Interact or Twist: Cosmological Correlators from Field Redefinitions Revisited

TL;DR

This paper demonstrates that local field redefinitions in cosmology can produce correlators identical to bulk interactions, revealing overlooked operators that could impact primordial signals like the Higgs in inflation.

Contribution

It provides a counterexample showing that field redefinitions can mimic bulk interactions in cosmological correlators, challenging previous distinctions.

Findings

Correlators from local field redefinitions can match bulk interaction results.

Field redefinitions can produce contact correlators with a total-energy singularity.

Overlooked lower-dimensional operators may generate observable signals in cosmology.

Abstract

In cosmology, correlation functions on a late-time boundary can arise from both field redefinitions and bulk interactions, which are usually believed to generate distinct results. In this letter, we propose a counterexample showcasing that correlators from local field redefinitions can be identical to the ones from bulk interactions. In particular, we consider a two-field model in de Sitter space, where the field space gets twisted by field redefinitions to yield a nontrivial reheating surface. We then exploit conformal symmetry to compute the three-point function, and show that the result takes the form of contact correlators with a total-energy singularity. Our finding suggests that in the effective field theory, a class of lower-dimensional operators, which were overlooked previously, may lead to nontrivial signals in cosmological correlators. As an illustration, we apply our result to cosmic inflation and derive a possibly leading signature of the Higgs in the primordial bispectrum.