How is the Horizon Problem really a problem?

[Ganesh Ujwal]

I always thought the uniformity in the temperature of the CMB was supposed to be expected, since it's a much more probable initial condition for the universe, what I mean in much better words:

Horizon problem isn't really a problem

If we examine from statistical mechanics principles what thermal equilibrium really means, we see that it is the most probable macrostate for a system (in other words, the state with highest entropy). Systems evolve towards thermal equilibrium not because nature has any sort of preference for evening out energy among all degrees of freedom, but simply because having a roughly equal partition of energy among degrees of freedom is OVERWHELMINGLY probable.

For exactly the same reason why it is overwhelmingly probable for a closed system to move toward thermal equilibrium, it is overwhelmingly probable for a completely randomly selected initial condition to be in thermal equilibrium. No causal contact is necessary.

 

 

The only "counter-argument" I could find for that, ironically enough, comes from Jason Lisle (link):

(...) in the early universe, the temperature of the CMB would have been very different at different places in space due to the random nature of the initial conditions.

 

 

But if that "random nature of the initial conditions" is of the same order of magnitude as quantum fluctuations, wouldn't that apply to the early instants of inflation too? If so, how would thermal equilibrium be even possible under such quantum fluctuations during inflation?

Edited December 23, 2014 by Ganesh Ujwal

[Mordred]

The problem stemmed from having to deal with how such a vast region of space had such a fine tuned uniformity. Without inflation that same volume could not have maintained the same uniformity once you consider the mean free path between the particles. Thermal equilibrium requires not only a high temperature. It also requires a sufficient density to allow the reverse reactions to occur.

 

Prior to inflation the temperature and density is sufficient. Then inflation occurs. That sudden volume change would normally cause a sudden cooling. If inflation has multiple waves or perturbations there would have been anistropies crop up. However the slow roll process at the end of inflation caused a significant reheating effectively wiping slate clean of any previous anistropies and previous particles that were not in equilibrium. This makes determing which inflation out of the 70+ inflation models more difficult.

 

The latest Planck dataset favors an inflation model with a single scalar and low kinetic term. However this does not rule out multiscalar models.

http://arxiv.org/pdf/hep-th/0503203.pdf"Particle Physics and Inflationary Cosmology" by Andrei Linde

http://www.wiese.itp.unibe.ch/lectures/universe.pdf:"Particle Physics of the Early universe" by Uwe-Jens Wiese Thermodynamics, Big bang Nucleosynthesis

These articles will help the finer details see chapter 3 of the second one.

http://arxiv.org/abs/1303.3787

 

Here is encyclopedia inflationaris.

Inflationary paradigm after Planck 2013 Allen Guth is one of the authors. He is accredited with the original inflation theory false vacuum. However he was also involved in the slow roll approximation as well as chaotic eternal inflation in his efforts to solve the "run away inflation problem.

http://arxiv.org/abs/1312.7619

The reheating phase applies to your latter question in regards to pre inflationary thermodynamics

Which is also evidence towards the slow roll approximation. You will notice that particular model is used as a measuring standard of the other 70+ model database on the Encyclopedia inflationaris article which is updated every 6 months or so.

PS judging from your previous posts you are an avid physicists in study. Check out my signature and the numerous tools and articles under it. You will definetely find the material and the links handy. Incuding the expansion redshift calculator.

I'm currently working on page two for the cosmology101 site.

http://cosmology101.wikidot.com/articles

PS please please please inform me of any non textbook or non concordance material. I don't want any article not supportive of the educational studies.

Forgive me for sounding scattered. Just got home from a north pole tour. So a little pleasant thanks to a little inducement

[Ganesh Ujwal]

The problem stemmed from having to deal with how such a vast region of space had such a fine tuned uniformity. Without inflation that same volume could not have maintained the same uniformity once you consider the mean free path between the particles. Thermal equilibrium requires not only a high temperature. It also requires a sufficient density to allow the reverse reactions to occur.

 

Prior to inflation the temperature and density is sufficient. Then inflation occurs. That sudden volume change would normally cause a sudden cooling. If inflation has multiple waves or perturbations there would have been anistropies crop up. However the slow roll process at the end of inflation caused a significant reheating effectively wiping slate clean of any previous anistropies and previous particles that were not in equilibrium. This makes determing which inflation out of the 70+ inflation models more difficult.

 

The latest Planck dataset favors an inflation model with a single scalar and low kinetic term. However this does not rule out multiscalar models.

http://arxiv.org/pdf/hep-th/0503203.pdf"Particle Physics and Inflationary Cosmology" by Andrei Linde

http://www.wiese.itp.unibe.ch/lectures/universe.pdf:"Particle Physics of the Early universe" by Uwe-Jens Wiese Thermodynamics, Big bang Nucleosynthesis

These articles will help the finer details see chapter 3 of the second one.

http://arxiv.org/abs/1303.3787

 

 

That doesn't address the main point that the original conditions of the universe would favor uniformity, which already solves the Horizon Problem. No causal contact is necessary to maintain equilibrium if the system is already in equilibrium.

[Mordred]

Ah but was it uniform? What caused inflation? False vacuum for example (the original inflation model) is a process of quantum tunnelling from a high energy region (true vacuum) tunneling to a lower vacuum energy density region(false vacuum). So non uniformity must exist for this process to occur.

 

When precisely did inflation start?

When did it end?

How many e- folds occurred during inflation?

 

We don't have any certainty on any of the above questions. Nor do we know when the matter anti matter assymmetry occured. Nor do we know what caused baryogenesis or leptogenesis

 

 

However this isn't really what the horizon problem about. Let's use wikis description.

 

"The horizon problem is a problem with the standard cosmological model of the Big Bang which was identified in the late 1960s, primarily by Charles Misner. It points out that different regions of the universe have not "contacted" each other because of the great distances between them, but nevertheless they have the same temperature and other physical properties. This should not be possible, given that the transfer of information (or energy, heat, etc.) can occur, at most, at the speed of light.

 

One solution to the horizon problem is the theory of cosmic inflation."

 

So the horizon problem is basically how the universe we see today and at the time of the CMB has the same thermodynamics.

 

Part of the solution is inflation which tells us those regions started in causal connection. The other part is that original volume had uniformity.

Keep in mind we cannot see past the CMB due to the reduced mean free path of photons during the dark ages. So the region Misner was concerned about is our observable universe from the CMB forward.

Or rather the observable portion at the time of the problems development. We didn't have much data on the CMB itself in the 60's

[MigL]

I would say that inflation is the only solution.

If you remove the inflation mechanism, and just wind back the expansion backwards, parts of the universe will not be in causal contact at the time the universe becomes transparent ( CMB appears ).

Without causal contact there is no way to achieve equilibrium and establish uniformity to one part in 10000. So inflation is definitely needed.

 

But, if the original volume was not uniform, because of fluctuations and what-not, it would have quickly become so due to the then existing causal contact. In effect, there is no need for the original volume to be uniform; no matter the initial conditions, uniformity would have resulted regardless.

[Mordred]

I would have to agree any previous anistropies would probably be wiped. After all we have 60+ e-folds resulting in a super cooling . Then this is followed by the reheating phase.