ISO(4,1) Symmetry in the EFT of Inflation

TL;DR

This paper demonstrates that the ISO(4,1) symmetry in the EFT of inflation constrains the cubic interactions and correlation functions, linking them to the speed of sound and revealing symmetry origins of inflationary dynamics.

Contribution

It shows that the ISO(4,1) symmetry uniquely determines the cubic action in the EFT of inflation, connecting it to the Goldstone mode and the speed of sound c_s.

Findings

ISO(4,1) symmetry constrains cubic interactions

Correlation functions depend on the speed of sound c_s

ISO(4,1) reduces to Galilean symmetry as c_s approaches 1

Abstract

In DBI inflation the cubic action is a particular linear combination of the two, otherwise independent, cubic operators \dot \pi^3 and \dot \pi (\partial_i \pi)^2. We show that in the Effective Field Theory (EFT) of inflation this is a consequence of an approximate 5D Poincar\'e symmetry, ISO(4,1), non-linearly realized by the Goldstone \pi. This symmetry uniquely fixes, at lowest order in derivatives, all correlation functions in terms of the speed of sound c_s. In the limit c_s \to 1, the ISO(4,1) symmetry reduces to the Galilean symmetry acting on \pi. On the other hand, we point out that the non-linear realization of SO(4,2), the isometry group of 5D AdS space, does not fix the cubic action in terms of c_s.