Perturbation theory challenge for cosmological parameters estimation: Matter power spectrum in real space

TL;DR

This paper evaluates the accuracy of analytical perturbation theories in estimating cosmological parameters from the matter power spectrum in real space at weakly nonlinear scales, using N-body simulations and MCMC methods.

Contribution

It compares standard, regularized, and effective field theory perturbation methods for parameter estimation, identifying the most effective approach at redshift 1.

Findings

Two-loop calculations fit the measured power spectrum down to k ~ 0.2 h/Mpc.

Regularized perturbation theory with one free parameter yields the highest FoM.

All models provide unbiased parameter estimates within their validity range.

Abstract

We study the accuracy with which cosmological parameters can be determined from real space power spectrum of matter density contrast at weakly nonlinear scales using analytical approaches. From power spectra measured in $N$-body simulations and using Markov chain Monte-Carlo technique, the best-fitting cosmological input parameters are determined with several analytical methods as a theoretical template, such as the standard perturbation theory, the regularized perturbation theory, and the effective field theory. We show that at redshift 1, all two-loop level calculations can fit the measured power spectrum down to scales $k \sim 0.2 \, h \, \mathrm{Mpc}^{-1}$ and cosmological parameters are successfully estimated in an unbiased way. Introducing the Figure of bias (FoB) and Figure of merit (FoM) parameter, we determine the validity range of those models and then evaluate their relative performances. With one free parameter, namely the damping scale, the regularized perturbation theory is found to be able to provide the largest FoM parameter while keeping the FoB in the acceptance range.