On the factor ordering problem in stochastic inflation

TL;DR

This paper addresses ambiguities in stochastic inflation models by proposing a criterion based on invariance under time reparametrizations, which uniquely determines the Ito factor ordering and discusses related issues.

Contribution

It demonstrates that requiring physical invariance under time reparametrizations uniquely fixes the factor ordering in stochastic inflation, resolving a key ambiguity.

Findings

Invariance under time reparametrizations selects the Ito ordering.

The approach clarifies ambiguities related to non-trivial kinetic terms.

Provides methods to constrain additional ambiguities.

Abstract

The stochastic approach to inflation suffers from ambiguities due to the arbitrary choice of the time variable and due to the choice of the factor ordering in the corresponding Fokker-Planck equation. Here it is shown that both ambiguities can be removed if we require that the factor ordering should be set in such a way that physical results are invariant with respect to time reparametrizations. This requirement uniquely selects the so-called Ito factor ordering. Additional ambiguities associated with non-trivial kinetic terms of the scalar fields are also discussed, as well as ways of constraining these ambiguities.