Impact of bias and redshift-space modelling for the halo power spectrum: Testing the effective field theory of large-scale structure

TL;DR

This study evaluates how different bias and redshift-space models affect the halo power spectrum fit, finding that more complex models improve fit quality but with diminishing returns, guiding model choice for future galaxy surveys.

Contribution

It systematically compares various bias and redshift-space models, including effective field theory, to determine optimal modeling strategies for the halo power spectrum.

Findings

More permissive models improve chi-square but show diminishing returns.

Standard perturbation theory up to one-loop provides a good balance between fit quality and complexity.

Evidence of overfitting appears with the most complex models.

Abstract

We study the impact of different bias and redshift-space models on the halo power spectrum, quantifying their effect by comparing the fit to a subset of realizations taken from the WizCOLA suite. These provide simulated power spectrum measurements between $k_{\rm min}$ = 0.03 h/Mpc and $k_{\rm max}$ = 0.29 h/Mpc, constructed using the comoving Lagrangian acceleration method. For the bias prescription we include (i) simple linear bias; (ii) the McDonald & Roy model and (iii) its coevolution variant introduced by Saito et al.; and (iv) a very general model including all terms up to one-loop and corrections from advection. For the redshift-space modelling we include the Kaiser formula with exponential damping and the power spectrum provided by (i) tree-level perturbation theory and (ii) the Halofit prescription; (iii) one-loop perturbation theory, also with exponential damping; and (iv) an effective field theory description, also at one-loop, with damping represented by the EFT subtractions. We quantify the improvement from each layer of modelling by measuring the typical improvement in chi-square when fitting to a member of the simulation suite. We attempt to detect overfitting by testing for compatibility between the best-fit power spectrum per realization and the best-fit over the entire WizCOLA suite. For both bias and the redshift-space map we find that increasingly permissive models yield improvements in chi-square but with diminishing returns. The most permissive models show modest evidence for overfitting. Accounting for model complexity using the Bayesian Information Criterion, we argue that standard perturbation theory up to one-loop, or a related model such as that of Taruya, Nishimichi & Saito, coupled to the coevolution bias model, is likely to provide a good compromise for near-future galaxy surveys operating with comparable $k_{\rm max}$.