations in space-time in the very, very early universe revealing themselves due to the gravitational waves that they generated. And these gravitational waves in turn caused a small curling effect on the cosmic microwave background, until the time of decoupling of radiation and matter. This is seen in the image at angular scales of a few degrees.

At age 380,000 years the universe became transparent to the CMB radiation and it traveled for another 13.8 billion years and underwent a redshift by a factor of 1500 as the universe expanded. So what was optical radiation at that time, becomes microwave radiation today, with a characteristic temperature of 2.7 Kelvins (degrees above absolute zero), while still retaining the curly pattern seen by BICEP2.

This is the first observation that provides some direct insight into extremely high energy scales within the context of a single experiment. We are talking here of approximately a trillion times higher energy than the Large Hadron Collider, the world’s most powerful particle accelerator, where the Higgs boson was discovered.

The BICEP2 results are a single experiment that for the first time apparently ties quantum mechanics and gravity together. It supports the quantum nature of gravity, which occurs at very high energy scales. The Planck scale at which space-time would be quantized corresponds to an energy level of 10^18 or 10^19 GeV (ten million trillion GeV), and inflation in many models begins when the universe has an energy level somewhat lower, at 10^16 GeV (ten thousand trillion GeV, where 1 GeV is a little more than the rest mass-energy of a proton).

And take a look at this interview of Sean Carroll by PBS’s Gwen Ifill to get some more context around this (hopefully correct!) universe-expanding discovery. Other astronomers are already racing to confirm it.

References:

http://www.cfa.harvard.edu/CMB/bicep2/ – BICEP2 web site at Harvard-Smithsonian Center for Astrophysics

http://www.theguardian.com/science/2014/mar/17/bicep2-how-hot-big-bang-science-dark-energy

http://www.scientificamerican.com/article/gravity-waves-cmb-b-mode-polarization/

## Inflation

Graphic for History of the Universe (Credit: NASA/WMAP Science Team)

The Big Bang theory found great success explaining the general features of the universe, including the approximate age, the expansion history after the first second, the relative atomic abundances from cosmic nucleosynthesis, and of course the cosmic microwave background radiation. And it required only general relativity, a smooth initial state, and some well-understood atomic and nuclear physics. It assumed matter, both seen and unseen, was dominating and slowing the expansion via gravity. In this model the universe could expand forever, or recollapse on itself, depending on whether the average density was less than or greater than a certain value determined only by the present value of the Hubble constant.

However, during the late 20th century there remained some limitations and concerns with the standard Big Bang. Why is today’s density so relatively close to this critical value for recollapse, since it would have had to be within 1 part in 1000 trillion of the critical density at the time of the microwave background to yield that state? How did galaxies form given only the tiny density fluctuations observed in the microwave background emitted at the age of 380,000 years for the universe? And why was the microwave background so uniform anyway? In the standard Big Bang model, regions only a few degrees away from each other would not be casually connected (no communication even with light between the regions would be possible).

There are four known fundamental forces of nature. These are electromagnetism and gravity and two types of nuclear forces, known as the strong force and the weak force. Physicists believe all the forces but gravity unify at energies around  10,000 trillion times the rest mass-energy (using E = mc^2) of the proton (1 Giga-electron-Volt). At some point very early in the life of the universe, at even higher energies equal to the Planck energy of 10 million trillion times the proton mass, all of the four forces would have been unified as a single force or interaction. Gravity would separate from the others first as the universe’s expansion began and the effective temperature dropped, and next the strong force would decouple.

We also must consider the vacuum field, that represents the non-zero energy of empty space. Even empty space is filled with virtual particles, and thus energy. At very early times the energy density of the vacuum would be expected to be very high. During the very earliest period of the development of the universe, it could have decayed to a lower energy state in conjunction with the decoupling of the strong force from the unified single force, and this would also have driven an enormous expansion of space and deposited a large amount of energy into the creation of matter.

In the inflationary Big Bang model postulated by Alan Guth and others, the decay of the vacuum field would release massive amounts of energy and drive an enormous inflation (hyperinflation really) during a very short period of time. The inflation might have started one trillionth of one trillionth of one trillionth of a second after the beginning. And it might have lasted until only the time of one billionth of one trillionth of one trillionth of a second. But it would have driven the size of the entire universe to grow from an extremely microscopic scale up to the macroscopic scale. At the end of the inflation, what was originally a tiny bubble of space-time would have grown to perhaps one meter in size. And at the end of the inflationary period, the universe would have been filled with radiation and matter in the form of a quark-gluon plasma. Quarks are the constituent particles of ordinary matter such as protons and neutrons and gluons carry the strong force.

The doubling time was extremely short, so during this one billionth of one trillionth of one trillionth of a second the universe doubled around 100 times. In each of the 3 spatial dimensions it grew by roughly one million times one trillion times one trillion in size! This is much greater than even Zimbabwe’s inflation and happens in a nearly infinitesimal time! The inflationary period drove the universe to be very flat topologically, which is observed. And it implies that the little corner of the universe we can observe, and think of as our own, is only one trillionth of one trillionth of the entire universe, or less. There is good observational support for the inflationary Big Bang model from the latest observations concerning the flatness of the universe, given that the mass-energy density is so close to the critical value, and also from the weight of the evidence concerning the growth of original density fluctuations to form stars and galaxies.