Location: Helsinki Institute for Physics.
In this talk I will describe progresses in considering general relativistic effects in the dynamics of structure formation in cosmology. First I will briefly describe results obtained with a nonlinear post-Friedman approach, a kind of post-Newtonian formalism, results validated and extended by others. Then I will focus on recent full numerical relativity simulations in cosmology. The recent detections of gravitational waves and of binary black holes have validated the accuracy of numerical relativity codes that are now publicly available. The application of numerical relativity to cosmology is in its infancy, but in the next few years can be a fundamental tool to understand to which extent we can have reliable predictions from standard newtonian N-body simulations; it is indeed clear that, to match the precision of future cosmological measurements, we need theoretical predictions that are not only equally precise, but also accurate at the same level. I will illustrate the first results of these numerical relativity simulations, representing the fully nonlinear GR evolution of perturbations in a Einstein de Sitter background: 1) we find that back-reaction effects on the overall expansion of the mode are tiny; 2) voids expansion rate is significantly higher than that of the background and close to that of an open universe; 3) over-densities can reach turn-around much earlier than predicted by the standard top-hat model. I will conclude with an outline of future work that is needed to establish the real significance of these results.