From the big bang theory to the theory of a stationary universe
Abstract
We consider chaotic inflation in the theories with the effective potentials which at large φ behave either as φ^{n} or as e^{αφ}. In such theories inflationary domains containing a sufficiently large and homogeneous scalar field φ permanently produce new inflationary domains of a similar type. This process may occur at densities considerably smaller than the Planck density. Selfreproduction of inflationary domains is responsible for the fundamental stationarity which is present in many inflationary models: properties of the parts of the universe formed in the process of selfreproduction do not depend on the time 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 φ at a given time at a given point, or a stationary distribution of probability P_{p} to find a given field φ at a given time in a given physical volume. If any of these distributions is stationary, we will be speaking of a global stationarity of the inflationary universe. In all 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 selfreproducing inflationary universe shows that the center of this distribution moves towards greater and greater φ with increasing time. It is argued, however, that the probability of inflation (and of the selfreproduction of inflationary domains) becomes strongly suppressed when the energy density of the scalar field approaches the Planck density. As a result, the probability distribution P_{p} rapidly approaches a stationary regime, which we have found explicitly for the theories λ/4φ^{4} and e^{αφ}. In this regime the relative 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. Each of the two types of stationarity mentioned above constitutes a significant 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.
 Publication:

Physical Review D
 Pub Date:
 February 1994
 DOI:
 10.1103/PhysRevD.49.1783
 arXiv:
 arXiv:grqc/9306035
 Bibcode:
 1994PhRvD..49.1783L
 Keywords:

 98.80.Cq;
 98.80.Bp;
 98.80.Hw;
 Particletheory and fieldtheory models of the early Universe;
 Origin and formation of the Universe;
 General Relativity and Quantum Cosmology;
 Astrophysics;
 High Energy Physics  Lattice
 EPrint:
 No changes to the file, but original figures are included. They substantially help to understand this paper, as well as eternal inflation in general, and what is now called the "multiverse" and the "string theory landscape." High quality figures can be found at http://www.stanford.edu/~alinde/LLMbigfigs/