FROM THE BIG-BANG-THEORY TO THE THEORY OF A STATIONARY UNIVERSE

We consider chaotic inflation in the theories with the effective poten tials which at large phi behave either as phi(n) or as e(alphaphi). In such theories inflationary domains containing a sufficiently large an d homogeneous scalar field phi permanently produce new inflationary do mains of a similar type. This process may occur at densities considera bly smaller than the Planck density. Self-reproduction of inflationary domains is responsible for the fundamental stationarity which is pres ent in many inflationary models: properties of the parts of the Univer se formed in the process of self-reproduction do not depend on the tim e when this process occurs. We call this property of the inflationary Universe local stationarity. In addition to it, there may exist either a stationary distribution of probability P(c) to find a given field p hi at a given time at a given point, or a stationary distribution of p robability P(p) to find a given field phi at a given time in a given p hysical volume. If any of these distributions is stationary, we will b e speaking of a global stationarity of the inflationary Universe. In a ll realistic inflationary models which are known to us the probability distribution P(c) is not stationary. On the other hand, investigation of the probability distribution P(p) describing a self-reproducing in flationary universe shows that the center of this distribution moves t owards greater and greater phi with increasing time. It is argued, how ever, that the probability of inflation (and of the self-reproduction of inflationary domains) becomes strongly suppressed when the energy d ensity of the scalar field approaches the Planck density. As a result, the probability distribution P(p) rapidly approaches a stationary reg ime, which we have found explicitly for the theories lambda/4phi4 and e(alphaphi). In this regime the relative fraction of the physical volu me 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 t ime, both at the stage of inflation and after it. Each of the two type s of stationarity mentioned above constitutes a significant deviation of inflationary cosmology from the standard big bang paradigm. We comp are our approach with other approaches to quantum cosmology, and illus trate some of the general conclusions mentioned above with the results of a computer simulation of stochastic processes in the inflationary Universe.