Positivity in the effective field theory of cosmological perturbations

TL;DR

This paper explores how positivity bounds, derived from fundamental principles like causality and unitarity, constrain the effective field theories used in cosmological perturbation models, especially during inflation.

Contribution

It extends positivity bounds to cosmological EFTs, incorporating cosmological corrections, and analyzes their implications for inflation models with beyond-Horndeski operators.

Findings

Cosmological positivity bounds can be stronger or weaker than flat space bounds.

Derived bounds include corrections of order H^2/Λ^2.

Application to slow-roll inflation constrains beyond-Horndeski operators.

Abstract

Requiring the existence of a unitary, causal and local UV-completion places a set of positivity bounds on the corresponding effective field theories (EFTs). We discuss the obstructions and possibility in applying the positivity bound to cosmology, in particular the EFT of cosmological perturbations. Taking a $c_T=1$ beyond-Horndeski EFT as an illustrative example, we derive such bounds, which incorporate the cosmological correction of order $H^2/\Lambda^2$, $\Lambda$ being the cutoff scale. The derived bounds are applied to slow-roll inflation with beyond Horndeski operators. It is found that the cosmological positivity bounds may be either stronger or weaker than their flat space counterpart.