Euclid preparation. Simulated galaxy catalogues for non-standard cosmological models

Stage-IV galaxy surveys will provide the opportunity to test cosmological models and the underlying theory of gravity with unparalleled precision. In this context, it is crucial for the Euclid mission to leverage its spectroscopic and photometric probes to systematically investigate and incorporate non-standard cosmological models, including modified gravity, alternative dark energy scenarios, massive neutrinos, and primordial non-Gaussianity. We produce and release publicly simulated galaxy catalogues from a broad suite of non-standard cosmological simulations, which we processed through a model-independent analytical pipeline, making use of Rockstar for halo identification, and a modified version of the SciPic library for the galaxy-halo connection using the halo occupation distribution framework. We investigate their galaxy-clustering characteristics via the multipoles of the 2PCF in redshift space and VDG, a highly performant model for galaxy clustering. Across a wide range of models, the linear growth rate multiplied by the matter density within spheres of radius 12,Mpc, fs12, exhibits a notable robustness to the choice of cosmological template. Compared to previous works, our study extends this result to numerous scenarios with markedly distinct gravitational or dark energy dynamics. We find that the most of the scatter in cosmological parameter inference already appears when using the cosmological model of the simulations as templates. Using a `wrong' template can also introduce an additional scatter, although with smaller amplitude. Often, we find deviations much larger than error bars, meaning that the Gaussian approximation for the covariance might need to be further studied. Future cosmological investigations must broaden their scope to include a diverse array of non-standard theoretical frameworks, extending beyond LCDM and rudimentary dynamic dark energy models.