Relativistic effects in cosmology: from the evaluation of H0 local to the galaxy number count bispectrum

In the near future cosmology will enter a new era in which the use of Newtonian gravity will no longer be sufficient in studying large scale structure (LSS). The next generation of LSS survey will probe the Universe with high precision and at very different scales, where relativistic effects can play a key role. In this seminar, I will present two cases in which such relativistic effects play a role. First, I will show how local measurements of the Hubble expansion rate are affected by structures like galaxy clusters or voids, presenting a fully relativistic treatment of this effect. Then, after having shown how to evaluate the galaxy number counts to second order in cosmological perturbation theory, using the non-perturbative result obtained in the recently proposed ”geodesic light-cone” gauge, I will evaluate the probably most important new terms in the number count bispectrum, comparing the outcome with the usual term from weakly non-linear Newtonian gravitational clustering.