Assessing non-linear models for galaxy clustering – II. Model validation and forecasts for Stage IV surveys

Abstract

We provide a detailed comparison of two different models for the halo redshift space power spectrum, namely the commonly applied TNS model and an effective field theory of large scale structure (EFTofLSS) inspired model. In a least χ 2 analysis using simulation data, we determine ranges of validity for the models. In all our analyses we vary all nuisance parameters and the growth rate of structure, f , using survey specifications typical of Stage IV galaxy surveys. We determine that the TNS model with a Lorentzian damping and using standard Eulerian perturbative modelling outperforms other variants of the TNS model. But we also find that the EFTofLSS-based model is able to fit the data down to smaller scales compared to this optimal TNS variant at z = 0.5, while the two models perform equally well at z = 1. We then conduct an exploratory Fisher analysis to investigate parameter degeneracies, using the full anisotropic power spectrum. Next, we move on to a Bayesian MCMC analysis utilising the monopole, quadrupole, and hexadecapole spectra, with a restricted range of scales for the latter in order for the f constraints to remain unbiased. In contrast to the exploratory Fisher matrix forecasts, our MCMC analysis finds that the EFTofLSS-based model provides tighter marginalised constraints on the growth rate at z = 0.5 than the TNS model, despite having additional nuisance parameters. The two perform comparatively at z = 1. We also investigate the impact of priors on nuisance parameters which can be reasonably obtained from higher order statistics or external data sets. We find that conservative priors have limited impact on the constraints. Finally, we extend previous work to provide a consistent comparison between Fisher matrix and MCMC forecasts for the EFTofLSS model using the multipole expansion formalism, and reach good agreement between them.

Nonlinear contributions to angular power spectra

“…The values of the counter term coefficients have been determined by fitting to the COLA simulations. This follows a similar procedure to [29]. We refer the reader to this work for justifications and details of this procedure.…”

“…This model was introduced in [16] and is one of the best approaches to perturbation theory known at present, having been applied in the recent BOSS galaxy clustering analysis [4,8]. It has also been thoroughly validated against simulations and has stood up to other perturbative models [9,18,20,29,47,[56][57][58][59][60][61]. The model is given by [16]…”

“…We refer the reader to [16,29] for a detailed description of the components A, B and C of the model but we give some basic expressions in Appendix B.…”

“…One key reason for the poor fit at µ = 1 is the lack of damping within the SPT spectrum which the EFT counter terms cannot suppress efficiently. The inclusion of resummation is expected to improve the fit (see for example [29]) but we leave this to future work.…”

“…[26][27][28]) that have a very high redshift resolution, it is important to model the theoretical galaxy power spectrum as accurately as possible. Even at scales as large as those of baryon acoustic oscillations, we need to go beyond linear perturbation theory [8,29].…”