Some Cosmological Aspects of Unified Theories.

Mathematics – Logic

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Scientific paper

Available from UMI in association with The British Library. In this thesis we try to determine some cosmological consequences of two particular unified theories. Initially we consider N = 2 6-D supergravity and calculate the early universe evolution for an M ^4 times S ^2 ansatz. We also determine the initial conditions to be used for this calculation by use of the wavefunction for the theory. The wavefunction is calculated on a three dimensional lattice using both the Wheeler-De Witt equation and the Hartle-Hawking definition of the wavefunction. We are able to compare this solution with other analytic results in certain regions and we find general agreement. In concensus with other work we find there is little possibility of sufficient inflation in this model. The current theory of superstrings is also considered in the same way. We try to include all the relevant physical effects and to obtain a consistent dimensional reduction. To obtain an inflationary phase we note we require 1-loop quantum corrections and reheating terms. We also require a non zero field strength HMNP and the presence of a gluino condensate. The possibility of a torsional connection on the internal space is allowed for but for inflation and zero cosmological constant we require this to be absent. Given these constraints we find that superstrings can provide a cosmology that has several attractive features. They are, sufficient inflation, a possible zero cosmological constant and a reheating temperature sufficient for most theories of baryosynthesis. In the latter part of this thesis we turn to a consequence of several unified theories, that of cosmic strings, and study the effects of matter on the behaviour of a string. We consider the specific case of a black hole background and obtain the evolution numerically. We note the features of cusps and loops are generated in this background. We continue the study of loop formation on an arbitrary background and show that tidal forces can prevent the formation of loops. We also calculate the critical impact parameter for capture and show its functional form is similar to that of a test particle.

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