Euclid preparation. CXV. Galaxy power spectrum and bispectrum modelling

Higher-order correlation functions of the large-scale galaxy distribution offer access to information beyond that contained in standard two-point statistics, such as the power spectrum. In this work we assess the potential of the Euclid mission to provide such functions using synthetic catalogues of H,α galaxies based on the 54Ģpc Flagship 1 simulation, which is designed to reproduce the 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 yielded unbiased cosmological constraints for the bispectrum up to ̊m max = 0.15̨Mpc in real space and 0.08 , (0.1)̨Mpc 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. A simple rescaling of the statistical uncertainties to a Euclid -like volume indicates similar conclusions, highlighting the additional information gain from the bispectrum for the forthcoming data. Our analysis also provides the first detailed characterisation of the non-linear bias model of H,α emitters, showing that bias relations calibrated on low-resolution N-body simulations do not adequately describe the clustering of H,α galaxies at low redshift, whereas excursion-set and co-evolution relations for tidal biases remain accurate. Finally, we benchmarked six independent modelling codes, finding excellent agreement under matched assumptions, which testifies to the robustness of our results and provides a benchmark for the official analysis pipeline. Euclid