Renormalization-group flow of the effective action of cosmological large-scale structures

TL;DR

This paper develops a renormalization group approach to study the effective dynamics of cosmological large-scale structures, enabling controlled predictions of matter and velocity spectra by accounting for small-scale interactions.

Contribution

It introduces a non-perturbative RG framework for cosmological structures, deriving flow equations for effective viscosity and sound velocity, and demonstrates IR attractor behavior reducing UV sensitivity.

Findings

RG flow exhibits IR attractor behavior

Effective viscosity and sound velocity become less dependent on UV initial conditions

Self-contained computation of matter and velocity power spectra

Abstract

Following an approach of Matarrese and Pietroni, we derive the functional renormalization group (RG) flow of the effective action of cosmological large-scale structures. Perturbative solutions of this RG flow equation are shown to be consistent with standard cosmological perturbation theory. Non-perturbative approximate solutions can be obtained by truncating the a priori infinite set of possible effective actions to a finite subspace. Using for the truncated effective action a form dictated by dissipative fluid dynamics, we derive RG flow equations for the scale dependence of the effective viscosity and sound velocity of non-interacting dark matter, and we solve them numerically. Physically, the effective viscosity and sound velocity account for the interactions of long-wavelength fluctuations with the spectrum of smaller-scale perturbations. We find that the RG flow exhibits an attractor behaviour in the IR that significantly reduces the dependence of the effective viscosity and sound velocity on the input values at the UV scale. This allows for a self-contained computation of matter and velocity power spectra for which the sensitivity to UV modes is under control.