Mathematics – Logic
Scientific paper
Sep 1997
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997phdt........10w&link_type=abstract
Thesis (PHD). TUFTS UNIVERSITY , Source DAI-B 58/03, p. 1332, Sep 1997, 149 pages.
Mathematics
Logic
Anthropic Principle
Scientific paper
In this thesis I present a summary of research on observational consequences of models of the early Universe based on cosmological inflation. I explore the arguments used to extract observational predictions from models which allow a range of 'constants of Nature' and cosmological parameters to be observed at the present time. Particular attention is paid to observational consequences of models of 'eternal inflation' which are more difficult to obtain. An overview of inflationary cosmology is presented in the first chapter. I describe particular inflationary models that will be explored in later chapters. The second chapter is devoted to the stochastic approach to inflation using a Fokker-Planck (FP) equation. After reviewing the deterministic evolution, I present the general form of the FP equation with an arbitrary parametrization of time and factor ordering and analyze its properties in the contest of eternal inflation. In the third chapter I consider the ensemble of Universes with different values of the 'constants of Nature' and other cosmological parameters such as the cosmological density parameter Ω. I review the anthropic argument used to extract predictions from models describing such an ensemble. The argument is based on comparing the volumes of parts of the Universe that have certain values of physical constants. In the case of eternal inflation, the argument runs into a difficulty of comparing infinite volumes, and I present regularization procedures developed to cope with this problem. A recipe for extracting predictions based on the FP equation is presented. In the last two chapters I explore the application of the regularization procedures of chapter 3 to particular models of 'new' and 'open' inflation. In the fourth chapter, I investigate the dependence of the results obtained through that method on the choice of the time variable and factor ordering in the FP equation. It is shown, both analytically and numerically, that the variation of the results due to factor ordering ambiguity inherent in the model is of the same order as their variation due to the choice of the time variable. Therefore, the resulting predictions are, within their accuracy, free of the spurious dependence on the time parametrization. The problem of making predictions in an eternally inflating universe which thermalizes by bubble nucleation is considered in the last chapter. A regularization procedure is applied to find the probability distribution for the ensemble of thermalized bubbles. The resulting probabilities are shown to be independent of the choice of the time parametrization. This formalism is then applied to models of 'open' inflation Ω < 1. Depending on the parameters of the model, the probability distribution for Ω is found to have a peak either very close to Ω = 1, or at an intermediate value of Ω in the range 0.03 ~
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