The Devil Went Down to de Sitter: Divergent Effective Field Theory Expansions in Cosmology

Abstract

Effective field theories (EFTs) in de Sitter space, and in accelerating cosmologies more generally, must capture phenomena absent in flat space, most notably long-range correlations generated by spontaneous particle production. When heavy physics is integrated out in such time-dependent backgrounds, these effects leave an imprint on the EFT expansion: even at tree level, this is generically an asymptotic rather than convergent series. This is not a failure of EFT. The large-order behavior of the expansion coefficients encodes physical information inaccessible at any finite order, so cosmological EFTs contain hidden data. Using resurgence analysis, we show how this information can be systematically extracted to recover exact and non-perturbative predictions from the perturbative expansion. In the example we study, the resurgent completion is naturally organized in terms of the de Sitter $S$-matrix. This leads us to conjecture a prescription for extracting $S$-matrix data from cosmological EFTs in general. The framework extends to any setting where particle production, or a similar non-perturbative phenomenon, renders the EFT expansion asymptotic. A longer companion paper will provide a more detailed and pedagogical treatment.