Testing General Relativity with Relativistic Redshift-Space Distortions in Clustering Statistics

The large-scale structure of the Universe offers a powerful probe of fundamental cosmological information on structure formation, dark matter and dark energy content. Clustering statistics, in particular the 2-point auto-correlation function and the 2-point cross-correlation function, are among the most widely used tools in this field. The observed number density of tracers of the matter field is affected by several perturbative effects, which induce distortions in the redshift. While the dominant contribution arises from cosmological expansion, further corrections, such as peculiar velocities, must be included to avert misinterpretations. Recent studies point towards modelling first-order relativistic effects, These corrections can induce a dipole signal in the cross-correlation between differently biased populations. This thesis aims to validate state-of-the art models of the various contributions to the large-scale dipole signal in the cross-correlation function at large scales. Disentangling all the different contributions in real survey is non-trivial, requiring both high-precision redshift measurements and very large data sets. This work relies on numerical simulations. We used, in particular, the full-sky light-cone realisation of the RayGalGroupSims numerical simulation suite. Adopting a fiducial Λ-cold dark matter (ΛCDM) model based on general relativity, we find that the dipole is largely dominated by the relativistic Doppler term over all the scales considered. After modelling different contributions, the resulting reduced chi-squared values falled within the range [0.3, 2.9] for all tested configurations, but for potential terms. We finally perform Markov Chain Monte Carlo (MCMC) fits for two cross-correlation cases, constraining the linear growth rate f and bias parameters, and compare the results with those from the auto-correlation. Agreement with model predictions is discussed in light of the obtained constraints.