# Renormalisation group improvement in the stochastic formalism

## TL;DR

This paper develops a renormalisation group improved stochastic formalism for inflationary spacetimes, providing a more consistent way to include UV effects in IR dynamics, exemplified with Yukawa theory.

## Contribution

It introduces a new formalism combining stochastic IR resummation with renormalisation group effects, improving upon naive methods.

## Key findings

- Derived improved stochastic Langevin and Fokker-Planck equations including RG effects.
- Showed differences between the new formalism and naive potential replacement.
- Applied the formalism to Yukawa theory during inflation, highlighting key differences.

## Abstract

We investigate compatibility between the stochastic infrared (IR) resummation of light test fields on inflationary spacetimes and renormalisation group running of the ultra-violet (UV) physics. Using the Wilsonian approach, we derive improved stochastic Langevin and Fokker-Planck equations which consistently include the renormalisation group effects. With the exception of stationary solutions, these differ from the naive approach of simply replacing the classical potential in the standard stochastic equations with the renormalisation group improved potential. Using this new formalism, we exemplify the IR dynamics with the Yukawa theory during inflation, illustrating the differences between the consistent implementation of the UV running and the naive approach.