Cosmological implications of field space geometry

Abstract

PhD ThesisOne of the most fascinating aspects of recent endeavours in theoretical cosmology has been the investigation of the quantum e ects of scalar elds in eld-spaces with non-trivial geometries, in the early universe. The objective of this thesis is the presentation of a series of original research topics that result from such considerations. The rst part of this work explores an extension to Starobinsky's model of stochastic in ation. The functional integral describing the stochastic dynamics of a spectator eld during in ation is reviewed. Comparisons are drawn between the diagrammatic expansion resulting from action and the one obtained directly from a perturbative solution of the corresponding Langevin equation. The Feynman rules for computing arbitrary temporal n-point functions are stated and illustrative computations are presented. The role played by the functional Jacobian determinant in the path integral is given increased attention. Multiplicative noise is also brie y considered; allowing the eld to contribute to the expansion rate introduces additional vertices and exciting insights on the dependence of observable results on the discretization prescription are motivated. The second part presents a covariant under eld rede nitions E ective Field Theory proposed towards the resolution of the existing tension of conformal frame dependence. We are motivated by the meta-stability of the Higgs vacuum which, in the early universe, can lead to complications. It is shown, here, that the e ective Higgs potential at large eld values can be derived in a way that is independent of the choice of conformal frame for the spacetime metric, resulting in unambiguous answers to questions about physical observables (eg.vacuum stability). This approach leads to new relations for the evolution of the coupling coe cients with the energy scale and motivates improved limits on the allowed values of the Higgs-curvature coupling. The third part investigates the dynamics of a multi eld in ation model with curved eld-space. Abandoning the assumption of a single in aton, which is both unphysical and not motivated by higher energy theories, results in the introduction of a scalar multiplet, with non-trivial kinetic terms. The recently proposed and topical Hyperin ation model is reviewed and a concise treatment of the evolution of the background and the quantum perturbations is introduced. Thus, bounds for the cosmological observables are established and comparisons with experimental data are drawn, resulting in restrictions in the admissible values of the eld-space curvature paramete