Inflation, Universality and Attractors

TL;DR

This thesis explores universal features of inflation related to fundamental UV-physics, deriving new bounds on inflationary parameters and demonstrating attractor mechanisms in supergravity models that unify inflation and dark energy.

Contribution

It introduces a novel, stronger field-range bound and demonstrates how hyperbolic K"ahler geometries induce attractors for inflationary observables in supergravity.

Findings

Derived a field-range bound two orders of magnitude stronger than Lyth's.

Showed that hyperbolic K"ahler geometries induce attractors for spectral tilt and tensor-to-scalar ratio.

Unified inflation and dark energy via a nilpotent sector enhances attractor behavior.

Abstract

In this PhD thesis, we investigate generic features of inflation which are strictly related to fundamental aspects of UV-physics scenarios, such as string theory or supergravity. After a short introduction to standard and inflationary cosmology, we present our research findings. On the one hand, we show that focusing on universality properties of inflation can yield surprisingly stringent bounds on its dynamics. This approach allows us to identify the regime where the inflationary field range is uniquely determined by both the tensor-to-scalar ratio and the spectral index. Then, we derive a novel field-range bound, which is two orders of magnitude stronger than the original one derived by Lyth. On the other hand, we discuss the embedding of inflation in supergravity and prove that non-trivial hyperbolic K\"ahler geometries induce an attractor for the inflationary observables: the spectral tilt tends automatically to the center of the Planck dome whereas the amount of primordial gravitational waves is directly controlled by curvature of the internal manifold. We identify the origin of this attractor mechanism in the so-called $\alpha$-scale supergravity model. Finally, we show how the inclusion of a nilpotent sector, allowing for a unified description of inflation and dark energy, implies an enhancement of the attractor nature of the theory. The main results of this thesis have been already published elsewhere. However, here we pay special attention to present them in a comprehensive way and provide the reader with the necessary background.