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Much of the low energy phenomenology which can be extracted from the field theory limit of the intrinsically ten dimensional E 8 ® E 8 heterotic superstring depends upon the topological and geometrical properties of the six dimensional compactified component of spacetime. After briefly reviewing the topological constraints on the latter manifold which ensure the survival of N=l four dimensional supersymmetry, we present and apply the mathematics necessary for the rigorous construction of vacuum solutions and the determination of the four dimensional massless field content. Two phenomenologically attractive classes of solutions, with unbroken E8 ⨂ SU(5) and E8 ⨂ SO(10) gauge groups, arise if the vacuum configuration contains a Ricci flat Kahler manifold with SU(3) holonomy (Calabi-Yau manifold), which admits certain SU(5) or SU(4) vector bundles. Further reduction of the gauge group and emergence of naturally light weak Higgs doublets may also occur by flux breaking if the Calabi Yau manifold is multiply connected. We analyse the feasibility of such scenarios for Calabi Yau manifolds with any possible fundamental group. Phenomenological considerations place severe constraints on the dimensions and transformation properties of certain cohomology groups and thereby lead to a highly restricted class of acceptable models. We then present the mathematical analysis of a three generation heterotic superstring inspired model, with E8 ⨂ E6 gauge symmetry. A detailed description of the manifold of compactification is given, along with a determination of its Hodge numbers and of the associated light supermultiplet structure. For a particular choice of vacuum moduli we derive this manifold's symmetry group, and determine its action on the massless fields in the theory. Preliminary investigation indicates that these transformation properties give rise to a remarkably realistic model. In the second volume we derive cosmological constraints on a supersymmetric extension of the standard model in which weak gauge symmery breaking is triggered at the tree level by a Higgs singlet superfield. The fermionic component of this gauge singlet (the "nino") is shown to be the lightest supersymmetric particle with a relic abundance near the critical closure density for a surprisingly wide range of the unconstrained parameters. The previously favoured photino dark matter scenario has been eliminated by the non observation of high energy solar neutrinos. After briefly reviewing this argument, we extend the analysis to eliminate Higgsino dark matter scenarios with and#60H1°and#62 ≠ and#60H2°and#62. We show that the nino produces an acceptably low level of solar neutrinos and that it may also account for the anomalously high level of cosmic ray antiproton flux.

In this thesis, several theoretical concepts relating to the large-scale structure of the universe are presented. In particular, various aspects of the hierarchical scenario are investigated. The initial perturbation field and its early evolution are discussed in Chapter 3. Chapter 4 is concerned with two-point correlation functions for galaxies, clusters and super-clusters. In Chapter 5, some effects of using velocity as a distance measure are examined. In particular, it will be argued that caustics in redshift space are an almost inevitable feature of the hierarchical scenario. Chapter 6 concentrates on the possibity that quasar Ly-α absorption lines are redshift caustics.