Speaker: Eleonora Villa

Roughly speaking, cosmologists study large, linear scales and small, non-linear scales in two different ways: relativistic perturbation theory around a homogeneous and isotropic background describes scales where the growth of structures is at an early stage. At smaller scales, well inside the Hubble horizon, the relativistic effects are supposed to be completely negligible and General Relativity is replaced by Newtonian gravity. A post-Newtonian type approximation is a crucial improvement of this simple paradigm as it bridges the gap between relativistic perturbation theory and Newtonian structure formation, providing a unified approximation scheme including also the mildly non-linear stage. I focus on the post-Newtonian corrections for both the Eulerian and the Lagrangian approaches to gravitational dynamics and provide the connection between the two.

I finally present the post-Newtonian extension of the Zel’dovich solution for the plane parallel dynamics and its application in the context of the cosmological back-reaction proposal.