Cosmological functional renormalisation group, extended Galilean invariance and the sweeping effect

TL;DR

This paper applies the functional renormalisation group to cosmic structure formation, deriving flow equations influenced by extended Galilean invariance and the sweeping effect, providing insights into non-linear late-time universe dynamics.

Contribution

It introduces an extended symmetry related to Galilean invariance into the renormalisation group framework for cosmology, deriving related Ward identities and solving flow equations analytically.

Findings

Derived closed RG flow equations for two-point functions at small scales.

Connected the flow equations to the sweeping effect in turbulence.

Provided analytical solutions in a non-perturbative approximation.

Abstract

The functional renormalisation group is employed to study the non-linear regime of late-time cosmic structure formation. This framework naturally allows for non-perturbative approximation schemes, usually guided by underlying symmetries or a truncation of the theory space. An extended symmetry that is related to Galilean invariance is studied and corresponding Ward identities are derived. These are used to obtain (formally) closed renormalisation group flow equations for two-point correlation functions in the limit of large wave numbers (small scales). The flow equations are analytically solved in an approximation that is connected to the 'sweeping effect' previously described in the context of fluid turbulence.