Relativistic galaxy number counts to second order: bispectrum

In this talk, I will present the evaluation of the galaxy number counts to second order in cosmological perturbation theory in the Poisson gauge. The calculation is performed using an innovative approach based on the recently proposed ”geodesic light-cone” gauge, which allows us to determine the number counts in a purely geometric way. 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.