Testing dynamic distortion models to infer the linear growth rate from clustering multipoles

Redshift-space distortions in galaxy clustering is one of the main probes to test General Relativity on the largest cosmological scales. In this Thesis work we investigate state-of-the-art models of galaxy clustering to validate their accuracy in constraining the linear growth rate of cosmic structures from dynamic distortions in the two-point correlation function multipole moments. The redshift-space distortion models are tested on Euclid-like mock catalogues, which mimic the precision expected from the Euclid Space Telescope spectroscopic wide survey, using Bayesian statistics, at four different redshifts z=1.79, 1.53, 1.19, and 0.9. Moreover, we investigate the accuracy of the linear growth rate constraints for different values of the minimum scale used in the fit, rmin, up to a maximum scale of rmax=200 h^{-1} Mpc. Comparing the results obtained from the different models, we found that the extended-Taruya-Nishimichi-Saito (eTNS) model is the most accurate one, being consistent within about 1sigma at all redshifts, and for rmin= 30 h^{-1} Mpc. Thus we conclude that the eTNS model is sufficiently accurate for analysing the data sets of next-generation projects, allowing us to push the analysis down to mildly nonlinear scales. The whole statistical analysis done in this Thesis has been performed with the CosmoBolognaLib, a free software set of numerical libraries for different types of cosmological calculations.