Euclid preparation. Galaxy power spectrum and bispectrum modelling

TL;DR

This study validates perturbation theory models for galaxy power spectrum and bispectrum using Euclid-like simulations, demonstrating their potential to enhance cosmological parameter constraints.

Contribution

It provides the first detailed validation of bispectrum modeling for Euclid Hα galaxy samples, showing its significant impact on cosmological constraints.

Findings

Bispectrum modeling yields unbiased cosmological constraints up to specified scales.

Adding bispectrum improves constraints on scalar perturbations and matter density by up to 30%.

Bias models calibrated on low-resolution simulations are inadequate for low-redshift Hα galaxies.

Abstract

Higher-order correlation functions of the large-scale galaxy distribution offer access to information beyond that contained in standard 2-point statistics such as the power spectrum. In this work we assess this potential for the $\textit{Euclid}$ mission using synthetic catalogues of H$\alpha$ galaxies based on the 54 $\, h^{-3} \, {\rm Gpc}^3$ Flagship I simulation, designed to reproduce the $\textit{Euclid}$ spectroscopic sample. We comprehensively validate the one-loop galaxy power spectrum and tree-level bispectrum predictions from perturbation theory in both real and redshift space. Assuming scale cuts consistent with our previous power spectrum study on the same catalogues, this modelling yields unbiased cosmological constraints for the bispectrum up to $k_{\rm max} = 0.15\,\, h \, {\rm Mpc}^{-1}$ in real space and $0.08 \, (0.1)\,\, h \, {\rm Mpc}^{-1}$ at the lowest (highest) redshift, corresponding to $z=0.9$ ($z=1.8$), for the monopole and quadrupole in redshift space using statistical uncertainties corresponding to the full simulation volume. With these scale cuts, adding bispectrum information to the power spectrum improves constraints on the amplitude of scalar perturbations and the matter density by up to 30 %, increasing the overall figure of merit for key cosmological parameters by a factor of about 2.5. Similar conclusions hold when statistical uncertainties are rescaled to a $\textit{Euclid}$-like volume, highlighting the importance of the bispectrum for fully exploiting the forthcoming $\textit{Euclid}$ data. Our analysis also provides the first detailed characterisation of the nonlinear bias model of H$\alpha$ emitters, showing that bias relations calibrated on low-resolution \textit{N}-body simulations do not adequately describe the clustering of H$\alpha$ galaxies at low redshift, whereas excursion-set and co-evolution relations for tidal biases remain accurate.