On the range of validity of perturbative models for galaxy clustering and its uncertainty

TL;DR

This study assesses the validity range of one-loop perturbative models for galaxy clustering in redshift space, revealing that the model's accuracy diminishes with larger simulation volumes and that uncertainties in the reach are significant.

Contribution

It introduces a comprehensive framework to evaluate the validity of perturbative models using multiple diagnostics and explores the impact of simulation volume on model accuracy and parameter estimation.

Findings

Median model reach decreases with larger simulation volumes.

Significant uncertainty exists in the model's reach, with potential reductions up to 40%.

Adding hexadecapole information yields minimal improvement in growth rate estimation.

Abstract

We explore the reach of analytical models at one-loop in Perturbation Theory (PT) to accurately describe measurements of the galaxy power spectrum from numerical simulations in redshift space. We consider the validity range in terms of three different diagnostics: 1) the goodness of fit; 2) a figure-of-bias quantifying the error in recovering the fiducial value of a cosmological parameter; 3) an internal consistency check of the theoretical model quantifying the running of the model parameters with the scale cut. We consider different sets of measurements corresponding to an increasing cumulative simulation volume in redshift space. For each volume we define a median value and the associated scatter for the largest wavenumber where the model is valid (the $k$-reach of the model). We find, as a rather general result, that the median value of the reach decreases with the simulation volume, as expected since the smaller statistical errors provide a more stringent test for the model. This is true for all the three definitions considered, with the one given in terms of the figure-of-bias providing the most stringent scale cut. More interestingly, we find as well that the error associated with the $k$-reach value is quite large, with a significant probability of being as low as 0.1$\, h \, {\rm Mpc}^{-1}$ (or, more generally, up to 40% smaller than the median) for all the simulation volumes considered. We explore as well the additional information on the growth rate parameter encoded in the power spectrum hexadecapole, compared to the analysis of monopole and quadrupole, as a function of simulation volume. While our analysis is, in many ways, rather simplified, we find that the gain in the determination of the growth rate is quite small in absolute value and well within the statistical error on the corresponding figure of merit.