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Abstract:
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The thesis begins with a review of basic elements of general theory of relativity
(GTR) which forms the basis for the theoretical interpretation of the
observations in cosmology. The first chapter also discusses the standard model
in cosmology, namely the Friedmann model, its predictions and problems. We
have also made a brief discussion on fractals and inflation of the early universe
in the first chapter. In the second chapter we discuss the formulation of a new
approach to cosmology namely a stochastic approach. In this model, the dynam
ics of the early universe is described by a set of non-deterministic, Langevin type
equations and we derive the solutions using the Fokker—Planck formalism. Here
we demonstrate how the problems with the standard model, can be eliminated
by introducing the idea of stochastic fluctuations in the early universe. Many
recent observations indicate that the present universe may be approximated by
a many component fluid and we assume that only the total energy density is
conserved. This, in turn, leads to energy transfer between different components
of the cosmic fluid and fluctuations in such energy transfer can certainly induce
fluctuations in the mean to factor in the equation of state p = wp, resulting in
a fluctuating expansion rate for the universe. The third chapter discusses the stochastic evolution of the cosmological parameters in the early universe, using the new approach. The penultimate chapter is about the refinements to be made in the present model, by means of a new deterministic model The concluding chapter presents a discussion on
other problems with the conventional cosmology, like fractal correlation of galactic
distribution. The author attempts an explanation for this problem using the stochastic
approach. |