Stochastic Quantization of Scalar Fields in de Sitter Spacetime

TL;DR

This paper applies stochastic quantization to scalar fields in de Sitter spacetime, calculating the two-point function at first order in coupling and discussing regularization to handle divergences.

Contribution

It introduces a covariant stochastic regularization method for scalar fields in de Sitter space and computes the two-point function up to first order in coupling.

Findings

Two-point function evaluated at first order in coupling

Asymptotic behavior of the two-point function analyzed

Covariant stochastic regularization renders the two-point function finite

Abstract

We consider the stochastic quantization method for scalar fields defined in a curved manifold. The two-point function associated to a massive self-interacting scalar field is evaluated, up to the first order level in the coupling constant $\lambda$, for the case of de Sitter Euclidean metric. Its value for the asymptotic limit of the Markov parameter $\tau\to\infty$ is exhibited. We discuss in detail the covariant stochastic regularization to render the one-loop two-point function finite in the de Sitter Euclidean metric.