Does Inflation have a Homogeneity Problem?

Inflation is proposed as a solution to the horizon or homogeneity problem.  The problem is the cosmic microwave background (CMB) is extremely homogenous, pretty much the same no matter which direction you look despite the areas we are looking at not having been in anything near close proximity since 300,000 years after the Big Bang about 13.77 billion years ago.  That is to say, these regions that we are looking at are not “causally related”.

 

The generally accepted solution to the problem is that from about 10^-36s after the Big Bang, during a period of about 10^-32s, the universe expanded by a factor of at least 10²⁶.  (These are folds of expansion, so I am reading it as the radius is increased by that factor.  If they are talking about volume, then the radius increases by about 10⁹, but the sizes generally talked about imply radius, for example Guth estimates that universe could have been about marble size after inflation starting from one billionth the size of a proton and this is consistent with talking about the radius.)

 

Recall that nothing travels faster than light (in space) which is part of the reason that we have the horizon problem with causally independent patches of the sky looking the same.  But if space is expanding as fast as proposed for the inflationary epoch, then the pre-CMB isn’t going to be causally related then either - so how was the slowdown of the exponential inflationary expansion orchestrated?  It would have to be exquisitely fine-tuned so that the smoothness we see today is maintained or some bits of space would be expanding slightly faster than others during the slowdown.  It’s not like there’s a mechanism that can operate on the entire universe simultaneously because there is no simultaneity per Relativity.  Even if there were a notional code to expand this much for this long and no longer, there’s a problem in assuming that all the notional clocks would remain precisely in sync.

 

Perhaps there’s an answer to this, but it’s not immediately obvious to me.

 

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I posted a version of this question to Reddit at r/AskPhysics and got a couple of interesting responses.

 

The first, from Aseyhe, pointed at the graceful exit problem and the models designed to avoid it.  I still have a problem with the array of (notional) clocks all ticking in sync while the inflaton field evolves to a point where inflation stops, simultaneously, everywhere (in our universe, but not in the greater “inflaverse”, a term that I can’t find anywhere else, but by which I mean the portion of an eternal inflation universe is still evolving, retaining the term “universe” to refer more easily to what we might otherwise need to refer to as “our universe”).  Any deviation from perfect simultaneity of the deceleration process, given the rate of inflation (equivalent to about H=10⁶⁰), would have led to gaping holes in the CMB.  The poster u/Aseyhe was confident that the (notional) clocks would tick in unison because they would not deviate from the state that they were in “before inflation scattered them”.  I can understand that, but the CMB is not perfectly homogenous and isotropic, there’s reason to believe that there could have been zones in which time would have been progressing slightly differently due to admittedly miniscule irregularities in the distribution of mass-energy.  Look at the CMB to see what I mean (from ESA where you can download a more detailed image):

The accompanying text reads:

 

The anisotropies of the Cosmic microwave background (CMB) as observed by Planck. The CMB is a snapshot of the oldest light in our Universe, imprinted on the sky when the Universe was just 380 000 years old. It shows tiny temperature fluctuations that correspond to regions of slightly different densities, representing the seeds of all future structure: the stars and galaxies of today.

 

Now, it’s true that the CMB is from 380 thousand years after inflation is thought to have ended, but to avoid an inhomogenous CMB the homogeneity and istropy at the beginning of inflation would not just have to have been “pretty good”, it would have to have been perfect.  And it’s that that I struggle with.  I do understand that we are talking about 10^-36s after the Big Bang (although that concept once we bring the inflaverse into the discussion seems a bit rubbery), but recall that 10^-36s is in the order of about a billion units of Planck time.  A billion iterations of anything would seem enough to introduce slight inhomogeneities.

 

Then there was turnpikelad, who talked about the end of inflation being the same thing as false vacuum collapse.  I think “similar to” or “driven by” would be better than “the same thing as” since false vacuum decay (rather than collapse) is the sort of thing behind potential ends of the universe, such as proton decay (and eventual heat death).  It’s also thought, by some, to be the driver behind cosmic inflation, which would align better with what turnpikelad seemed to be saying.

 

Anyway, the intriguing notion raised by turnpikelad was that “the inflaton field can collapse at any point at any time” and “(that) collapse spreads from that point in a perfectly spherical bubble at the speed of light”.  So a universe expanding with the speed of light, one which, after a period of 13.77 billion years would have a radius of 13.77 billion light years and, if the equation of state parameter w=-1/3, would have a Hubble parameter of about H=71km/s/Mpc and, if flat, would have a density equal to the critical density, which is the density that we appear to have.  Like our universe.

 

It's not precisely the universe that I imagined at Imagine a Universe, but it’s another way to get to what we appear to have.  And I don’t see that it’s impossible to have a universe condensing from the inflaverse that spouts off into two equal but opposite time directions.  It’s even possible that the mirrored universes of the CPT symmetry model of Boyle, Finn and Turok might be compatible with being spawned from an inflaverse.