Galaxy number counts at second order: an independent approach
  Next generation surveys will be capable of determining cosmological
parameters beyond percent level. To match this precision, theoretical
descriptions should look beyond the linear perturbations to approximate the
observables in large scale structure. A quantity of interest is the Number
density of galaxies detected by our instruments. This has been focus of
interest recently, and several efforts have been made to explain relativistic
effects theoretically, thereby testing the full theory. However, the results at
nonlinear level from previous works are in disagreement. We present a new and
independent approach to computing the relativistic galaxy number counts to
second order in cosmological perturbation theory. We derive analytical
expressions for the full second order relativistic observed redshift, for the
angular diameter distance and for the volume spanned by a survey. Finally, we
compare our results with previous works which compute the general
distance-redshift relation, finding that our result is in agreement at linear
order.
