Relativistic Cosmology in the linear and non-linear regime

In the first part of the seminar I will discuss the lensing and relativistic effects in the Large Scale Structure (LSS) observables. The lensing and relativistic effects are corrections to the newtonian approximation due to the geodesic motion of photons, which travel in a clumpy universe from the source to the observer. I will review their relevance for forthcoming redshift surveys, focusing on two aspects: which is the effect of neglecting their contributions in standard clustering analysis and which are the perspective of their detection. The second part will be devoted to the non-linear regime of structure formation. In particular I will present the status of a project I am currently working on, which aims to compute and study the vorticity field from N-body simulations, with the relativistic code gevolution. This work is relevant for improving our theoretical understanding of the rotational content of the cosmic flow and for modelling its impact on galaxy clustering in redshift space.