From the Big Bang Theory to the Theory of a Stationary Universe

We consider chaotic inflation in the theories with the effective potentials $\phi^n$ and $e^{\alpha\phi}$. In such theories inflationary domains containing sufficiently large and homogeneous scalar field $\phi$ permanently produce new inflationary domains of a similar type. We show that under certain conditions this process of the self-reproduction of the Universe can be described by a {\it stationary} distribution of probability, which means that the fraction of the physical volume of the Universe in a state with given properties (with given values of fields, with a given density of matter, etc.) does not depend on time, both at the stage of inflation and after it. This represents a strong deviation of inflationary cosmology from the standard Big Bang paradigm. We compare our approach with other approaches to quantum cosmology, and illustrate some of the general conclusions mentioned above with the results of a computer simulation of stochastic processes in the inflationary Universe.