Statistics – Computation
Scientific paper
Jan 1996
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996phdt.........7m&link_type=abstract
Thesis (PH.D.)--STANFORD UNIVERSITY, 1996.Source: Dissertation Abstracts International, Volume: 57-05, Section: B, page: 3267.
Statistics
Computation
Stationarity, Self Reproduction, Quantum Cosmology, Inflationary
Scientific paper
We consider chaotic inflation in theories with effective potentials dominated by scalar fields. In such theories inflationary domains containing sufficiently large and homogeneous scalar field phi permanently produce new inflationary domains of a similar type. Self-reproduction 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 self-reproduction 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 a stationary distribution of probability Pp to find a given field phi at a given time in a given physical volume. 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. We call this property a global stationarity of the inflationary universe. Each of the two types of stationarity mentioned above constitutes a significant deviation of inflationary cosmology from the standard big bang paradigm. To describe these features we developed a novel branching diffusion approach to the stochastic dynamics of the inflationary universe. The very existence of stationary regime leads not only to important consequences for our understanding of the global structure of the universe, but also to a possible observable traces of such significance as openness of the visible universe (Omega<1) or local violations of Copernican principle. We compare our approach with other approaches to quantum cosmology. In particular, we devote substantial attention to the question of the time reparametrization and regularization scheme dependence of computations in quantum cosmology. We conclude that, although we are still far from complete understanding of the nature of the universe, but we have made a significant progress towards that ultimate goal of the physical science by capturing some of the most essential features of the evolution of the universe in general yet quantitative framework.
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