# Why inflation (again)?

1. Sep 25, 2014

### CKH

There are several threads in the forum on this subject, but I see no satisfying reason that we need inflation.

The explanation I typically see is that assuming homogeneity of early universe as an initial condition presents a "fine tuning" problem. Why so much weight on that problem? One could as well argue that the approach to infinite density of the entire universe at a precise finite time in the past is also a fine tuning problem.

So I'm wondering if there are other issues that force us toward inflation. E.g. is it possible that, even if the start was uniform, this uniformity would quickly deteriorate (perhaps due to random quantum fluctuations or some sort of early clumping on small scales)?

I am familiar with the argument that no matter how close you get to the BB event, there are neighboring sections of the universe that are not in causal contact (because the expansion is too fast). But so what? The beginning is beyond our ken so why not just assume uniformity, if that fixes the problem?

Even if we assume initial non-uniformity, how can we possibly know the magnitude of this non-uniformity? Nevertheless, theorists seem to be estimating how many e-folds of inflation are needed to reach the current CMB uniformity. How can they do that with unknown initial conditions?

Inflation theory appears to be very important to cosmologist. All sorts of mechanisms have been proposed. There is a lot of debate about inflation (not so much about whether it occurred, but how it occurred). Papers concerning inflation are published daily. Yet it's not a very appealing theory because it forces us to give up a simple account of the BB and look for a much more complex account involving unknown physics.

This leads me to believe that there is indeed a real need for inflation beyond avoidance of special initial conditions. So my question is what is this need, if there is one?

2. Sep 25, 2014

### cristo

Staff Emeritus
You touched on one reason that we need inflation, but another is the so-called "horizon problem". We see that the temperature of the CMB is the same on opposite patches of the sky. If the universe had been expanding uniformly for its entire history, then there is no way that these two patches were in causal contact, and therefore no physical process through which the temperature could be the same. Including a period of inflation, where the universe accelerated in its expansion, ensure that these two regions could have been in causal contact in the past, and therefore can share the same temperature.

Additionally, what inflation gives you that it wasn't designed to do, is fluctuations around a homogeneous and isotropic background. Quantum fluctuations of the field driving inflation are made classical during inflation by being pushed outside the horizon. The spectrum of the fluctuations matches the observed spectrum very well.

3. Sep 25, 2014

### Ich

That's not the same problem. Given homogeneity, the Big Bang is everywhere at the same time in the past. Deviations from homogeneity would shift this time a little bit when you calculate backwards, with overdense regions collapsing a bit earlier. No problem there, the singularity theorems make sure that - no inflation presumed - everything started from a singularity, i.e. a hot, dense state.

A real problem is the flatness problem. Calculating backwards, any deviation now must have been much, much smaller in the past. Ridiculously small, in fact, which also begs an explanation.

4. Sep 25, 2014

### George Jones

Staff Emeritus
For opinions on the stuff in cristo's post, see this post:

Last edited: Sep 25, 2014
5. Sep 25, 2014

### CKH

I'm not understanding this claim. Aside from an argument claiming we know what the deviations were in the early universe, why should perturbations (deviations) get smaller in magnitude closer to the singularity? Calculating backwards everything must have been much, much denser, ridiculously dense, right? Suppose we look at the CMB perturbations and ask how they relate to the initial perturbations. Isn't it a simple scaling principle? The magnitude of the perturbations decrease with expansion because the perturbations are stretched as the density decreases. Imagine stretching a sheet of metal with bumps on it. As you stretch, the bumps get shallower and the density (thickness) gets lower.

Suppose that at the origin of the CMB, the magnitude of perturbations was P and the spatial density of the perturbations was D. In a uniform expansion, the ratio P/D remains constant. If p is the magnitude of perturbations at time t and d is the density of the universe at time t, then you have P/D = p/d. I don't see a fine tuning problem. Magnitude versus density remains constant. So if it is 1 part in 10,000 now, it could have been close to that as you approach the singularity.

OK but if inflation is required, then those QM fluctuations must have been far too small (about 50 orders of magnitude too small in size) to serve as the origin of large scale fluctuations in the CMB in a uniform expansion. So we just decide that a super expansion must have occurred to make that explanation work? How natural or plausible is that? This seems a bizarre leap to make an hypothesis work.

In one argument the initial perturbations may have been too large to account for current smoothness (and in the other argument we know the size (and magnitude) of the early perturbations from QM somehow, but they are far too small in size to account for the CMB. The arguments seem to oppose one another. So it seems from the above quotation that the first argument is old and has been abandoned, but the second argument is mainstream.

I think my question has been answered: inflation is required to support the hypothesis that quantum fluctuations account for the CMB fluctuations.

Is there anything else involved? If not then I wonder what is so compelling about the QM hypothesis that we need to hypothesize something outside of SM, QM and GR to support it.

Also, it seems that we have a separate theory of the CMB that accounts for perturbations caused by the combined effects of baryonic matter and DM (the BAO). I suppose the inflated QM fluctuations are the perturbations that cause the BAO?

6. Sep 26, 2014

### bapowell

It is a relatively easy exercise to demonstrate that perturbations in the global geometry of the universe grow with time. Any deviations from flatness that existed around the time of the big bang would have grown by the present time to give a universe either observably open or closed. The fact that the present-day universe is flat to within 1% means that it needed to be much flatter (something around a factor of $10^60$ flatter) at the time of the big bang. That is the flatness problem. Yes, you can assume initial flatness and initial homogeneity but these are highly symmetric and specialized arrangements. A more conservative view is to *not* make these assumptions because as you say -- the nature of the universe at the earliest times is beyond our ken.
What do you mean by small? Amplitude? 50 orders of magnitude smaller than what?
No, this is backwards. Inflation was conceived to address the flatness, horizon, and monopole problems of the classic big bang cosmology. The fact that quantum fluctuations can be converted to classical perturbations in an inflationary spacetime was a discovery made subsequently. Nobody supposed that CMB anisotropies were of quantum origin until inflation made this possibility manifest.
Involved in what...the motivation for inflation? The motivation includes a resolution of the three classic problems just mentioned and inflation has built into it an elegant mechanism for the generation of large scale structure that has been well-corroborated by cosmological observations. There is nothing "outside" SM, QM, and GR needed. Inflation is based on quantum field theory in curved spacetime -- all that is required for the most basic models is the existence of scalar fields in nature. The recent discovery of the Higgs might have just cleared this as a hurdle.
Yes.

7. Sep 26, 2014

### CKH

8. Sep 26, 2014

### bapowell

I am unable to quote parts your message because of how you posted...something weird going on there. I will try to answer your questions.

1) Yes, this is easy to show using GR. Start with the density parameter $\Omega - 1 = \frac{k}{a^2H^2}$ and take the time derivative of $|\Omega - 1|$. It is positive (evolving away from flatness) unless $\ddot{a} > 0$, that is, unless the expansion is accelerating.

2) Yes, the quantum fluctuations are stretched to superhorizon scales by the inflating background. As far as the actual reasoning behind the proposal, there really isn't any -- it is a consequence of the theory. Keep in mind that while it was known prior to the advent of inflation that a nearly scale invariant spectrum of initial density perturbations was needed to describe galaxy distributions, it was not suspected (even dreamed, I would venture) that these perturbations would be correlated across superhorizon scales. These seemingly "acausal" correlations are a prediction of inflation and have been observed in the CMB.

3) Curvature does not require non-uniform density. The global curvature of the universe -- the curvature that is the basis of the flatness problem -- is not dependent on any sort of inhomogeneity. There are three unique geometries appropriate to homonegeneous spaces: spherical, hyperbolic, and flat. If the universe is spherical or hyperbolic, it becomes more so as it evolves under decelerated expansion.

4) GR and QM play reasonably well together within certain limits. As you say, we should be wary so-called semiclassical gravity in regions of high density. However, inflation is generally expected to occur at or about the GUT scale, several orders of magnitude below the Planck scale where we might expect the forced marriage of GR and QM to break apart.

There is a Higgs model of inflation, but I was not referring to any specific model. Just that generic inflation models employ scalar fields; prior to the discover of the Higgs (which may have nothing directly to do with inflation), we had no reason to believe that fundamental scalar fields even existed in nature. Now we know they do, and to me this is an important proof of concept that inflation, as currently modeled within the context of scalar fields, is possible.

5) Indeed, it *is* ironic that the origin of structure -- of tiny inhomogeneities -- is the consequence of a mechanism expected to render a totally smooth universe. Of course, classically the inflationary universe is smooth; it's the quantum effects that make it lumpy.

I have to run now, but I will be back later to answer your question about how we figure out the required number of efolds.

9. Sep 26, 2014

### CKH

Sorry. Something wrong in my quotes, they were rebooting when I tried to edit the post and now it won't let me edit it. Why is that?

By superhorizon scales, do you mean the horizon gets larger during expansion, so that we can now see in the CMB parts of the universe that could not have been in causal contact earlier? I guess regions can come back into contact because expansion slows due to gravity while c remains constant?

You are saying that there is a unique family of geometries that are consistent with homogeneity in GR. All are equally possible when we observe homogeneity. But somehow we can also measure the actual curvature (how?) and we find it smack on the flat one.

We think this is an odd coincidence since expansion increases any curvature dramatically. So now we suggest this solution. Suppose you took a tiny piece of the early universe so small that it is very flat (even though the early universe is somewhat wrinkled). If we abruptly blow up that piece by 10^60 it will remain flat enough to account for current flatness. Is there something about inflation that prevents the expected dramatic increase in curvature due to expansion? Or are you saying that a tiny enough piece will be flat enough to expand without the expansion creating more curvature than we can measure? In the later case, there is not enough time for a uniform expansion to expand that much, hence we invoke inflation?

It seems that how much inflation we need depends on how wrinkled the universe was. How can we possibly know?

OK.

Some folks don't think the Higgs field will work, but why not another I suppose.

10. Sep 27, 2014

### timmdeeg

CKH, perhaps this article is of help. It is quite easy to see why any flatness deviation in the planck era is flattened out after inflation, but instead grows dramatically in case of 'normal' (non-exponential) expansion. So, in the latter case the chance to observe the tiny deviation from flatness today would imply fine tuning then in the order of one in 1060.

Last edited by a moderator: Sep 27, 2014
11. Sep 27, 2014

### CKH

timmdeeg,

Thanks, that article is helpful. I learned that the geometry is not only dependent on homogeneity but also density. Apparently something related to QM and the Planck scale allows us to calculate the number of e-folds needed in an inflation hypothesis. I won't even ask how that works. It is also now clear that the inflation hypothesis dramatically affects the density of the universe. The "inflation field" seems to continually pump energy into the universe to keep the density constant as it expands by a factor of roughly 10^60. This changes the way in which curvature is affected by expansion.

While the hypothesis may solve the fine tuning problems and the monopole problem (which arises in some other speculative theories), it seems rather arbitrary and thus contrived to remove these fine tuning problems from the main theory (BBT). One might instead ask, is there something wrong with BBT itself? The prevailing scientific opinion appears to be that expansion is undeniable in the face of observational evidence. So, cosmologist are forced to either dismiss the fine tuning problem as a real problem or find another solution like the anthropomorphic principle or inflation. Perhaps a bounce theory could also solve the problem while removing the singularity as well.

12. Sep 28, 2014

### timmdeeg

There are other ideas tempting to avoid the BB, e.g. http://www.mnn.com/earth-matters/sp...ck-hole-in-a-higher-dimensional#ixzz39vAvVeP5
There are also bounce theories.
I am not too optimistic that the mystery related to the origin of the universe (means, how came this initial hot and dense state into existence?) will ever be resolved by a physical theory.

Last edited: Sep 28, 2014
13. Sep 28, 2014

### Chronos

CKH, it appears you presume we can 'observe' evidence of quantum fluctuations that predates the CMB. That is, at least at present, impossible.

14. Sep 28, 2014

### CKH

Nor am I. The presumption of an origin is problematic for any physical theory of causes. Physics may be able to describe an eternal universe, but not one with an origin.

Perhaps our need for an origin is a physiological issue rather than real. People argue that there must be a first cause, but one can still ask the cause of that first cause leading to an infinite regress. If there is a beginning of the Universe, then it popped into existence without any cause and thus the origin is non-physical. No explanation is possible for an origin. Is that somehow better than an eternal universe that has no origin in the past?

15. Sep 28, 2014

### bapowell

I would not consider the earlier implementations of inflation too contrived. While studying the properties of GUT fields in the early universe, it is inevitable that thermal effects "restore" the GUT symmetries so that the GUT Higgs fields exist in a false vacuum for some time. The result is a well understood phase transition studied mostly in condensed matter physics -- supercooling. In the cosmological setting, as the inflaton sits trapped in the false vacuum, the universe undergoes supercooling in the form of exponential expansion. The inflationary mechanism is quite analogous to the supercooling of ordinary liquid beyond its freezing point. Inflation ends when the phase transition finally completes, and the field decays to the true vacuum releasing its energy (analogous to the latent heat of the ordinary phase transition) to reheat the universe.

The possibility of inflation in the early universe is therefore not contrived, as in "put in by hand". As long as we agree that there are scalar fields associated with gauge symmetries as part of our particle physics models, then once we place these fields into the universe the possibility of inflation exists. Now, there are of course additional questions about how difficult it might be for the inflaton energy to dominate a sufficiently homogeneous region of the universe to get inflation started. It is also apparent that the inflaton potential function needs to have a rather special form -- it must be very flat in the region of the metastable point in order to support sufficient inflation and to produce the appropriate power spectra. These are real difficulties that make the particular kind of inflation that occurred in our universe maybe look contrived (or tuned, or unnatural) on the basis of our current understanding, but the concept of inflation as a phase transition in the early universe is quite natural, if not inevitable.

16. Sep 28, 2014

### CKH

I'm not sure where you got that impression. No I don't. The CMB is a sort of curtain that we cannot see through, although BICEP2 experimenters are making some claims.

17. Sep 29, 2014

### CKH

bapowell,

That's interesting, but to me inflation is speculative. Evidence is based on need, unconfirmed theories and the mere possibility that an inflation field could exist. Papers, with different twists on inflation theory, are published almost daily. As you mentioned, inflation may have come full circle, itself requiring fine tuning.

Cosmologists are exploring possibilities in a very dark territory, more so than other sciences. They push beyond the limits of tested theory and direct observations, but perhaps that's all they can do. IMO, it's unfortunate that these speculations are presented to the lay public as fact in the popular press.

Do you think future experiments with the LHC will have any bearing on inflation or are the energies far too low? We are in some suspense now about Supersymmetry (unconfirmed for over 40 years) which is relevant to potential DM particles.

18. Sep 29, 2014

### julcab12

.. Inflation, bounce, etc. are proposed dynamics that are able to explain a majority of our data's, observations and experiments with certain consistencies about our universe. Inflation is more than speculation and it is an attractive postulate that can possibly explain flatness, horizon paradox, spectrum of density fluctuations and the problem in the classical version of the friedmann Universe---expansion was always decelerated with time.

19. Sep 29, 2014

### bapowell

Will you feel differently if the BICEP2 result pans out?

It's certainly possible but my feeling is that the inflationary scale is closer to the GUT scale.

20. Sep 29, 2014

### CKH

I'm not knowledgeable enough to comment. The idea is that patterns of polarization imply gravitational waves expected from models of inflation. Being naive, perhaps I would still wonder if that is the only possible cause, particularly if the detection is not robust. Even gravitational waves have yet to be detected aside from the inferences from orbits of pulsars. The BICEP2 experimenters obviously felt that they had concrete evidence of inflation, but they apparently made an error in the treatment of backgrounds so the issue isn't settled yet. The problem with clarity is that we are working in an area where experiment is not possible.

Cosmology is really difficult. The only evidence we have is observational and there are many confounding factors to sort out.

OK, but the supersymmetry implications will be interesting. Of course there are variations on the theory so it probably cannot be ruled out, at these energy levels.