Inflation with Stochastic Boundary

TL;DR

This paper models inflationary dynamics as a stochastic process with boundaries, analyzing how fields and boundaries undergo Brownian motion, and explores implications for inflation models through hitting probabilities and e-fold calculations.

Contribution

It introduces a stochastic boundary framework for inflation, analyzing both drift and diffusion regimes, and computes key probabilistic quantities relevant to inflationary scenarios.

Findings

Derived first hitting probabilities for boundary crossing.

Calculated mean number of e-folds before boundary hit.

Explored implications for different inflation regimes.

Abstract

We study the Brownian motion of a field where there are boundaries in the inflationary field space. Both the field and the boundary undergo Brownian motions with the amplitudes of the noises determined by the Hubble expansion rate of the corresponding dS spacetime. This setup mimics models of inflation in which curvature perturbation is induced from inhomogeneities generated at the surface of end of inflation. The cases of the drift dominated regime as well as the diffusion dominated regime are studied in details. We calculate the first hitting probabilities as well as the mean number of e-folds for the field to hit either of the boundaries in the field space. The implications for models of inflation are reviewed.