Breaking discrete symmetries in the effective field theory of inflation

TL;DR

The paper investigates breaking discrete symmetries during inflation within the model-independent EFT of inflation, allowing simultaneous breaking of time and spatial diffeomorphisms and a small background anisotropy in the EMT. It classifies the leading quadratic operators that violate parity and time-reversal, and analyzes their impact on linearized fluctuations. The main results are the absence of propagating vector modes at linear order in the anisotropy, a direction-dependent phase in the scalar sector, and a chiral phase in the tensor sector, with potential higher-order observational signatures despite unchanged power spectra. These findings open avenues for signatures in non-Gaussianity and tensor correlations, motivating further work on the third-order action and concrete realizations.

Abstract

We study the phenomenon of discrete symmetry breaking during the inflationary epoch, using a model-independent approach based on the effective field theory of inflation. We work in a context where both time reparameterization symmetry and spatial diffeomorphism invariance can be broken during inflation. We determine the leading derivative operators in the quadratic action for fluctuations that break parity and time-reversal. Within suitable approximations, we study their consequences for the dynamics of linearized fluctuations. Both in the scalar and tensor sectors, we show that such operators can lead to new direction-dependent phases for the modes involved. They do not affect the power spectra, but can have consequences for higher correlation functions. Moreover, a small quadrupole contribution to the sound speed can be generated.