This thesis investigates the non-abelian dynamics of D-Brane systems in String Theory, specifically focussing on the fate of the open string Tachyon. Starting from the action of two coincident non-BPS D9-branes, we investigate kink configurations of the U(2) matrix tachyon field, considering both symmetrised (Str) and conventional (Tr) prescriptions for the trace over gauge indices of the non-BPS action. Non-abelian tachyon condensation in the theory with Tr prescription, and the resulting fluctuations about the kink profile, are shown to give rise to a theory of two coincident BPS D8-branes. Next we investigate magnetic monopole solutions of the non-abelian Dirac- Born-Infeld (DBI) action describing two coincident non-BPS D9-branes in flat space. These monopole configurations are singular in the first instance and require regularization. We discuss a suitable non-abelian ansatz which describes a pointlike magnetic monopole and show it solves the equations of motion to leading order in the regularization parameter. Fluctuations are studied and shown to describe a codimension three BPS D6-brane, a formula is derived for its tension. Finally, we investigate the dynamics of a pair of coincident D5 branes in the background of k NS5 branes. We extend Kutasov's original proposal to the nonabelian case of multiple D-Branes and find that the duality still holds provided one promotes the radial direction to a matrix valued field associated with a nonabelian geometric tachyon and a particular parametrization for the transverse scalar fields is chosen. Analytic and numerical solutions for the pair's equations of motion are found in certain simplified cases in which the U(2) symmetry is broken to U(1) U(1). For certain range of parameters these solutions describe periodic motion of the centre of mass of the pair bouncing off a finite sized throat whose minimum size is limited by the D5 branes separation.

String theory remains the most popular paradigm for the unification of gravity and quantum field theory, but it has had little success in producing predictions that can be verified in experiments. One outstanding problem is the presence of a large number of physically inequivalent vacua. At low energies these are parameterised by scalar fields called moduli. This thesis will examine two aspects of their phenomenology. Firstly we study the possibility of spontaneous CP violation in string models with the dilaton field -a modulus determining the gauge coupling - stabilised at a phenomenologically acceptable value. We consider three mechanisms to stabilise the dilaton: multiple gaugino condensates, a nonperturbative Kähler potential, and a superpotential based on S-duality, and analyze consequent CP phases in the soft SUSY breaking terms. These models are unable to produce a realistic phenomenology, typically over-producing EDMs and giving a CKM phase that is too small, unless the potential controlling the moduli stabilisation is allowed to contain singularities. Secondly we compute the moduli Kähler potential for M-theory on a compact manifold of G2 holonomy in a large radius approximation. Our method relies on an explicit G2 structure with small torsion, its periods and the calculation of the approximate volume of the manifold. As a verification of our result, some of the components of the Kibler metric are computed directly by integration over harmonic forms. We also discuss the modification of our result in the presence of co-dimension four singularities and derive the gauge-kinetic functions for the massless gauge fields that arise in this case

Cosmology motivated by string theory has been studied extensively in the recent literature. String theory is promising because it has interesting features such as unifying gravity, electromagnetic, weak and strong nuclear forces. However, even the energy scale of the experiments at the Large Hadron Collider (~TeV) is too low to detect any strong evidence for string theory. The energy scale of inflation can be above ~ 109 TeV. Therefore, it is expected to find some signature of string theory in cosmology. String theory predicts ten space-time dimensions. In the brane world scenario, our four dimensional Universe is confined onto the higher dimensional object called the Brane in the ten dimensional space time. The Dirac-Born-Infeld (DBI) inflation is based on this idea. DBI inflation predicts a characteristic statistical feature in the Cosmic Microwave Background (CMB) temperature anisotropies. In this thesis, we study the predictions of the DBI inflation models on the CMB temperature anisotropies. In chapter 1, the idea of inflation in the early stage of the Universe is introduced after explaining why we need inflation in addition to the standard Big Bang scenario. At the end of this chapter, we introduce the CMB observables that quantify the statistical properties of the CMB anisotropies. In chapter 2, we introduce the cosmological perturbation theory for general multi-field inflation including DBI inflation. After studying the linear perturbation theory, we introduce the higher order perturbations that produce the non- Gaussianities. The analytic formulae for the CMB observables that are valid in cases with the effective single field dynamics around horizon crossing are summarised at the end of this chapter. In chapter 3, the idea of DBI inflation is introduced. Some analytic predictions for the CMB observables are given in a simple single field DBI inflation model. After introducing the microphysical constraint that excludes the single field DBI inflation, we show that this constraint can be significantly relaxed if the trajectory in the field space is bent in multi-field DBI inflation models. In chapter 4, we study the specific two-field DBI inflation model with a potential that is derived in string theory. The potential contains only the leading order term ignoring all other possible corrections in string theory. After studying how curves in the trajectories in the field space affect the CMB observable, we show that this model is excluded by observation in the regime where the analytic formulae introduced in chapter 2 are valid. At the end of this chapter, we discuss the cases where we cannot use the analytic formulae and discuss possible implications In chapter 5, we study the two-field DBI inflation model with a potential that has the essential feature of the potential obtained with other corrections in addition to the leading term in string theory. In this model, inflation is driven by the motion of a D3 brane along the radial direction and at later times instabilities develop in the angular directions. It is shown that it is actually possible to satisfy the microphysical constraint with a turn in the trajectory in the field space. However, this particular choice of potential is excluded with the constraint on the local type non-Gaussianity by the latest CMB observations of the PLANCK satellite. We discuss the future perspective of DBI inflation models in the last chapter.

In this work we explore the correspondence between the physical processes associated with inflationary models inspired by string theory and the subsequent non-Gaussian signatures imprinted in the primordial density perturbations. Specifically, we have chosen multiple-DBI inflation as a representative model to understand the effect of multiple-field dynamics and non-canonical kinetic terms on the resultant form of non-Gaussianity. We begin by introducing inflation as a mechanism to naturally lay down the initial conditions necessary for the hot big bang. Since the primordial density perturbations provide the best way to constrain inflationary models, we then review cosmological perturbation theory and provide the predictions of standard single-field, slow-roll inflation. Thereafter, we briefly review extensions to this model and introduce non-Gaussianity as a way to observationally discern between these otherwise degenerate scenarios. Thereafter, we study the effect of non-trivial sound speeds on local-type non-Gaussianity during multiple-field inflation. To this end, we use the δN formalism and a sum separable Hubble parameter to derive an analytic expression for the local-type non-linearity parameter in the two-field case, valid beyond slow variation. We find that non-trivial sound speeds can, in principle, curve the trajectory in such a way that significant local-type non- Gaussianity is produced. Deviations from slow variation, such as rapidly varying sound speeds, enhance this effect. To illustrate our results we consider inflation in the tip regions of two warped throats and find large local-type non-Gaussianity produced towards the end of the inflationary process. We then consider the equilateral contribution to the bi-spectrum by first calculating the full third-order action for the field fluctuations using the Arnowitt-Deser-Misner formalism. We then derive the corresponding three-point function for the field fluctuations at horizon-exit, to leading order in slow variation and small sound speeds. Thereafter, we again use the δN formalism and a separable Hubble parameter to present the combined local and equilateral contributions to the bi-spectrum of the curvature perturbation. We then revisit the case of inflation in two cutoff throats and find that the corresponding equilateral contribution is prohibitively large in this case. As an application of the above, we then explore further the parameter space of multiple- DBI inflation and, in particular, the dependence of large local-type non Gaussianity on initial conditions. To this end, we consider an alternative model of inflation in two cutoff throats that allows analytical solutions for the trajectories. We begin by considering the canonical limit of the model in which local-type non-Gaussianity is produced by the curvature of the potential. We find that such behaviour is highly dependent on the initial values of the fields. We then consider inflation in the tip regions of two cutoff throats and find that the production of large local-type non-Gaussianity through rapidly varying sound speeds is similarly dependent on initial conditions. Moreover, the equilateral contribution remains prohibitively large in such cases. Finally, we summarise our results and identify directions for future research, before providing a wider outlook for the inflationary paradigm in light of recent results from Planck.

In this thesis, we consider heterotic string vacua based on a warped product of a four-dimensional domain wall and a six-dimensional internal manifold preserving only two supercharges. Thus, they correspond to half-BPS states of heterotic supergravity. The constraints on the internal manifolds with $SU(3)$ structure are derived. They are found to be a generalization of half-flat manifolds with a particular pattern of torsion classes and they include half-flat manifolds and Strominger's complex non-Kahler manifolds as special cases. We also verify that heterotic compactifications on half-flat mirror manifolds are based on this class of solutions. Furthermore, within this context, we construct specific examples based on six-dimensional nearly-Kahler homogeneous manifolds and non-trivial vector bundles thereon. Our solutions are based on three specific group coset spaces satisfying the half-flat torsion class conditions. It is shown how to construct line bundles over these manifolds, compute their properties and build up vector bundles consistent with supersymmetry and the heterotic anomaly cancellation. It turns out that the most interesting solutions are obtained from SU(3)/U(1)². This space supports a large number of vector bundles leading to consistent heterotic vacua with GUT group and, for some of them, with three chiral families.

This thesis treats several topics in the study of extra-dimensional models of the world, concerning Heterotic M-Theory and the dynamics of branes. We describe a reduction to five dimensions, over a Calabi-Yau manifold, of an improved version of Heterotic M-Theory, which is valid to all orders in the gravitational coupling. This provides a starting point for considering the consequences of the improved theory for the very fruitful phenomenology of the original. We investigate the singularities formed by the collision of gravitating branes in scalar field theory. By considering the asymptotic structure of the spacetime, the properties of the horizons formed and the growth of the curvature we argue that the singularity is not a black brane, as one might have expected, but rather a big crunch. Finally, we construct a restricted class of multi-galileon theories as braneworld models with codimension greater than one, developing in the process some of the formalism needed for the general construction.