On "dynamical mass" generation in Euclidean de Sitter space

TL;DR

This paper develops a systematic perturbative approach to analyze the dynamical mass generation of a massless scalar field in Euclidean de Sitter space, resolving infrared divergences and connecting with stochastic methods.

Contribution

It introduces a non-perturbative treatment of the zero-mode and derives the dynamical mass using diagrammatic expansions and Schwinger-Dyson equations.

Findings

Dynamical mass scales as sqrt(lambda) H^2.

Infrared divergences are self-regulated by zero-mode dynamics.

Long-wavelength two-point function matches stochastic results.

Abstract

We consider the perturbative treatment of the minimally coupled, massless, self-interacting scalar field in Euclidean de Sitter space. Generalizing work of Rajaraman, we obtain the dynamical mass m^2 \propto sqrt{lambda} H^2 of the scalar for non-vanishing Lagrangian masses and the first perturbative quantum correction in the massless case. We develop the rules of a systematic perturbative expansion, which treats the zero-mode non-perturbatively, and goes in powers of sqrt{lambda}. The infrared divergences are self-regulated by the zero-mode dynamics. Thus, in Euclidean de Sitter space the interacting, massless scalar field is just as well-defined as the massive field. We then show that the dynamical mass can be recovered from the diagrammatic expansion of the self-energy and a consistent solution of the Schwinger-Dyson equation, but requires the summation of a divergent series of loop diagrams of arbitrarily high order. Finally, we note that the value of the long-wavelength mode two-point function in Euclidean de Sitter space agrees at leading order with the stochastic treatment in Lorentzian de Sitter space, in any number of dimensions.