ABSTRACT
The idea of old inflation is that the inflaton scalar field is not varying, but sitting instead at a metastable minimum in its scalar potential. In general, inflation models allow the possibility of eternal inflation, although there may be exceptions such as inflection point inflation or power-law inflation. Fast-roll inflation demonstrates that slow-roll is a sufficient but not necessary condition for inflation. So far we have seen that the potential may become too steep or curved to support slow-roll and yet we may still have inflation, such as fast-roll or oscillating inflation. Thus, thermal inflation is one way to make sure that, initially, the inflaton field finds itself at the top of the potential hill. Statistically, eternal inflation never ends, but locally the inflaton field always eventually exits the diffusion zone and after a period of classical inflation, thermalises and gives rise to a local Big Bang universe, which is called a pocket universe.
