Title:

Scalar fields in cosmology and astrophysics

This thesis examines various applications of particle physics to topics in cosmology and astrophysics, with particular attention paid to the possible roles of scalar fields. The work can be broken down into four distinct, though related, pieces. The first of these pieces comprises both chapters two and three while the remainder, each one chapter long, are chapters four, five and six. The first two topics are cosmology based, examining the dynamics of cosmological solutions to various particle theories with consideration of compactification and inflation respectively. The remaining two are astrophysical in nature, with particular attention paid to compact stellar objects such as neutron stars and boson stars. Chapter one provides an overview of the relevant parts of particle physics, cosmology and astrophysics in a nontechnical manner, to introduce the ideas present throughout the rest of the thesis, and contains notes on the conventions used within it. In chapters two and three, we investigate various cosmological solutions in ten dimensional supergravity, viewed as a low energy limit of the heterotic string theory. We use the three form field H to split up the nine spatial dimensions into three 3spaces, and examine the influence of the scalar dilaton field. Both analytic and numerical means are used to examine two specific models, and the nature of approach to an initial cosmological singularity is examined. In one case, the future behaviour is governed by the existence of an unusual type of attractor, which precludes the possibility of compactification, while in the other, where the H field arises solely on one 3space, sensible compactification scenarios can be obtained. The model is then enhanced by considering a simple mechanism for particle production using scalar field couplings to other (fermion) fields to provide viscous forces. The effect of this particle production on both the previous scenarios is examined. In chapter four, models exhibiting power law inflation are considered and an exact solution specified. Once more, viscous forces from the inflaton's couplings are included and are found, primarily by numerical techniques, to improve the efficiency of the inflation. The basic ideas are then implemented in a specific particle theory in which the scalar field has a potential of the desired type, and it is illustrated how an inflationary model may be constructed from these ideas which is consistent with constraints from observations. Chapter five considers the effect which higher dimensional theories may have on the structure of neutron stars. In particular, we examine the simplest KaluzaKlein theory in which the size of the extra dimension behaves as a scalar field. The equations of stellar structure are derived and then solved numerically, with particular attention given to the function of total mass against the central density and to the description of matter in a five dimensional theory. Only some descriptions of matter are allowed, and they can lead to exterior solutions differing from the conventional Schwarzchild one. Finally, a sample model for dynamical gravitational collapse in these theories is examined, and surprisingly it is found that it can be solved analytically. Unfortunately, difficulties in attaching an exterior solution outside the collapsing matter conceal the full nature of this solution. Chapter six examines the possibility of stellar objects comprised of both bosons and fermions, thus generalising the separate notions of neutron stars and boson stars. Again, the basic equations are derived, and numerical simulation is once more necessary to obtain solutions to them. Attention is given to the units used and the mass function is again of primary interest. A rudimentary stability analysis based on the binding energy of the stars is carried out, and an examination made of the results of varying the mass of the bosonic constituents. Briefly, the effect of an explicit interaction term between the bosons and fermions in the Lagrangian is considered. Chapter seven provides some conclusions and details areas in which future work may be fruitful.
