General relativistic effects in large scale galaxy clustering

The size of galaxy redshift surveys has constantly increased over the latest years in terms of solid angle and redshift coverage; therefore, the future large-volume galaxy surveys (e.g. SKA, Euclid) will allow us to measure galaxy clustering on scales comparable with the Hubble radius. For such large scales and at high redshifts, general relativistic effects alter the observed galaxy number overdensity through projection onto our past lightcone. They consist mainly in redshift space distortions and gravitational lensing convergence; however, further corrections may now be measured and should be taken into account, including Doppler, standard and integrated Sachs-Wolfe effect, and time delay contributions. These corrections lead to new terms in wide-angle two-point correlation functions, going beyond the plane-parallel and Newtonian approach. The aim of this thesis is to investigate and compute the full general relativistic expression for the angular correlation functions, including all redshift-space distortions, wide-angle, lensing and gravitational potential effects on linear scales. In particular, this angular power spectrum is written in order to generalise the 2-FAST algorithm recently developed in literature, which circumvents the direct integration of highly oscillating spherical Bessel functions. The Limber's approximation is also applied for large multipole moments l in order to give a simplified expression of the angular power spectrum, more suitable for further numerical integration.