The Perils of Analytic Continuation

TL;DR

This paper discusses the issues and debates surrounding the graviton propagator on de Sitter space, emphasizing the importance of de Sitter breaking and clarifying misconceptions about analytic continuation and invariance.

Contribution

It clarifies the remaining disputes on graviton propagators in de Sitter space, emphasizing the necessity of de Sitter breaking and correcting previous misconceptions.

Findings

Tachyonic scalars' decay leads to de Sitter breaking in two-point functions.

De Sitter invariant solutions involve non-meromorphic derivatives at zero mass.

Noninvariant propagators correctly reproduce the tensor power spectrum.

Abstract

A nice paper by Morrison demonstrates the recent convergence of opinion that has taken place concerning the graviton propagator on de Sitter background. We here discuss the few points which remain under dispute. First, the inevitable decay of tachyonic scalars really does result in their 2-point functions breaking de Sitter invariance. This is obscured by analytic continuation techniques which produce formal solutions to the propagator equation that are not propagators. Second, Morrison's de Sitter invariant solution for the spin two sector of the graviton propagator involves derivatives of the scalar propagator at $M^2 = 0$, where it is not meromorphic unless de Sitter breaking is permitted. Third, de Sitter breaking does not require zero modes. Fourth, the ambiguity Morrison claims in the equation for the spin two structure function is fixed by requiring it to derive from a mode sum. Fifth, Morrison's spin two sector is not "physically equivalent" to ours because their coincidence limits differ. Finally, it is only the noninvariant propagator that gets the time independence and scale invariance of the tensor power spectrum correctly.