Euclid preparation. Simulating thousands of Euclid spectroscopic skies

We present two extensive sets of 3500+1000 simulations of dark matter haloes on the (past-)light-cone, and two corresponding sets of simulated (‘mock’) galaxy catalogues that represent the Euclid spectroscopic sample. The simulations were produced with the latest version of thePinocchio code, and provide the largest, public set of simulated skies. Mock galaxy catalogues were obtained by populating haloes with galaxiesusing an halo occupation distribution (HOD) model extracted from the Flagship galaxy catalogue provided by Euclid Collaboration. The Geppettoset of 3500 simulated skies is obtained by tiling a 1.2 h−1 Gpc box to cover a light-cone whose sky footprint is a circle of 30◦radius, for an areaof 2763 deg2and a minimum halo mass of 1.5 × 1011 h−1 Mpc. The relatively small box size makes this set unfit for measuring very large scales.The EuclidLargeBox set consists in 1000 simulations of 3.38 h−1 Gpc, with the same mass resolution and a footprint that covers half of the sky.From this we produced a set of 1000 EuclidLargeMocks on the 30◦radius footprint, whose comoving volume is fully contained in the simulationbox. We validate the two sets of catalogues by analysing number densities, power spectra, and 2-point correlation functions, showing that theFlagship spectroscopic catalogue is consistent with being one of the realisations of the simulated sets, with little deviations of the quadrupole atk > 0.2 h Mpc−1. We infer cosmological parameters from these catalogues and demonstrate that using one realisation of EuclidLargeMocks inplace of the Flagship produces the same posteriors, to within the expected shift given by sample variance. These simulated skies will be used forthe galaxy clustering analysis of Euclid’s Data Release 1 (DR1).Key words. Methods: numerical; Surveys; Cosmology: observations; Large-scale structure of Universe; Cosmological parameters