Inflation and Creation of Matter in the Universe

Inflationary theory was proposed 20 years ago. In the beginning it looked like an interesting piece of science fiction. During the last 20 years it changed quite a lot and became a broadly accepted cosmological paradigm. New versions of this theory do not require any assumptions about initial thermal equilibrium in the early universe. Inflation is no longer based on the mechanism of supercooling and exponential expansion in the false vacuum state. It was proposed in order to resolve various problems of the big bang theory, and in particular to explain the extraordinary homogeneity of the observable part of the universe. However, later we have learned that while making the universe locally homogeneous, inflation can make it extremely inhomogeneous on a vary large scale. According to the simplest versions of inflationary theory the universe is not a single, expanding ball of fire produced in the big bang, but rather a huge eternally growing fractal. It consists of many inflating balls that produce new balls, which in turn produce more new balls, ad infinitum. Even now we continue learning new things about inflationary cosmology, especially about the stage of reheating of the universe after inflation. In this paper we will briefly describe the history of inflationary cosmology, and then we will give a review of some recent developments.