Type IIb Kähler moduli : inflationary phenomenology

The inflationary paradigm of standard big bang cosmology provides a mechanism to generate primordial curvature perturbations and explain the large scale homogeneity and isotropy of the observable universe. This is achieved through requiring a period of accelerated expansion during the early universe and requires a deep understanding of particle physics for its correct formulation. With the emergence of string theory as a potential description of a fundamental laws of nature provides a the natural framework in which we can construct realistic models of inflation seems plausible. A common feature of string theories is the requirement of extra dimensions and, in the absence of a complete formulation of the theory, it is necessary to dimensionally reduce the theories to give a 4d effective theory. String compactifications provide a promising approach through which this can be done. However compactifications lead to the generation of a large number of massless scalar fields (moduli) which would mediate unobserved 'fifth forces'. Methods of stabilising these fields give rise to exponentially flat potentials which provide the means of obtaining inflation quite naturally. In the introductory chapters a review of Type IIb flux compactifications gives methods to stabilise the complex structure moduli and dilaton through the use of fluxes. In order to stabilise the Kähler moduli additional non perturbative corrections to the superpotential are required. We introduce the well know class of meta stable de Sitter string vacua obtained when such corrections are included. An additional class vacua at large volume are discussed, these are found when leading order perturbative corrections to the Kähler potential are also considered. The large volume vacua are then shown to give rise to a model of inflaton using a Kähler modulus as an inflaton field. We show that there exists a large class of inflationary solutions corresponding to a constant volume V of the compactification manifold. In a second chapter on this inflationary model the existence of a basin of attraction for inflation with a constant volume is described. We also find a larger class of inflationary solutions when we evolve the axionic components of the Kähler moduli and the phenomenological aspects are discussed. We finally review the standard slow roll analysis and discuss its use in multiple field inflationary models. We introduce two multiple field extensions to the standard single field slow roll approach. We proceed with an investigation into the suitability of the multiple field slow roll approaches in predicting the slow roll footprint of Supergravity models of inflation. This is achieved through comparing the results with single field results and numerical simulation data when more complex models are considered