Non-linear matter power spectrum from Time Renormalisation Group: efficient computation and comparison with one-loop

TL;DR

This paper introduces an efficient semi-analytic module for computing the non-linear matter power spectrum using the Time Renormalization Group method, compares it with other approaches, and validates against simulations.

Contribution

It implements and optimizes the TRG method in the CLASS code, providing a fast, accurate tool for non-linear power spectrum calculation in LCDM models.

Findings

TRG results depend on initial bispectrum assumptions.

TRG and one-loop methods agree when starting from the same initial conditions.

All methods over-predict non-linear corrections compared to simulations.

Abstract

We address the issue of computing the non-linear matter power spectrum on mildly non-linear scales with efficient semi-analytic methods. We implemented M. Pietroni's Time Renormalization Group (TRG) method and its Dynamical 1-Loop (D1L) limit in a numerical module for the new Boltzmann code CLASS. Our publicly released module is valid for LCDM models, and optimized in such a way to run in less than a minute for D1L, or in one hour (divided by number of nodes) for TRG. A careful comparison of the D1L, TRG and Standard 1-Loop approaches reveals that results depend crucially on the assumed initial bispectrum at high redshift. When starting from a common assumption, the three methods give roughly the same results, showing that the partial resumation of diagrams beyond one loop in the TRG method improves one-loop results by a negligible amount. A comparison with highly accurate simulations by M. Sato & T. Matsubara shows that all three methods tend to over-predict non-linear corrections by the same amount on small wavelengths. Percent precision is achieved until k~0.2 h/Mpc for z>2, or until k~0.14 h/Mpc at z=1.