A Closure Theory for Non-linear Evolution of Cosmological Power Spectra

TL;DR

This paper introduces a closure theory approach from turbulence applied to cosmological perturbation theory, deriving equations that accurately model non-linear matter power spectra and match established renormalized results.

Contribution

It develops a novel closure framework for non-linear cosmological evolution, providing analytic solutions that align with previous renormalized perturbation theory results.

Findings

Closure equations recover one-loop perturbation results

Analytic integral expressions match renormalized one-loop spectra

Non-linear power spectra evaluated via first-order Born approximation

Abstract

We apply a non-linear statistical method in turbulence to the cosmological perturbation theory and derive a closed set of evolution equations for matter power spectra. The resultant closure equations consistently recover the one-loop results of standard perturbation theory and beyond that, it is still capable of treating the non-linear evolution of matter power spectra. We find the exact integral expressions for the solutions of closure equations. These analytic expressions coincide with the renormalized one-loop results presented by Crocce & Scoccimarro (2006,2007). By constructing the non-linear propagator, we analytically evaluate the non-linear matter power spectra based on the first-order Born approximation of the integral expressions and compare it with those of the renormalized perturbation theory.