The early universe: fundamental physics meets cosmology

If we go back in time from the moment when the radiation and matter densities were equal, then we are in a radiation-dominated universe. Eventually, when we are only about about 200s away from the Big Bang, the temperature rises to about 50 keV, the mass difference between a neutron and a proton. This is the temperature at which nuclear reactions among protons and neutrons come into equilibrium with each other. Above this energy all the baryons were free. As the universe cooled through this temperature, some heavier elements were formed: mainly 4He, but also small amounts of 3He, Li, B, and traces of other light elements. All the lithium and helium we see in the universe today was formed at this time: processes inside stars tend to destroy light elements, not make them. The final abundances of these elements is very sensitive to the rate at which the universe was expanding at this time. From extensive computations of the reaction networks, astrophysicists have been able to show that the universe contains no significant amounts of light or massless particles other than photons and the three types of neutrinos that are known from particle-physics experiments. If there were others, their self-gravity would have slowed the universe more strongly, which means that to match the Hubble expansion today, a universe with such extra particles would have had to have been expanding faster than the nucleosynthesis computations allow. If there are extra particles, they must have an energy density today that is significantly less than that of the photons, which have γ 10−5. Gravitational waves from the Big Bang must, therefore, satisfy this nucleosynthesis bound.

Notice that we are already within 200 s of the Big Bang in this discussion, and still we are in the domain of well-understood physics. At about 1 s, the temperature was around 500 keV, which is the mass of the electron. In this plasma, therefore, there was an abundance of electrons and positrons, constantly annihilating against one another and being created again by photons. Much earlier than this the rest mass of the electrons is negligible, so the number and energy density of photons and of electrons and positrons was similar. As the universe expanded through this 500 keV temperature and cooled, the electrons and positrons continued to annihilate, but no more were produced. After a few seconds, there were apparently essentially no positrons, and there was about one electron for every 109 photons. This ratio of 109 is called the specific entropy of the universe, a measure of its disorder.

Why were there any electrons left at all after this annihilation phase? Why, in other words, was there any matter left over to build into planets and people? Extensive observational programs, coupled to numerical simulations, have convincingly established that there is no ‘missing’ antimatter hidden somewhere, no anti-stars or anti-galaxies: significant amounts of antimatter just do not exist any more. Clearly, during the equilibrium plasma phase, electrons and positrons were not produced in equal numbers. The same must also have happened at a much earlier time, when protons and antiprotons were in equilibrium with the photon gas, when the temperature was above a few hundred MeV (only 10 μs after the Big Bang): something must have favored protons over antiprotons in the same ratio as for electrons over positrons, so that the overall plasma remained charge-neutral. This is one

of the central mysteries of particle physics. Something in the fundamental laws of physics gave a slight preference to electrons. Nature has a mattter-antimatter asymmetry.

At times earlier than 10−5s, there are no protons or neutrons, just a plasma of quarks and gluons, the fundamental building blocks of baryons. According to particle theory, quarks are ‘confined’, so that we never see a free one detached from a baryon. But at high enough temperatures and densities, the protons overlap so much that the quarks can stay confined and still behave like free particles.

We can even push our perspective another step higher in temperature, to around 10 TeV, which is the frontier for current accelerators. Physics is not well understood at these energies, and the Large Hadron Collider at CERN in Geneva will soon (end of 2008) start doing experiments to look for the Higgs particle and to find evidence for supersymmetry. Both of these are theoretical constructs designed to solve deep theoretical problems in fundamental physics. In particular, supersymmetry has the advantage of making it easier within particle physics theories to predict a value of the cosmological constant in the range of what we observe. If supersymmetry is found, it will encourage the idea that the dark energy can be accommodated within the current framework of fundamental physics theory. At 10 TeV, we are just 10−14s after the Big Bang. Although physics is poorly known, it is unlikely that anything happened at this point that will challenge the picture presented here of what happened later.

In this scheme there is one important thing that is missing: we have mentioned no mechanism in any of this physics for generating the density irregularities in the dark matter that led to galaxy formation. We observe them in the microwave background, and we know that they are needed in order to trigger all the processes that eventually led to our own evolution. But even at 10−14s, they are simply an initial condition: they have to be there, at a much smaller amplitude than we see them in the microwave background because the irregularities grow as the universe expands, but they must be there. And known physics has no explanation for how they got there. The exciting answer to this problem lies in the scenario of inflation, which we come back to below.

But the density perturbations are not the only feature of the early universe that is not explained. Right from the start we have assumed homogeneity and isotropy, based on observations. We have had to accept a small amount of inhomogeneity in the density distribution at the time of decoupling, but that was inevitable: our assumption of homogeneity does not hold on small scales, where galaxies and planets form. On the large scale, we need to ask, why is the universe so smooth? This is particularly difficult to explain because in the standard Big Bang, there is no physical process that could work to smooth things out. This needs some explanation.

Consider the primordial abundance of helium. It was fixed when the universe was only five minutes old. When we look with our telescopes in opposite directions on the sky, we can see distant quasars and galaxies that appear to have the same element abundances as we do, and yet they are so far away from each other that they could not have been in communication: they are outside each other’s particle horizon in the standard cosmological model. One way to ‘explain’ this is simply to postulate that the initial conditions for the Big Bang were the same everywhere, even in causally disconnected regions. But it would be more satisfying physically if some process could be found that enabled these

regions to communicate with each other at a very early time, even though they appear to be disconnected. Again, inflation offers such a mechanism. Inflation. The basic idea of inflation (Starobinsky 1980, Guth 1981, Linde 1982) is that, at a very early time like 10−35s, the universe was dominated by a large positive cosmological constant, much larger than we have today, but one that was only temporary: it turned on at some point and then turned off again, for reasons we will discuss below. But during the time when the universe was dominated by this constant, the matter and curvature were unimportant, and the universe expanded according to the simple law

If this exponential expansion lasted 20 or 30 e-foldings, then a region of very small size could have been inflated into the the size of a patch that would be big enough to become the entire observable universe today. The idea is that, before inflation, this small region had been smoothed out by some physical process, which was possible because it was small enough to do this even in the time available. Then inflation set in and expanded it into the initial data for our universe.

This would explain the homogeneity of what we see: everything did indeed come from the same patch. And inflation also explains the fluctuation in the cosmic microwave background. Here we have to go into more detail about the mechanism for inflation. Attempts to compute the cosmological constant today focus on the vacuum energy of quantum fields, which we used in order to explain the Hawking radiation in the previous chapter. The vacuum energy is attractive for this purpose because the vacuum must be invariant under Lorentz transformations: there should not be any preferred observer for empty space in quantum theory. This means that any stress-energy tensor associated with the vac-

uum must be Lorentz invariant. Now, the only Lorentz-invariant symmetric tensor field of

type 02 is the metric tensor itself, so any vacuum-energy explanation of dark energy will automatically produce something like a cosmological constant, proportional to the metric tensor.

In some models of the behavior of the physical interactions at very high energies, beyond the TeV scale, it is postulated that there is a phase transition in which the nature of the vacuum changes, and a large amount of vacuum energy is released in the form of a cosmological constant, powering inflation. But this is a dynamical process, which sets in when the phase change occurs and then stops when the energy is converted into the real energy that eventually becomes the particles and photons in our universe. So for a limited time, the universe inflates rapidly. Now, at the beginning there are the usual vacuum fluctuations, and the remarkable thing is that the exponential inflation amplifies these fluctuations in much the same way as a nonlinear oscillator can pump up its oscillation amplitude. When inflation finishes, what were small density perturbations on the quantum scale have become much larger, classical perturbations.

When physicists perform computations with this model, it does very well. The amplitude of the fluctuations is reasonable, their spectrum matches that which is inferred from the cosmic microwave background, and the physical assumptions are consistent with modern views of unification among the various interactions of fundamental physics. Inflation will remain a ‘model’ and not a ‘theory’ until either a full theory unifying the nuclear forces is found or until some key observation reveals the fields and potential that are postulated within the model. However, it is a powerful and convincing paradigm, and it is currently the principal framework within which physicists address the deepest questions about the early universe.

Beyond ge neral relativity

Inflation goes beyond standard physics, making assumptions about the way that the laws governing the nuclear interactions among particles behave at the very high energies that obtained in the early universe. But it does not modify gravity: it works within classical general relativity. Nevertheless, as we have remarked before, the classical theory must eventually be replaced by a quantum description of gravitation, and the search for this theory is a major activity in theoretical physics today.

Although no consistent theory has yet emerged, the search has produced a number of exciting ideas that offer the possibility of new kinds of observations, new kinds of explanations. One approach, called loop quantum gravity, directly attacks the problem of how to quantize spacetime, ignoring at first the other forces in spacetime, like electromagnetism. On a fine scale, presumably the Planck scale, it postulates that the manifold nature of spacetime breaks down, and the smaller-scale structure is one of nested, tangled loops. There are a number of variants on this approach, with different structures, but the common idea is that spacetime is a coarse-grained average over something that has a much richer topology. These ideas come from the mathematics in a natural way. A recent triumph of loop quantum gravity is to show that the Big Bang may not have been singular after all, that going backwards in time the universe is able to pass through the Big Bang and become a classical collapsing universe on the other side (Bojowald 2005).

Even more active, in terms of the number of physicists working in it, is the string-theory approach to quantum gravity. Here the aim is to unify all the interactions, including gravity, so the theory includes the nuclear and electromagnetic interactions from the start. String theory seems to be consistent, in the sense of not having to do artificial things to get rid of infinite energies, only in 11 spacetime dimensions. We live in just four of these, so physicists are beginning to ask questions about the remaining ones.

The first assumption was that they never got big: that attached to each point is a Plancksized seven-sphere offering the possibility of exiting from our four-dimensional universe only to things that are smaller than the Planck length. This would not be easy to observe. But it is also possible that some of these extra dimensions are big, and our four-dimensional universe is simply a four-surface in this fiveor more-dimensional surrounding. This surface has come to be called a brane, from the word ‘membrane’. String theory on branes has a special property: electromagnetism and the nuclear forces are confined to our brane,