3.1. Friedmann's Equation Exponential Expansion
One way to describe inflation is that during inflation, a inf term dominates Eq. 11. Thus, during inflation we have,
(22) (23) (24) (25) (26) |
where ti and Ri are the time and scale factor at the beginning of inflation. To get Eq. 26 we have assumed 0 ti << t < te (where te is the end of inflation) and we have used Eq. 22. Equation 26 is the exponential expansion of the Universe during inflation. The e-folding time is 1/H. The doubling time is (ln 2) / H. That is, during every interval t = 1/H, the size of the Universe increases by a factor of e = 2.718281828... and during every interval t = (ln 2) / H the size of the Universe doubles.