Euclid Preparation. XLIV. Modelling Spectroscopic Clustering on Mildly Nonlinear Scales in Beyond-Lcdm Models

The space satellite mission will measure the large-scale clustering of galaxies at an unprecedented precision, providing a unique probe of modifications to the Lambda CDM model. We investigated the approximations needed to efficiently predict the large-scale clustering of matter and dark matter halos in the context of modified gravity and exotic dark energy scenarios. We examined the normal branch of the Dvali--Gabadadze--Porrati model, the Hu--Sawicki $f(R)$ model, a slowly evolving dark energy model, an interacting dark energy model, and massive neutrinos. For each, we tested approximations for the perturbative kernel calculations, including the omission of screening terms and the use of perturbative kernels based on the Einstein--de Sitter universe; we explored different infrared-resummation schemes, tracer bias models and a linear treatment of massive neutrinos; we investigated various approaches for dealing with redshift-space distortions and modelling the mildly nonlinear scales, namely the Taruya--Nishimishi--Saito prescription and the effective field theory of large-scale structure. This work provides a first validation of the various codes being considered by for the spectroscopic clustering probe in beyond-Lambda CDM scenarios. We calculated and compared the $ statistic to assess the different modelling choices. This was done by fitting the spectroscopic clustering predictions to measurements from numerical simulations and perturbation theory-based mock data. We compared the behaviour of this statistic in the beyond-Lambda CDM cases, as a function of the maximum scale included in the fit, to the baseline Lambda CDM case. We find that the Einstein--de Sitter approximation without screening is surprisingly accurate for the modified gravity cases when comparing to the halo clustering monopole and quadrupole obtained from simulations and mock data. Further, we find the same goodness-of-fit for both cases -- the one including and the one omitting non-standard physics in the predictions. Our results suggest that the inclusion of multiple redshift bins, higher-order multipoles, higher-order clustering statistics (such as the bispectrum), and photometric probes such as weak lensing, will be essential to extract information on massive neutrinos, modified gravity and dark energy. Additionally, we show that the three codes used in our analysis, namely PBJ Pybird and MG-Copter exhibit sub-percent agreement for $k Mpc $ across all the models. This consistency underscores their value as reliable tools.