Classical and quantum fluctuations in superstring cosmology

In this thesis we will examine cosmological models of the early universe through semi-classical perturbations. In Chapter 1 we review standard cosmology, inflation and string cosmology. In Part I we consider the pre-big bang scenario proposed by Gasperini and Veneziano which is based on the low-energy vacuum solutions derived from the superstring effective action. Using the SL(2,R) and SL(3,R) symmetry groups to parameterise the scalar fields of the effective action, it has been found that the resulting perturbation spectra of axion fields always has at least one negatively (red) tilted spectrum. In Chapter 4 we show how extending the symmetry group to SL(4,R) can produce positively tilted (blue) axion spectra in a limited region of parameter space which may provide seed perturbations of an appropriate amplitude for large-scale structure in our universe. In Part II we examine the cosmological perturbations produced in an alternative string-inspired model, the brane-world scenario with one extra infinite dimension. In Chapter 5 we introduce the 5D background and the 4D Einstein equations on the brane and briefly summarise essential results for the evolution of FRW brane-world cosmologies in a Schwarzschild-Anti-de Sitter bulk, which we shall use as our unperturbed background solution. In Chapter 6 we introduce linear perturbations of the bulk metric split into scalar, vector and tensor perturbations (defined with respect to 3D spatial hypersurfaces in an arbitrary gauge. It is trivial to construct quantities independent of the 3D-spatial gauge, and this is sufficient to give gauge-invariant vector and tensor perturbations, but there are alternative choices of temporal and bulk gauges and hence different choices of gauge-invariant scalar perturbations. In Section 6.2 we define gauge-invariant quantities coinciding with metric perturbations in the 5D longitudinal gauge, whereas in Section 6.3 we construct quantities in a Gaussian normal gauge where the 5D bulk metric perturbations coincide with the induced 4D metric perturbations on the brane. This is particularly suited for imposing the perturbed junction conditions, which allows us to interpret the effect of bulk metric perturbations as seen by the brane-bound observer. We show that one can construct gauge-invariant perturbations in order to describe the evolution of the Weyl tensor perturbations throughout the bulk which may provide a distinctive signature of the brane-world scenario. In Section 8 we examine inhomogeneous perturbations about a homogeneous and isotropic cosmology on the brane and the possibility of an observational signature of brane-world cosmology via a spectrum of vector perturbations with de Sitter expansion on the brane. (author)