Stochastic Inflation in Compact Extra Dimensions

TL;DR

This paper extends stochastic inflation theory to models with Dirac Born Infeld (DBI) kinetic terms, incorporating string-inspired geometric constraints into the quantum fluctuation analysis of the inflaton field.

Contribution

It generalizes stochastic inflation to include non-canonical DBI kinetic terms, respecting string-theoretic field restrictions at the quantum level.

Findings

Modified the stochastic inflation framework for DBI models

Identified how string-inspired constraints affect quantum fluctuations

Provided a new approach for analyzing inflaton trajectories in string theory scenarios

Abstract

While moving down the potential on its classical slow roll trajectory, the inflaton field is subject to quantum jumps, which take it up or down the potential at random. In "stochastic inflation", the impact of these quantum jumps is modeled by smoothing out the field over (at least) Hubble-patch sized domains and treating fluctuations on smaller scales as noise. The inflaton thus becomes a stochastic process whose values at a given time are calculated using its probability distribution. We generalize this approach for non-canonic kinetic terms of Dirac Born Infeld (DBI) type and investigate the resulting modifications of the field's trajectory. Since models of DBI inflation arise from string-inspired scenarios in which the scalar field has a geometric interpretation, we insist that field value restrictions imposed by the model's string origin must be respected at the quantum level.