Galaxy number counts to second order via geodesic light-cone coordinates

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 talk, I will present a new coordinate system, called geodesic light-cone (GLC) coordinates, useful to take in account such non-linear effects. I will show how, using the GLC gauge, one can solve non-perturbative the geodesic deviation equation, obtain an exact solution of the Jacobi Map and, through a coordinate transformation, obtain perturbative expression for cosmological observables in the Poisson gauge. In particular, I will present the evaluation of the galaxy number counts to second order in cosmological perturbation theory.