Safely smoothing spacetime: backreaction in relativistic cosmological simulations

A persistent theme in the study of dark energy is the question of whether it really exists or not. It is often claimed that we are mis-calculating the cosmological model by neglecting the effects associated with averaging over large-scale structures. In the Newtonian approximation this is clear: there is no effect. Within the full relativistic picture this remains an important open question, owing to the complex mathematics involved. We study this issue using numerical N-body simulations which account for all relevant relativistic effects without any problems from shell crossing. In this context we show for the first time that the backreaction from structure can differ by many orders of magnitude depending upon the slicing of spacetime one chooses to average over. In the worst case, where smoothing is carried out in synchronous spatial surfaces, the corrections can reach ten percent and more. However, when smoothing on the constant time hypersurface of the Newtonian gauge, backreaction contributions remain 3–5 orders of magnitude smaller. (paper)