STATIONARY UNIVERSE

If the Universe contains at least one inflationary domain with a suffi ciently large and homogeneous scalar field phi, then this domain perma nently produces new inflationary domains of all possible types. We sho w that under certain conditions this process of the self-reproduction of the Universe can be described by a stationary distribution of proba bility, which means that the fraction of the physical volume of the Un iverse in a state with given properties (with given values of fields, with a given density of matter, etc.) does not depend on time. This re presents a strong deviation of inflationary cosmology from the standar d Big Bang paradigm.