Galaxy number counts to second order via geodesic light-cone coordinates: theory and application

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 non-linear and relativistic effects can play a key role. In this seminar, I will present a new coordinate system, called geodesic light-cone (GLC) coordinates, useful to take in account such non-linear effects. In particular, I will show how, using the GLC gauge, one can determine the galaxy number counts in a purely geometric way, and up to second order in cosmological perturbation theory in the Poisson gauge. To conclude, I will present the numerical results for the leading non-linear and relativistic contributions to the number counts bispectrum, comparing  them with the usual term from weakly non-linear Newtonian gravitational clustering and showing how to neglect integrated relativistic terms can bring significant bias.