Cosmology with relativistic effects

Since the 1970s, the size of galaxy catalogs has constantly increased in terms of solid-angle and redshift coverage as well as in sampling rate. The next generation of surveys will provide us with the possibility to measure galaxy clustering on scales comparable with the Hubble radius (for example: Euclid, DESI, SKAII, etc.). Theoretical analysis suggests that several relativistic effects might be detectable on these scales. In order to fully exploit the potential of the new datasets, it is therefore imperative to develop analysis tools that include these effects. I have developed a fully general relativistic formalism which recovers and generalizes previous results in the plane-parallel (at-sky) and Newtonian wide-angle approximations. These corrections become important on large scales both at low and high redshifts, and lead to new terms in the wide-angle correlations. Now we need to work out how to apply this formalism for real data and understand which cosmological parameters are particularly affected. This will be important for future surveys and to guide the development on the next generation of large astrophysical experiments.