How fast was the universe expanding during the inflationary period?

Question

Compared to how fast it is expanding in the post-inflationary period (now)

Answer 1

There is no proven theory to describe inflation, in fact at the moment we can't even be sure what caused it, so you'll appreciate that any figures for the rate and duration of the inflationary period will be approximate. Having said that, I think it's generally accepted that during the inflationary period the universe was doubling in size about every $10^{-35}$ seconds. See Inflation factor and doubling time for more info on this.

We need to be a bit careful about what we mean by "doubling in size". The universe is probably infinite, in which case it has always been infinite, so it doesn't make sense to talk about the size of the universe. What we can say is that if you take two non-interacting test masses and measure the distance between them, then this distance doubles every $10^{-35}$ seconds. You could get even fussier and say that this only applies to distances measured in the comoving co-ordinates.

Anyhow, at present the universe is growing far, far more slowly than during inflation. The current rate of expansion is described by Hubble's constant. The universe is currently taking about $10^{18}$ seconds to double it's size so the expansion is about $10^{53}$ times slower.

The future rate of expansion is unlikely to get anywhere near the rate during inflation, but we're not entirely sure how the future expansion is going to go because we don't understand dark energy. There are theories that suggest the expansion rate will increase until it becomes infinite, so it would actually become greater than inflation. This theory is known as the Big Rip. I think it's fair to say that most physicists regard this as unlikely.