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Problems with the standard model

The standard cosmological model is very successful in explaining many observational facts, but it has some problems. (Who doesn't?)

The CMB streams to us from the surface of last scattering at z=1300. The cosmological horizon at that time looks on our sky as a region 20across - 4 times larger than the Moon or the Sun.

Two regions on the sky more than 20 apart never communicated with each other. How can they have the CMB temperature agree to one part to 100,000?

For its age the universe is way too large.

Observations tell us that $\Omega_{\rm TOTAL}$ is not very far from 1. Thus, the universe is not very far from being flat. As it expands, it moves away from being flat (becomes more and more ``non-flat''). If it is not very far from being flat now, it started incredibly close to being flat.


During the early stages of the evolution of the universe all kinds of elementary particles are created. Where are they now?


Why are we here? (In other words, how the fluctuations that became galaxies originated in the first place?)

The early universe spent for most of its life in thermal equilibrium. There should be no fluctuations there at all!

Inflation

In 1982 two cosmologists, American Alan Guth and Russian Alexei Starobinsky independently offered a solution:

This expansion has to be very fast, much faster than the universe is expanding today. This kind of expansion is called inflation.

Before inflation, our current horizon was a tiny-tiny region of the universe, much smaller than a horizon at that epoch. It had more than enough time to fully come into a thermal equilibrium.

``Superluminal expansion''

The region that before inflation was well within a horizon, now can be larger than a horizon. During normal expansion a horizon increases in size. This means that during inflation a horizon was decreasing in size.

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Two inertial observers that were within sight of each other could later move outside each other's horizon. This is sometimes called ``superluminal expansion''. This of course does not mean that the Special Relativity is violated, just that the horizon is moving inward rather than outward. This can happen when the expansion of the universe is accelerated.

\framebox{\Huge\bf ?}What can cause such a fast expansion?

A.
The speed of light became larger.
B.
The space-time exploded at the first moment.
C.
The gravity force became repulsive.
D.
The universe started expanding incredibly fast.

Accelerated expansion of the universe is caused by ``lambda matter'', the kind of matter which has repulsive gravity. Example of such matter is elementary particles called Higgs bosons. Higgs bosons are responsible for the separation of the electroweak force into electromagnetic and weak forces. There are other particles that have repulsive gravity.

If we leave in the universe with the lambda matter, as observations suggest, we are at the beginning of another inflation period.


During a tiny period of time (about 10-35 seconds) the universe expanded by a factor at least

1030,

or, more likely, by something like

101013 = 1010,000,000,000,000.

This number is totally incomprehensible!!!


How does inflation help with the problems of the standard model?

All the observable universe comes from a very small region, which was well in the thermal equilibrium then.


Since the universe inflated, it became much more flatter than it was in the beginning. Important prediction: If inflation indeed took place, the universe should be flat now.


The universe expanded so much, that all exotic particles are now very-very far from each other and are extraordinary rare.

In the standard model, the universe was in thermal equilibrium, thus all fluctuations should be suppressed.

There is, however, one kind of fluctuations which is never suppressed. In quantum mechanics the laws of conservation of energy and momentum are not exact, but are violated on a very small scales (like a size of an atomic nucleus) during very short time intervals (the time light travels across the atomic nucleus). Those fluctuations are called quantum fluctuations.

Those fluctuations exist only on very tiny scales. You cannot make galaxies out of these fluctuations unless...

\framebox{\Huge\bf ?}...what?

Inflation increases the size of the universe, and the scales of all fluctuations so much that quantum fluctuations become fluctuations on the scales of galaxies, clusters of galaxies, horizon scales, and even beyond.

Why don't these fluctuations get suppressed later, when the universe again gets into thermal equilibrium?

Fluctuations outside the horizon cannot grow or decay. After inflation the horizon increases with time. Fluctuations that were initially outside the horizon move inside it, and can begin being suppressed. Small scales fluctuations, that moved inside the horizon long time ago are indeed suppressed. However, fluctuations on galaxy scales and larger moved inside the horizon rather recently, after recombination, and the thermal equilibrium was not maintained at that time. They did not get suppressed, they grew due to gravity.

That is how galaxies (and everything inside them) formed.

The end of inflation and lambda matter

The inflationary expansion of the universe was driven by the repulsive gravity of the lambda matter. Sooner or later inflation stops.

The lambda matter possesses another unusual property: when it dense, it does not interact with other particles very well, but when it is sufficiently rarefied, it begins interacting (normal matter is vice versa). After the universe expanded very much, the lambda matter became rarefied enough and it began decaying into normal matter (quarks). Normal matter quickly came into thermal equilibrium.

Perhaps, not all lambda matter decayed into quarks, but some of it left over. This would be an explanation for the observed cosmological constant (lambda matter today).

We do not quite know how this happened since we have not detected the Higgs boson in the lab yet, and do not know all its properties.

Chaotic inflation and eternal universe

Inflation seemed to fit very well between the GUT era and quark era, until early 1990s.

Then Andrei Linde (used to be Russian, now professor at Stanford) realized that those quantum fluctuations that seed galaxies well after inflation, can create new universes during inflation!

The universe constantly recreates its initial conditions. Regions that expanded enough during inflation will continue inflating, creating huge homogeneous and isotropic regions (which we used to call a universe before). Other regions can be thrown back to the initial conditions by quantum fluctuations, and will begin everything anew, again creating new homogeneous and isotropic regions and new initial conditions.

Such a universe will exist forever, and may have existed forever. The Big bang will then be only a part of the universe, and the universe as a whole exists at all times in the infinite space.

Such a universe is eternal and infinite, it is not homogeneous or isotropic on very-very-very-... large scales ( 101013 light years or larger), but it contains very large regions (sub-universes) that are homogeneous and isotropic. Some of the physical laws do not have to be the same in various sub-universes. Different sub-universes may have very different cosmological parameters etc. We happened to live in one that has $\Omega_0\approx 0.3$. Others may have different omegas, Hubble constant, CMB temperatures, etc.

The explanation why our universe is such as it is then becames simple: there are infinite number of different universes, and we just happened to be in this one. This is, perhaps, the weakest possible form of the anthropic principle.

Quantum gravity

General Relativity explains gravity as curvature of space-time. On the other hand, Quantum Mechanics considers all interactions as being carried by special particles, bosons. In particularly, gravity should be carried by graviton.

The difficulty in unifying the GR and QM is in this difference: how a bunch of gravitons can look like the curved space-time?

We have no full understanding of this duality, but superstring theory offers at least a possible explanation.

Space-time foam

Since quantum fluctuations are present everywhere all the time, they should be present in quantum gravity as well. Since the space-time itself is a part of quantum gravity, there should be quantum fluctuations in space-time on Planck scales: 10-33 cm and 10-43 seconds. On this tiny spatial and time scales the space-time is not smooth, but fluctuates. This is often called the -time foam. We have no clear picture what it actually means.

The superstring theory

The superstring theory is based on the postulate that all truly elementary particles are tiny strings that move around, wiggle and form loops. The size of each of the string is about the Planck length and they move with the speed close to the speed of light.

The space-time is then woven out of graviton strings the same way as a cloth is woven out of threads. The superstring space-time is not necessarily four-dimensional. It may have more dimensions, some of which are compactified, i.e. extend only over a very short distance (about the Planck scale).

The superstring theory is being currently developed. It is not complete and has no experimental support (yet).

The birth of the universe

We really do not know how the universe was born. Perhaps, it exists ``forever'' as chaotic inflation envisions. Perhaps, it was born at one ``moment'' from the space-time foam, when one of the quantum fluctuations became quite large by chance, and started expanding. In both these cases the universe is infinitely larger than what we can see around us, and has infinitely many homogeneous and isotropic regions which we identified with the whole universe during most of this class.


Perhaps, we are still as far from the truth about the universe as Aristotle was from the correct description of the solar system. Then we would have a long way to go...