Recent Progress in Inflationary Cosmology
  We discuss two important modifications of inflationary paradigm. Until very recently we believed that inflation automatically leads to flatness of the universe, Omega = 1. We also thought that post-inflationary phase transitions in GUTs may occur only after thermalization, which made it very difficult to have baryogenesis in GUTs and to obtain superheavy topological defects after inflation. We will describe a very simple version of chaotic inflation which leads to a division of the universe into infinitely many open universes with all possible values of Omega from 1 to 0. We will show also that in many inflationary models quantum fluctuations of scalar and vector fields produced during reheating are much greater than they would be in a state of thermal equilibrium. This leads to cosmological phase transitions of a new type, which may result in an efficient GUT baryogenesis, in a copious production of topological defects and in a secondary stage of inflation after reheating. 
Andrei Linde