# How is the horizon problem really a problem?

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. I finally found someone explaining what I mean in much better words (link):

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?

• The problem is that the early universe is not in thermodynamic equilibrium. Assuming the predictions of ordinary GR, there is not enough time for it to settle into an equilibrium state before the expansion has "frozen" the temperature difference. The problem with this can be solved in a number of ways, one of which is inflation, which basically stretches "the lumps in the dough" so thin that they look homogeneous, or one can assume that the initial expansion was much slower than GR predicts, or that the universe was much larger and pre-mixed etc.. – CuriousOne Dec 16 '14 at 4:14
• @CuriousOne You're just stating the basic definition of the Horizon Problem. That's not really my question. – Wood Dec 16 '14 at 7:00
• I gave you three or four possible solutions... besides pointing out that the problem only occurs IF GR is assumed to be valid at that early era, which I personally would not assume. If anything, this could be the first clear hint that GR is not the correct theory. If I am not mistaken, the problem is not present in Einstein-Cartan theory (i.e. GR with torsion), and that's a totally straight forward extension of GR. – CuriousOne Dec 16 '14 at 7:23
• @CuriousOne It didn't "get into equilibrium", it always was in equilibrium. A "miraculous assumption" would be to think otherwise, since that would be far more unlikely. – Wood Dec 23 '14 at 10:53
• @Wood Don't worry, I at least understand your concern. But I've searched for years without finding a satisfactory answer, instead just seeing the same unjustified dogma repeated over and over. If you don't get a good answer over the next few days, feel free to ping me, since I would probably put my own bounty on the question then. – user10851 Dec 26 '14 at 23:42

I’m not sure I fully understand the question but I’ll try. The “curious one” says that if the initial condition is picked at random then it should be a state of thermal equilibrium (maximum entropy) since the overwhelming majority of states look equilibrium-like. Now there has to be something wrong with that in the cosmological context. States of thermal equilibrium are static and the world is manifestly not static.

What statistical mechanics actually says is that for a fixed total energy most states look like thermal equilibrium at a temperature that depends on the total energy. In other words, for a given energy most states maximize the entropy. If we don’t constrain the energy then the state of maximum entropy has infinite energy and is not really a state. Even more to the point, the idea of energy is very confusing in general relativity. In a cosmological setting the total energy is always zero. So the whole framework of statistical mechanics and maximum-entropy states is not well defined. To put it bluntly there is no theory of the initial state. That’s the problem.

What inflation does is it makes the later history very insensitive to the initial state. Whatever theory for the initial state is put on the table, inflation will wipe out its memory. The result of inflation is a “fixed point” or “attractor” which means a particular behavior that a very wide class of initial conditions will result in.

Leonard Susskind

• I'll repeat my very basic issue with this line of reasoning. At $t=0$, the universe was causally connected. Every point in the universe had the same temperature as every other point. At $t=0+\delta$, what physical process causes those points to have a different temperature from the point immediately adjacent to it? – user32023 Mar 22 at 13:28

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. – Wood Dec 26 '14 at 5:16