Why do Quantum Fluctuations need Inflation?

[Dr. Strange]

The general logic of Inflation is that some field popped into existence just long enough to flatten out the universe, then disappeared again. Before the field, the universe had tiny fluctuations in the plasma. Inflation blew these up from the size of an atom to the size of a grapefruit (If I understand the scale correctly). What I don't understand is: why was inflation needed? Why wouldn't these fluctuations grow in a normally expanding Big Bang scenario?

 

[PeterDonis]

The general logic of Inflation is that some field popped into existence just long enough to flatten out the universe, then disappeared again.

No. The inflaton field does not "pop into existence and disappear". It is always present; all that changes is its state. Most of the inflation models under consideration today, as I understand it, are "eternal inflation" models, in which the inflaton field has a large energy density into the infinite past; our universe is simply a bubble in which the field underwent a phase transition from a "false vacuum" state with a large energy density to a "true vacuum" state with a very small (or zero) energy density; the transition transfers the original large energy density to ordinary matter and radiation, which are left in a hot, dense, rapidly expanding state (the "Big Bang").

 

[Dr. Strange]

No. The inflaton field does not "pop into existence and disappear". It is always present; all that changes is its state. Most of the inflation models under consideration today, as I understand it, are "eternal inflation" models, in which the inflaton field has a large energy density into the infinite past; our universe is simply a bubble in which the field underwent a phase transition from a "false vacuum" state with a large energy density to a "true vacuum" state with a very small (or zero) energy density; the transition transfers the original large energy density to ordinary matter and radiation, which are left in a hot, dense, rapidly expanding state (the "Big Bang").

Thank you for the clarification. It would be great if you could answer the original question, though.

 

[PeterDonis]

Before the field, the universe had tiny fluctuations in the plasma.

No. The fluctuations were in the inflaton field itself. During inflation, there was no "plasma"; the Standard Model quantum fields (the ones associated with ordinary matter and radiation) were all in vacuum states.

Why wouldn't these fluctuations grow in a normally expanding Big Bang scenario?

They would, but not fast enough to be correlated in all parts of the sky we observe today. Without inflation, we would expect the temperature we observe in, for example, the CMB, to vary much more from one part of sky to another than it actually does, because the fluctuations in different parts of the sky we observe would be uncorrelated. The fact that the temperature varies so little (about 1 part in 100,000 for the CMB) is evidence that every part of the sky we see must have been causally connected in the past. A normally expanding Big Bang can't produce causal connections over that wide a range in only 13.7 billion years.

 

[Dr. Strange]

Let me restate this to see if I understand. Without Inflation, the fluctuations in the field (whatever field we'd have without Inflation) would have grown to cosmic proportions, but because there was no way to exchange information across horizons, we would expect them to grow independently and thus have a much larger ΔT/T range than what we see today in the CMB. Is that the general idea? Inflation explains why all the anisotropies are so uniform across the sky, not how the actual fluctuations grew to cosmic proportions?

 

[PeterDonis]

Is that the general idea? Inflation explains why all the anisotropies are so uniform across the sky, not how the actual fluctuations grew to cosmic proportions?

Actually, inflation is needed to an extent for the latter as well--at least, for the fluctuations to grow into what we see today in only 13.7 billion years. Ordinary expansion without inflation would not have magnified them to the same extent in that time; it needs a "jump start" of some period of inflation.

 

[Dr. Strange]

Actually, inflation is needed to an extent for the latter as well--at least, for the fluctuations to grow into what we see today in only 13.7 billion years. Ordinary expansion without inflation would not have magnified them to the same extent in that time; it needs a "jump start" of some period of inflation.

As I understand it, as long as you have dark matter and the overdensities represented by CMB, you can get the matter distribution we see in the universe today. I'm not sure I understand how inflation effects anything after CMB. Could you explain in more detail?

 

[George Jones]

As I understand it, as long as you have dark matter and the overdensities represented by CMB, you can get the matter distribution we see in the universe today. I'm not sure I understand how inflation effects anything after CMB. Could you explain in more detail?

What Peter wrote does not contradict this. From where do the anisotropies in the CMB come? According to recent grad/research level texts, inflation, via quantum fluctuations, gives the most plausible mechanism for the the generation of perturbations:

The most exciting aspect of the inflationary cosmological theories described in chapter 4 is that they provide a natural quantum mechanical mechanism for the origin of the cosmological fluctuations observed in the cosmic microwave background and in the large scale structure of matter, and that may in the future be observed in gravitational waves.

In the modern view, by far the most important function of inflation is to generate the primordial curvature perturbation ... It may generate other primordial perturbations too, including the isocurvature and tensor perturbations ... However, the historical motivation for inflation was rather different, and arose largely on more philosophical grounds concerning the question of whether the initial conditions required for the unperturbed Big Bang seem likely or not.

Originally inflationary scenarios were suggested as a pseudo-solution to certain pseudo-problems; these are only of historical interest today and the only reason to take the possibility of an inflationary phase in the early universe seriously is because it provides a mechanism for generation the initial perturbations.

 

[PeterDonis]

as long as you have dark matter and the overdensities represented by CMB

As long as you have dark matter and the overdensities represented by the CMB, with the magnitudes they had at the end of inflation. But a Big Bang model without inflation won't produce those magnitudes in the short time that would be required--at least, that's our current best understanding.

 

[Dr. Strange]

Yes, thank you. I'm trying to zero in on what problems, exactly, are solved by Inflation. That's why I needed the clarification. So let me try it again. You seem to be saying that tiny fluctuations in a normal quantum field would grow into densities that we see in the CMB (with much larger variations because they were not in causal contact), but it would have taken (guessing here) billions of years. Inflation solves the problem in that those fluctuations grow to the proper size (that we see in the CMB) in roughly 300,000 years.

 

[PeterDonis]

You seem to be saying that tiny fluctuations in a normal quantum field would grow into densities that we see in the CMB (with much larger variations because they were not in causal contact), but it would have taken (guessing here) billions of years. Inflation solves the problem in that those fluctuations grow to the proper size (that we see in the CMB) in roughly 300,000 years.

Not quite. From the end of inflation to the time of CMB production, roughly 300,000 years, we have normal (non-inflationary) expansion, so it is the same in both models (with and without inflation). The problem is the state at the start of that period--i.e., at the time referred to, in inflationary models, as "the end of inflation". At that time, we already have quantum fluctuations magnified to a certain point--enough to produce, after roughly 300,000 years of non-inflationary expansion, the fluctuations in the CMB. But without inflation, it would not be possible to get quantum fluctuations magnified to that point in such a short time. More precisely: in a non-inflationary model, the universe would only take about $10^{-32}$ seconds to get from the Planck scale to the temperature it was at the "end of inflation" time; but a non-inflationary model cannot magnify quantum fluctuations in such a short time to the magnitude they must have been at that point in time in order to produce the necessary fluctuations in the CMB 300,000 years later.

 

[Dr. Strange]

I'm trying to visualize this, but something is giving me trouble. At the end of inflation, were all the points of space in causal contact with each other?

 

[PeterDonis]

At the end of inflation, were all the points of space in causal contact with each other?

Not quite, because according to our best current models, the universe is spatially infinite. But what we now see as our observable universe was all in causal contact at the end of inflation--more than that, it was all in thermal equilibrium at the end of inflation, except for the quantum fluctuations that had been magnified by inflation.

 

[Dr. Strange]

Were all parts of the universe in causal contact before inflation?

 

[PeterDonis]

Were all parts of the universe in causal contact before inflation?

There might not have been any "before inflation"; in the "eternal inflation" models (which IIRC are the current front-runners), inflation extends into the infinite past, from the standpoint of our universe.

In models where there is a "before inflation", no, all parts of the universe (by which I assume you mean the observable universe--i.e., the region which ultimately expanded into what is our observable universe today) were not in causal contact before inflation.