Massless interacting quantum fields in deSitter spacetime

TL;DR

This paper develops a Mellin-Barnes-type representation for massless interacting quantum fields in deSitter spacetime, addressing perturbative complexities and IR behavior, and explores potential long-term quantum instabilities of the spacetime.

Contribution

It extends previous methods to massless fields, handling zero-mode issues and providing a framework for analyzing correlation functions in deSitter space.

Findings

Correlation functions do not have a well-defined zero-coupling limit.

Correlation functions grow at most polynomially at large time separations.

Results suggest possible quantum IR-instabilities in deSitter spacetime.

Abstract

We generalize key aspects of arXiv:1010.5367 (and also arXiv:1010.5327) to the case of {\em massless} $\lambda \phi^{2n}$ quantum field theory on deSitter spacetime. As in that paper, our key objective is to derive a suitable "Mellin-Barnes-type" representation of deSitter correlation functions in a deSitter-invariant state, which holds to arbitrary orders in perturbation theory, and which incorporates renormalization. The representation is suitable for the study of large distance/time properties of correlation functions. It is arrived at via an analytic continuation from the corresponding objects on the sphere, and, as in the massive case, relies on the use of graph-polynomials and their properties, as well as other tools. However, the perturbation expansion is organized somewhat differently in the massless case, due to the well-known subtleties associated with the "zero-mode" of the quantum field. In particular, the correlation functions do not possess a well-defined limit as the self-coupling constant of the field goes to zero, reflecting the well-known non-existence of a deSitter invariant state in the free massless scalar theory. We establish that generic correlation functions cannot grow more than polynomially in proper time for large time-like separations of the points. Our results thus leave open the possibility of quantum induced IR-instabilities of deSitter spacetime on very large time-scales.