Initial conditions for Inflation in an FRW Universe

TL;DR

This paper analyzes initial conditions leading to inflation across various models, showing that inflation is robust for a wide range of initial states, especially at higher energy scales, and clarifies misconceptions about plateau potentials.

Contribution

It provides a comprehensive phase-space analysis of initial conditions for multiple inflation models, including Higgs and Starobinsky, demonstrating robustness and clarifying misconceptions.

Findings

Inflation can arise from a broad set of initial conditions.

Higgs inflation is very robust under various initial conditions.

Higher initial energy scales increase the likelihood of inflation.

Abstract

We examine the class of initial conditions which give rise to inflation. Our analysis is carried out for several popular models including: Higgs inflation, Starobinsky inflation, chaotic inflation, axion monodromy inflation and non-canonical inflation. In each case we determine the set of initial conditions which give rise to sufficient inflation, with at least $60$ e-foldings. A phase-space analysis has been performed for each of these models and the effect of the initial inflationary energy scale on inflation has been studied numerically. This paper discusses two scenarios of Higgs inflation: (i) the Higgs is coupled to the scalar curvature, (ii) the Higgs Lagrangian contains a non-canonical kinetic term. In both cases we find Higgs inflation to be very robust since it can arise for a large class of initial conditions. One of the central results of our analysis is that, for plateau-like potentials associated with the Higgs and Starobinsky models, inflation can be realised even for initial scalar field values which lie close to the minimum of the potential. This dispels a misconception relating to plateau potentials prevailing in the literature. We also find that inflation in all models is more robust for larger values of the initial energy scale.