Hidden Adler zeros and soft theorems for inflationary perturbations

TL;DR

This paper derives universal soft theorems for inflationary perturbations from symmetries, showing they depend only on on-shell data and are valid to all perturbative orders, with implications for EFTs of inflation.

Contribution

It introduces a new hierarchy of soft limits ensuring the soft theorems depend solely on on-shell data, even with cubic vertices, and applies these to bootstrap superfluid EFT amplitudes.

Findings

Soft theorems depend only on on-shell data.

Enhanced soft scaling occurs for certain exchange diagrams.

Agreement with Hamiltonian analysis for superfluid EFTs.

Abstract

We derive soft theorems for on-shell scattering amplitudes from non-linearly realised global space-time symmetries, arising from the flat space and decoupling limits of the effective field theories (EFTs) of inflation, while taking particular care of on-shell limits, soft limits, time-ordered correlations, momentum derivatives, energy-momentum conserving delta functions and $i\varepsilon$ prescriptions. Intriguingly, contrary to common belief, we find with a preferred soft hierarchy among the soft momentum $q$, on-shell residue $p_a^0 \pm E_a$, and $\varepsilon$, the soft theorems do not have dependence on unconstrained off-shell interactions, even in the presence of cubic vertices. We also argue that the soft hierarchy is a natural choice, ensuring the soft limit and on-shell limit commute. Our soft theorems depend solely on on-shell data and hold to all orders in perturbation theory. We present various examples including polynomial shift symmetries, non-linear realisation of Lorentz boosts and dilatations on how the soft theorems work. We find that the collection of exchange diagrams whose soft momenta are associated with cubic vertices, that are indeterminate in the soft limit, exhibits an enhanced soft scaling. The enhanced soft scaling explains why the sum of such diagrams do not enter the soft theorems non-trivially. We further apply the soft theorems to bootstrap the scattering amplitudes of the superfluid and scaling superfluid EFTs, finding agreement with the Hamiltonian analysis.