Pedagoguery

Modern cosmology is built on the foundation of inflation. It has been a very successful hypothesis, explaining much of what we see today, but there may be some cracks appearing in that foundation. The question is whether these are steps on the road to make the theory better, or fundamental flaws.

Inflation relies on the existence of a particular form of energy, called the inflaton field. It must be dense, nearly of constant value across space, and have a negative gravitational effect. The shape of the potential energy profile must be like a shallow valley, surrounded by a gently sloping plateau. When the value is on the plateau, inflation is in progress, but when it drops into the valley, inflation stops. This aspect of inflation will prove critical to the further discussion.

Before moving on, let us first see where inflation is successful. First of all, inflation appears to be inevitable. Recent work in theoretical physics has identified a number of potential inflaton candidates, so that question appears to be how inflation can possibly be avoided. It is almost certain that in the chaotic environment of the early universe, somewhere, some combination of factors would favor inflation, and once that happened, that area would quickly expand to become the dominant region.

Secondly, inflation does a great job of explaining the uniformity of the universe on large scales. No one knows how uniform the immediate post-Big Bang universe was, but with inflation, it does not matter – all of the irregularities get inflated away.

Finally, inflation predicts very accurately the universe we see around us. Because of quantum fluctuations, the post-inflation universe would not be absolutely uniform, but would contain small fluctuations. These fluctuations would have a very definite property in that they would be what is called “scale invariant”. That is to say that they would be the same no matter how big or small a scale that you were looking at was. That is precisely what we observe.

However, inflation is not without its issues. Unlike most cases of a failing theory, the issue is not small discrepancies between predictions and observation. On the contrary, observations are in excellent accord with the predictions of inflation. No, here the issue is challenges to the logical foundations of the theory. There are two fundamental questions that are being raised. First, does the theory really work as advertised? Second, are the predictions originally made still the predictions of the model as we understand it today. There are reasons to believe that the answer to both questions is no.

The first challenge is to the inevitability argument.. As it turns out, if inflation is inevitable, then “bad” inflation is much more likely than “good” inflation. In this instance, “bad” inflation is defined as inflation that does not produce the results we see today. It all depends on the precise shape of the potential energy profile of the inflaton field. Current theories do not constrain the profile, so it could, in theory, take on any value at all. As it turns out, only a narrow range of values would produce the universe we see today. If the “bad” inflation would produce a universe incompatible with life, we could use the anthropic principal to ignore those results. However, that is not the case here. Many of the values of the inflaton field would produce larger temperature variations, which would in turn produce more stars and galaxies. Such a universe would be more conducive to life, not less. In addition, it is not necessary to invode inflation at all to produce a universe like ours. Doing a statistical analysis of the possible initial values of the inflaton field, physicist Roger Penrose found that there are far more possibilities of producing our universe without inflation than with inflation – by a factor of 10¹⁰⁰!

What of the powerful agreement between the predictions of inflation and observation? There is a potential problem there, as well. Those predictions were established in the 1980s when inflationary theory was developed. They may have been made on a naive understanding of the physics involved. One issue is that inflation is eternal – once it begins, it never ends. Certain regions of space may stop inflating, but since those that are inflating are growing at an exponentially larger rate, the non-inflating regions can never “join up” to become the dominant regions. Now, in itself, this is not a problem. The problem lies in the fact that how a region comes out of inflation is inherently random. That randomness can produce universes that look nothing like ours; they could be warped or strongly curved, they could even have fundamentally different physical laws. What's more, there would be an infinite number of such universes. According to Alan Guth, one of the architects of inflationary theory, “In an eternally inflating universe, anything that can happen will happen; in fact, it will happen an infinite number of times.” In such a circumstance, it would be impossible to determine whether our universe is the exception or the rule – you can't do statistics on an infinite set. And with that, the theory loses much of its predictive power, since literally anything can happen.

Is there any way out of this problem? There are some possibilities out there, such as brane theory or some sort of cyclic theory. However more work needs to be done to resolve the issues, and it's not clear how long that willtake.

Next time, the case of the missing galaxies.