Multiple Soft Limits of Cosmological Correlation Functions

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.

39 pages, 2 figures. v2: minor corrections, added references. Version to appear in JCAP

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Cited by in corpus (8)

• Constraints from Conformal Symmetry on the Three Point Scalar Correlator in Inflation
• Symmetry Constraints in Inflation, $\alpha$-vacua, and the Three Point Function
• Double Soft Limits of Cosmological Correlations
• Soft limits in holographic cosmology
• CMB Anisotropies from a Gradient Mode
• Non-local bispectra from super cosmic variance
• Inflation in Flatland
• The double-soft limit in cosmological correlation functions and graviton exchange effects