Perturbation theory challenge for cosmological parameters estimation II.: Matter power spectrum in redshift space

Abstract: Constraining cosmological parameters from large-scale structure observations requires precise and accurate tools to compute its properties. While perturbation theory (PT) approaches can serve this purpose, exploration of large parameter space is challenging due to the potentially large computational cost of such calculations. In this study, we show that a response function approach applied to the regularized PT (RegPT) model at 2-loop order, plus correction terms induced by redshift space distortion effects, can reduce the runtime by a factor of 50 compared to direct integration. We illustrate the performance of this approach by performing the parameter inference of five fundamental cosmological parameters from the redshift space power spectrum measured from $N$-body simulations as mock measurements, and inferred cosmological parameters are directly compared with parameters used to generate initial conditions of the simulations. From this \textit{PT challenge} analysis, the constraining power of cosmological parameters and parameter biases are quantified with the survey volume and galaxy number density expected for the \textit{Euclid} mission at the redshift $z = 1$ as a function of the maximum wave-number of data points $k_\mathrm{max}$. We find that RegPT with correction terms reproduces the input cosmological parameters without bias up to maximum wave-number $k_\mathrm{max}= 0.18 \, h\,\mathrm{Mpc}^{-1}$. Moreover, RegPT+, which introduces one free parameter to RegPT to handle the damping feature on small scales, delivers the best performance among the examined models and achieves tighter constraints without significant parameter bias for higher maximum wave-number $k_\mathrm{max} = 0.21 \, h\,\mathrm{Mpc}^{-1}$.