Generalised tensor fluctuations and inflation

TL;DR

This paper explores how breaking spatial diffeomorphism invariance in inflationary models affects tensor and scalar fluctuation spectra, revealing new possibilities for blue spectra and superhorizon curvature evolution.

Contribution

It introduces novel operators in effective field theory that break spatial diffeomorphisms, leading to unique inflationary signatures not previously considered.

Findings

Operators can produce a blue tensor spectrum without violating null energy condition

Scalar operators can cause non-conservation of curvature perturbation on superhorizon scales

Higher-derivative operators influence sound speed and mimic symmetry-breaking effects

Abstract

Using an effective field theory approach to inflation, we examine novel properties of the spectrum of inflationary tensor fluctuations, that arise when breaking some of the symmetries or requirements usually imposed on the dynamics of perturbations. During single-clock inflation, time-reparameterization invariance is broken by a time-dependent cosmological background. In order to explore more general scenarios, we consider the possibility that spatial diffeomorphism invariance is also broken by effective mass terms or by derivative operators for the metric fluctuations in the Lagrangian. We investigate the cosmological consequences of the breaking of spatial diffeomorphisms, focussing on operators that affect the power spectrum of fluctuations. We identify the operators for tensor fluctuations that can provide a blue spectrum without violating the null energy condition, and operators for scalar fluctuations that lead to non-conservation of the comoving curvature perturbation on superhorizon scales even in single-clock inflation. In the last part of our work, we also examine the consequences of operators containing more than two spatial derivatives, discussing how they affect the sound speed of tensor fluctuations, and showing that they can mimic some of the interesting effects of symmetry breaking operators, even in scenarios that preserve spatial diffeomorphism invariance.