The phase transition of the universe during inflation

Guth thought that If, as the universe cooled, it underwent some kind of phase transition—as occurs, for example, when water freezes to ice or a bar of iron becomes magnetized as it cools—then not only could the Horizon Problem be solved, but also the Flatness Problem (and, for that matter, the Monopole Problem).
If you like to drink really cold beer, you may have had the following experience: you take a cold beer bottle out
of the refrigerator, and when you open it and release the pressure inside the container, suddenly the beer freezes completely, during which it might even crack part of the bottle. This happens because, at high pressure, the preferred lowest energy state of the beer is in liquid form, whereas once the pressure has been released, the preferred lowest energy state of the beer is the solid state. During the phase transition, energy can be released because the lowest energy state in one phase can have lower energy than the lowest energy state in the other phase. When such energy is released, it is referred to as “latent heat.”
Guth realized that, as the universe itself cooled with the Big Bang expansion, the configuration of matter and radiation in the expanding universe might have gotten “stuck” in some meta-stable state for a while until ultimately, as the universe cooled further, this configuration then suddenly underwent a phase transition to the energetically preferred ground state of matter and radiation. The energy stored in the “false vacuum” configuration of the universe before the phase transition completed—the “latent heat” of the universe, if you will—could dramatically affect the expansion of the universe during the period before the transition.

It seems like he's saying that before inflation kicked in around 10^-36 or 10^-34 I forget which that the universe, I'm guessing from 10^-43 - 10^-36 was in some sort of false vacuum state, analogous to the way matter changes phase from gas to liquid. Is that right?

It's not that the universe itself was in this state - the field that drives inflation, the inflaton field, was in a false vacuum. Essentially, this field would have been trapped in a high density false vacuum, which would have produced an enormous negative pressure. In general relativity, negative pressures can drive the metric expansion of space.

Guth's original model of inflation held that, after the universe inflated exponentially for a short period of time, regions of the inflaton field would decay, through a process called quantum tunneling, into true vacuum 'bubbles'. These bubbles would collide, putting the whole universe in a true vacuum state, ending inflation. Guth actually realized that under his model of inflation, it tended to last forever, as the bubbles never were able to reach each other. He called this 'eternal inflation', which holds that the true vacuum bubbles never collide, and give rise to an inflationary multiverse.

However, Guth's 'old inflation' was replaced by new inflation, called slow-roll inflation. In this model, the inflaton field slowly rolls down a potential energy 'hill', until the inflaton field reaches a true vacuum, and decays into a hot bath of radiation.

It's not that the universe itself was in this state - the field that drives inflation, the inflaton field, was in a false vacuum.

Does anyone know what a false vacuum is like? For some reason or other I get the feeling that the false vacuum is E and a true vacuum is mc2

Guth's original model of inflation held that, after the universe inflated exponentially for a short period of time, regions of the inflaton field would decay, through a process called quantum tunneling, into true vacuum 'bubbles'.

what type of matter is in the bubbles?

In this model, the inflaton field slowly rolls down a potential energy 'hill', until the inflaton field reaches a true vacuum, and decays into a hot bath of radiation.

Then when the radiation cools to maybe 8000 k matter begins to form, right?

Does anyone know what a false vacuum is like? For some reason or other I get the feeling that the false vacuum is E and a true vacuum is mc2

A false vacuum is just a local minimum - rather than a true vacuum, which is the global minimum. False vacuums are unstable, as fields will, via instanton processes (e.g. quantum tunneling) tend to decay into a true vacuum, a desirable, low energy state.

what type of matter is in the bubbles?

They aren't literally bubbles (that's why I used quotations), they are regions in a true vacuum that are expanding at a normal rate, and not inflating. They're filled with a decayed inflaton field, which translations to a bath of radiation.

Then when the radiation cools to maybe 8000 k matter begins to form, right?

I'm not sure of the exact temperature, but that is the idea, yes. Once the radiation cooled, particle pair production created matter and anti matter. Somehow, matter managed to outnumber anti-matter by one part in a billion. After ~70,000 years, matter began to dominate radiation.