Cosmological Inflation with Multiple Fields and the Theory of Density Fluctuations

Abstract

Inflation is a stage of extremely rapid expansion in the very early universe. It was proposed to solve a number of problems in the standard Big Bang theory. In particular it others an explanation for the origin of structures like (clusters of) galaxies on the one hand (by generating small density fluctuations that act as gravitational seeds), and for the largescale homogeneity of the universe on the other hand (because of the enormous expansion). Inflation is driven by one or more scalar fields with an appropriate potential. In this thesis we develop an analytical formalism to describe the generation of density fluctuations during inflation with multiple scalar fields. We allow these fields to live on a non-trivial (curved) field manifold, as is often the case in high-energy theories. We also treat the evolution of the fluctuations after inflation, until the time of recombination when the cosmic microwave background radiation was formed. Using our formalism observations of the CMBR can then be used to set constraints on the parameters in (multiple-field) inflation models. In more detail this thesis covers the following topics. After introductory chapters on cosmology in general and single-field inflation, the theory of inflation with multiple fields and a general (non-trivial) field metric is derived. In particular we introduce a basis in field space that is induced by the background dynamics and allows a clear distinction between effectively single-field and truly multiple-field effects. The important slow-roll approximation is generalized to the case of multiple fields. Next we derive how scalar and tensor fluctuations are generated from a quantum origin during multiple-field inflation, paying special attention to the transition that occurs when a perturbation mode crosses the Hubble scale. Using some simplifying assumptions the evolution of both adiabatic and isocurvature perturbation modes after inflation is treated. The final results are expressions for the spectral amplitudes and indices, which can be measured in the CMBR, in terms of inflationary background quantities valid to .rst order in the slow-roll approximation. We discuss the new effects caused by the presence of multiple fields, which can be quite important, and define an observational quantity that will clearly indicate whether they are significant once the tensor perturbations can be observed with su.cient accuracy. Our analytical results are illustrated and checked numerically in various explicit models with a quadratic potential.