Scalar field effective potentials in de Sitter spacetime

TL;DR

This paper compares two definitions of scalar field effective potentials in de Sitter spacetime, showing that the constraint effective potential avoids infrared issues and aligns with stochastic theory, unlike the standard one.

Contribution

It explicitly computes and contrasts the standard and constraint effective potentials at one-loop order in de Sitter space, highlighting their differences and physical interpretations.

Findings

The standard effective potential fails to converge for light fields in de Sitter.

The constraint effective potential remains well-defined and perturbatively computable.

The constraint effective potential is supported as the correct choice in stochastic inflation theory.

Abstract

We investigate two different definitions of a scalar field effective potential in quantum field theory in de Sitter spacetime: the standard textbook definition, and the constraint effective potential proposed by O'Raifeartaigh et al. in 1986. While these definitions are equivalent in Minkowski spacetime, they differ significantly in de Sitter. We demonstrate this by computing them both explicitly at one-loop order in perturbation theory. It is well known that the perturbative expansion of the standard effective potential fails converge for light fields. In contrast, the constraint effective potential does not suffer from this infrared problem, and it can therefore be computed using perturbation theory. We discuss the physical interpretation of the two effective potentials. In particular, we provide evidence supporting an earlier conjecture that the constraint effective potential is the correct one to use in the stochastic Starobinsky-Yokoyama theory.