The Effective Theory of Shift-Symmetric Cosmologies

TL;DR

This paper derives model-independent observable consequences of an exact shift symmetry in single-clock cosmologies, revealing relations among effective coefficients that could help identify shift symmetry in nature.

Contribution

It establishes the first set of relations among effective field theory coefficients under shift symmetry, reducing the free parameters to a single function in certain cases.

Findings

Relations among effective coefficients linking non-Gaussianity to their time dependence

Reduction of free functions to a single one at leading order in derivatives

Application to superfluids coupled to gravity and driven superfluids

Abstract

A shift symmetry is a ubiquitous ingredient in inflationary models, both in effective constructions and in UV-finite embeddings such as string theory. It has also been proposed to play a key role in certain Dark Energy and Dark Matter models. Despite the crucial role it plays in cosmology, the observable, model independent consequences of a shift symmetry are yet unknown. Here, assuming an exact shift symmetry, we derive these consequences for single-clock cosmologies within the framework of the Effective Field Theory of Inflation. We find an infinite set of relations among the otherwise arbitrary effective coefficients, which relate non-Gaussianity to their time dependence. For example, to leading order in derivatives, these relations reduce the infinitely many free functions in the theory to just a single one. Our Effective Theory of shift-symmetric cosmologies describes, among other systems, perfect and imperfect superfluids coupled to gravity and driven superfluids in the decoupling limit. Our results are the first step to determine observationally whether a shift symmetry is at play in the laws of nature and whether it is broken by quantum gravity effects.