Inflation and the Fine-Tuning Problem

TL;DR

This paper introduces a stochastic approach to inflaton dynamics that addresses fine-tuning issues in inflationary models, providing exact solutions and predicting nearly scale-invariant Gaussian fluctuations with relaxed amplitude constraints.

Contribution

The paper presents a new stochastic method for inflaton dynamics, deriving exact solutions for a bb potential and demonstrating reduced fine-tuning requirements.

Findings

Predicts Gaussian fluctuations with high accuracy on all scales.

Achieves amplitude constraints at bb, easing fine-tuning.

Suggests the approach applies broadly to various potentials.

Abstract

I describe a recently derived stochastic approach to inflaton dynamics which can address some serious problems associated with conventional inflationary theory. Using this theory I derive an exact solution to the stochastic dynamics for the case of a $\lambda\phi^4$ potential and use it to study the generated primordial density fluctuations. It is found that on both sub and super-horizon scales the theory predicts gaussian fluctuations to a very high accuracy along with a near scale-invariant spectrum. Of most interest is that the amplitude constraint is found to be satisfied for $\lambda\sim 10^{-5}$ rather than $\lambda\sim 10^{-14}$ of the conventional theory. This represents a dramatic easing of the fine-tuning constraints, a feature likely to generalize to a wide range of potentials.