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

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.

In revised version, affiliations corrected

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• General relativistic non-ideal fluid equations for dark matter from a truncated cumulant expansion
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• Kinetic Field Theory: Perturbation theory beyond first order
• Gravitational Wave luminosity distance in viscous cosmological models
• Cosmological functional renormalisation group, extended Galilean invariance and the sweeping effect
• Cosmic structure from the path integral of classical mechanics and its comparison to standard perturbation theory
• Backreaction from inhomogeneous matter fields during large-scale structure formation