3.1. The definition of inflation

Inflation is defined to be any epoch during which the Universe is accelerating, > 0, with respect to cosmic time. We can rewrite this in several different ways

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The second of these is the most useful, because it has the most direct geometrical interpretation. It says that the Hubble length, as measured in comoving coordinates, decreases during inflation. At any other time, the comoving Hubble length increases. This is the key property of inflation; although typically the expansion of the Universe is very rapid, the crucial characteristic scale of the Universe is actually becoming smaller, when measured relative to that expansion.

Quite a wide range of behaviours satisfy the inflationary condition. The classic one is de Sitter expansion, which arises when the Universe is dominated by a cosmological constant, which we saw earlier gives a(t) exp(Ht). However realistic models of inflation usually deviate from this idealized situation, since inflation must come to an end to allow the successes of the standard Hot Big Bang to be reproduced after one second or so.