Multiple Soft Limits of Cosmological Correlation Functions

TL;DR

This paper derives new identities for inflationary correlation functions in the double-soft limit, constraining their behavior and extending these results to multiple soft legs, with implications for large-scale structure.

Contribution

It introduces novel identities for double-soft limits of inflationary correlators, derived via background-wave and Ward identity methods, extending to multiple soft legs and large-scale structure.

Findings

Derived identities constrain O(q^2) components in double-soft limits.

Validated identities in resonant non-Gaussianities and small sound speed models.

Extended relations to many-soft limits and implications for large-scale structure.

Abstract

We derive novel identities satisfied by inflationary correlation functions in the limit where two external momenta are taken to be small. We derive these statements in two ways: using background-wave arguments and as Ward identities following from the fixed-time path integral. Interestingly, these identities allow us to constrain some of the O(q^2) components of the soft limit, in contrast to their single-soft analogues. We provide several nontrivial checks of our identities both in the context of resonant non-Gaussianities and in small sound speed models. Additionally, we extend the relation at lowest order in external momenta to arbitrarily many soft legs, and comment on the many-soft extension at higher orders in the soft momentum. Finally, we consider how higher soft limits lead to identities satisfied by correlation functions in large-scale structure.