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.
Highlights
Understanding how density fluctuations in cold dark matter evolve under the influence of gravity is at the basis of analyzing data on large-scale structures and of constraining cosmological models from them
We find that the renormalization group (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
With the derivation of (4.11), we have shown how this originally heuristic procedure emerges from the functional renormalization group
Summary
Understanding how density fluctuations in cold dark matter evolve under the influence of gravity is at the basis of analyzing data on large-scale structures and of constraining cosmological models from them. Unequal-time correlators exhibit a damping due to the stochastic background of large-scale bulk flows This effect can be rather accurately described within an ideal fluid dynamical framework by resumming certain classes of perturbative contributions related to long-wavelength perturbations [15, 16]. In this way, the dependence on the coarse-graining scale of the non-perturbative parameters entering the effective dynamics of large-scale structure can be described explicitly by a set of coupled ordinary differential equations.
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