How is the horizon problem really a problem?

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