Galilean invariant resummation schemes of cosmological perturbations

TL;DR

This paper develops Galilean invariant resummation schemes for cosmological perturbations, ensuring invariance under time-dependent boosts, and introduces methods to quantify and correct GI breaking in existing schemes.

Contribution

It derives non-perturbative constraints from GI, proposes a way to measure GI breaking, and formulates fully GI-respecting resummation schemes within the Time-Flow framework.

Findings

Derived non-perturbative GI constraints on correlation functions

Introduced a method to quantify GI breaking in perturbation schemes

Formulated GI-respecting resummation schemes within the TRG framework

Abstract

Many of the methods proposed so far to go beyond Standard Perturbation Theory break invariance under time-dependent boosts (denoted here as extended Galilean Invariance, or GI). This gives rise to spurious large scale effects which spoil the small scale predictions of these approximation schemes. By using consistency relations we derive fully non-perturbative constraints that GI imposes on correlation functions. We then introduce a method to quantify the amount of GI breaking of a given scheme, and to correct it by properly tailored counterterms. Finally, we formulate resummation schemes which are manifestly GI, discuss their general features, and implement them in the so called Time-Flow, or TRG, equations.