What is the evidence for rapid inflation after the Big Bang?

Answer

There is no ‘proof’, but there are good indications. It’s not a simple story, but it’s all very fascinating.

When the inflation hypothesis was first launched, it was as an answer to a trio of “coincidences” that surfaced within the big bang theory:
(1) The horizon problem. The cosmic horizon is the distance within which causal contact may have already occurred since the Big Bang. Since no signal travels faster than the speed of light, that is the distance light could have traveled since the big bang. Today we find that signals are reaching us from different directions from areas that appear to be the same (in terms of density, temperature, homogeneity) but which, at the time the light was emitted, were much more light years apart than the universe was when old . This is especially the case with the cosmic background radiation (see below), which is a remnant of what the universe looked like after 400 thousand years. The problem then is how those areas knew they had to look the same if they had never heard of each other before.
(2) The flatness problem. The universe is expanding. Whether that will continue depends on the extent to which gravity opposes the expansion, and thus on the amount of mass in the universe. If the density is greater than a certain critical density, then the expansion stops sometime (‘closed’ universe), and everything starts to collapse again. If the density is less than that critical density, the expansion will never come to an end (‘open’ universe). A universe with a density equal to the critical density is called a ‘flat’ universe: then the expansion stops when the universe is infinitely old (ie never).
Today, with the matter we see, we find that the mass density is less than the critical density. Then what is the problem? Well, the true/critical density ratio changes over time. In a ‘closed’ universe the ratio quickly increases, in an open universe it quickly decreases, in a flat universe the ratio always remains equal to one. Now the curious thing is that to have the universe with a ratio of a few percent (as we seem to observe), that ratio must have been very close to one in the past. In other words, a universe as old as ours would normally have to be either almost completely empty or very dense (but then it would never have gotten that old). So it seems that we are dealing with a far-reaching form of ‘fine tuning’. The most acceptable alternative is perhaps that the universe is exactly flat, because such a universe always remains that way. That also means that there is more mass than the few percent that we see, and for all sorts of reasons that additional mass cannot all come from ‘ordinary’ matter.
(3) Heavy particles. During the first second of the universe, the temperature dropped rapidly. This gives rise to phase transitions where the different interactions are disconnected from each other (quite complicated…). The theoretical expectation is that – just as fracture lines always form in the ice when water freezes – a large number of condensations in the form of very heavy particles would have occurred. We don’t see that in our universe today.

This last argument comes from quantum physics, the theory of the ‘infinitely small’. Indeed, the big bang is the moment when the infinitely large was also infinitely small… In terms of quantum field theory, different quantities are described in the context of ‘fields’. So is the vacuum, the void, which is described as a minimum of a certain potential. There is the theoretical possibility that the vacuum changes to a deeper minimum, and then a huge amount of energy is released, resulting in an exponentially accelerated expansion, and that phase is called ‘inflation’. The inflation hypothesis is thus not just an ‘ad hoc’ proposal to explain some oddities, but is rooted in physical theories that are taken seriously.

How does inflation solve the problems mentioned above?
(1) During that inflation, the universe rapidly becomes very much larger, and points that were close to each other rapidly move away from each other at speeds that are large multiples of the speed of light. Areas that used to be in causal contact with each other disappear from each other’s horizons. Later they may reappear within each other’s horizons, but their former contact has smoothed the folds for good.
(2) A balloon that you inflate gets a flat surface locally. So is the universe. The same equations that teach that an initially slightly different density to critical density ratio of 1 diverges rapidly to zero or infinity in a decelerating expansion, teach that every ratio quickly tends to 1 in an accelerating universe.
(3) In this rapid expansion, the density of heavy particles quickly decreases to barely or imperceptibly proportions.

Inflation seemed like a panacea, but it also had its own problems. Like: how did she stop? And also: if the universe is flat today, the real energy density is considerably greater than what we see in the stars. But then the expansion must be seriously slowed down, and then we get an age of the universe that is too small compared to that of the oldest stars. The latter problem has now been solved, since it was discovered that a large part of the energy density is not in attractive matter, but in a component that rather accelerates the expansion, the so-called ‘dark energy’.

Very strong support for the inflationary hypothesis has now come from the accurate observations of the cosmological background radiation. The early universe was hot, which must mean that there was also a lot of radiation in addition to matter. During the first 400 thousand years, it was so hot that matter was completely ionized: atoms could not hold electrons. Radiation interacts strongly with charged particles, and both components were in equilibrium with each other. After 400 thousand years, when the universe became neutral, a last major phase change occurred: since then, what remains of that radiation hardly interacts with matter. The matter could then begin to gravitationally contract into stars and galaxies, but the radiation just continued to expand. To form those structures in the matter, (small) irregularities in the density distribution must have already existed before radiation and matter decoupled, and we must find these today in the background radiation, which has only continued to expand since that time (because before decoupling there were radiation and matter in equilibrium). This was found for the first time with the satellite COBE. A more recent satellite, WMAP, has mapped those irregularities much more accurately. And then it turned out that those density contrasts are ‘scale invariant’: this means that contrasts on small length scales and on large length scales are all approximately of the same order (of the order of one hundred-thousandth…). This was a prediction of inflation. There, density contrasts are predicted as ‘quantum fluctuations’ in the early universe; the earliest have become very large, because the universe has expanded a great deal afterwards, the latter have remained small, because then the inflationary period was almost over; but since they had the same cause, their amplitude was always the same. For example, inflation is nicely confirmed by the observed scale invariance, and immediately gives the physical cause of the contrasts that later evolved into galaxies.

Perhaps the main problem that remains is the following: inflation is therefore possible in field theories, but does not occur in all variants, perhaps only in a minority of possibilities. In those ways, we have “explained” some apparent improbabilities with a theory that may itself be improbable. Instead of three ‘coincidences’ you only have one, but it still has something of a circular reasoning. Our compatriot Thomas Hertog tries to find an answer to this with his promotor Stephen Hawking, by looking for physical arguments why universe models with an inflationary phase are more likely than others.