Inflationary_theory. Why did it slow?

The most widely accepted answer is that the universe got briefly 'stuck' in a false vacuum that generated negative pressure at all points of space-time. According to General Relativity, negative pressure will create a repulsive gravity that causes space-time to inflate. This all happened in a fraction of a second before the universe dropped out of the false vacuum into our current vacuum at which point the negative pressure dissipated (or at least dropped to a much lower level). At this point normal gravity started to slow the rate of inflation due to it's contracting effect (the expansion would keep going at a constant rate if nothing counters it). Normal gravity has been slowing the rate at which it expands for roughly half the age of the universe. At that point, the matter/energy density of the universe had gotten low enough where gravity could no longer decrease the rate of inflation. The discovery that the rate of inflation has actually been increasing for the last half of the universe has been attributed to some unknown 'dark' energy that may be related to what caused the initial expansion of the universe after the big bang.

*Edit: The idea behind 'supercooling' is that the energy level of the vacuum stays at a higher level than it should at a given temperature (e.g. the universe cooled but the energy of the vacuum stayed at a higher level than it should have - a false vacuum which generates negative pressure). This is highly unstable so matter/energy 'crystallizes' out of the excessive energy of the vacuum, dropping the energy level of the vacuum to what it should be for the temperature. Often the analogy is made with the supercooling of a liquid. If there are no impurities in the liquid it can actually cool down below its freezing temperature. However, a slight shock will cause ice crystals to form virtually instantly. When ice forms, it actually releases heat energy similar to what happened during the phase transition of the inflationary period.

As Neb, in particular, has indicated , at the end of the "Inflationary" period there was no further energy available from the original Inflaton field to continue driving the expansion, just its momentum -- so gravity took over

Edit :Space/universe did not / does not expand because it was "hot".

. Currently , space is at a temperature close to absolute zero -- but its rate of expansion is increasing because of dark Energy .

A similar energy was responsible for "inflation" , not temperature

Up until a few years ago, it had been thought that the expansion was slowing due to the gravity of the universe as a whole. Surprisingly, though, a previously unknown force has been discovered which is actually accelerating the expansion. Cosmologists are in a tizzy, and very eager to look into the nature of this force.

I think the first answer touches on something that is a whole lot more complex than stated, but the simple answer to your question about slowing is "gravity" which is hardly nothing.

The expansion started because the initial state (before which we have no information about how it came about, maybe God) was unstable and blew things apart because of the energy contained.