De Sitter Breaking through Infrared Divergences

TL;DR

This paper demonstrates that certain fields in de Sitter space exhibit infrared divergences that break de Sitter invariance, challenging the assumption that invariant propagators always exist for these fields.

Contribution

It reveals that infrared divergences cause de Sitter symmetry breaking for specific scalar and vector fields, even when their propagators satisfy invariant equations.

Findings

Infrared divergences occur for massive scalars with negative squared mass.

Infrared divergences occur for massive transverse vectors with specific mass bounds.

Dimensional regularization can incorrectly suggest de Sitter invariance where it does not exist.

Abstract

Just because the propagator of some field obeys a de Sitter invariant equation does not mean it possesses a de Sitter invariant solution. The classic example is the propagator of a massless, minimally coupled scalar. We show that the same thing happens for massive scalars with $M_S^2 < 0$, and for massive transverse vectors with $M_V^2 \leq -2 (D-1) H^2$, where $D$ is the dimension of spacetime and $H$ is the Hubble parameter. Although all masses in these ranges give infrared divergent mode sums, using dimensional regularization (or any other analytic continuation technique) to define the mode sums leads to the incorrect conclusion that de Sitter invariant solutions exist except at discrete values of the masses.