Ranku said:
The false vacuum of the inflationary universe is described as a 'peculiar state of matter'. We know that matter density in the big bang universe dilutes as ρM ∝ a-3. Is it possible to assign a dilution rate to the 'peculiar state of matter' of the false vacuum as well?
One problem here is that there are two completely different definitions of "matter" at work.
One is the classical definition extended to cosmology: matter is stuff with mass. In this cosmology case, this is extended a bit to mean "stuff with mass that has low temperature" (low temperature in this case means most of its energy is mass energy: at high temperature, most of the energy is kinetic energy, such that high-temperature matter behaves like radiation).
Another definition of matter that can be used stems from quantum field theory: it is possible to consider matter to be
any quantum field. With that definition of matter, electrons are matter, but so are photons and gluons. It makes a degree of sense there because all quantum fields behave in similar ways. There are differences, but it's not unreasonable to think of them all as belonging to one category of thing with lots of sub-categories. In this case, the inflaton, the quantum field that drives inflation, is considered matter just because it's a quantum field. But it's properties are quite alien to anything we experience as matter.
For driving the expansion, the quantum field that drives inflation
does decrease in energy density over time. But it only does so slowly. They way it does this is that the inflaton field is stuck, early-on, in a high-energy state. It tends to move to a lower energy state over time, but the rapid expansion of the universe during inflation actually puts the brakes on that process, so that even though its energy density falls, the rapid expansion keeps it from falling too quickly. In fact, its energy density decreases slowly, it decreases slowly enough that the expansion of the universe is
approximately exponential.
Side note: there's also a third definition of matter that is sometimes used: fermions and things made of fermions are matter, while fundamental bosons aren't, but I won't go into that here, as it's a bit off-topic.
Finally, on the point about a false vacuum, that's actually a different situation. The energy density of a false vacuum is actually constant, until it decays. The inflaton field drops in energy because it's moving towards a local energy minimum. The false vacuum is at a local energy minimum, so it just sits there. But it's a "false" vacuum because there are other ways to configure the vacuum that are lower in energy: it's just that there's no smooth way to get from here to there. So the false vacuum sits where it is with a constant energy density right up until there's a quantum tunneling event which causes it to decay. Then the universe is destroyed.
