Nonlinear Relativistic effects in Structure Formation in ΛCDM

In this talk I will give an overview of work on nonlinear structure formation in ΛCDM in the context of General Relativity (GR). Starting from briefly presenting a post-Friedmann approximation (similar to post-Minkowski, but on a cosmological background and assuming small peculiar velocities), I will show how at leading order the gravito-magnetic effect (AKA frame-dragging) can be extracted from standard Newtonian N-body simulations, as well as from N-body simulations with GRAMSES, an approximate GR code. In this context, one can conjecture about going beyond-leading order with the aim of computing  the  gravitational wave background.

I will then present full-GR simulations of a toy-model “cosmic web” of over-densities,  voids and filaments with the Einstein Toolkit fluid code, showing how the first shell-crossing at peaks of over-densities is very well predicted by the simple "top hat" model, while in the formation of the cosmic web a role is played by gravito-magnetism, especially around filaments. In the last part of the talk I will illustrate some work in progress, some aimed at extending the work on frame-dragging on smaller galactic scales, some aimed at understanding to what extent relativistic effects can play a role during collapse and past the first shall crossing and virialization. I will conclude with an outline of possible future work.