Bridging the gap between small and large scales: a nonlinear post-Friedmann framework for relativistic structure formation
18 March 2015
Time: 4:30pm Venue: Room 516
The London Relativity and Cosmology Seminar
Marco Bruni (Portsmouth)
Non-linear structure formation at scales much smaller than the Hubble horizon is traditionally studied with Newtonian methods, for instance N-body simulations, while early Universe and horizon scales perturbations are investigated with relativistic perturbation theory. In view of new large scale galaxy surveys that will provide data with an unprecedented accuracy, it seems timely to bridge the gap between these different approaches, going beyond the Newtonian approximation and unifying the study of the very large scales and the non-linear scales in a single theoretical framework.
In this talk I will describe a sort of post-Minkowskian (weak field) approach to cosmology, such that at leading order in a 1/c expansion Newtonian cosmology is recovered as a consistent approximate solution of Einstein equations, on top of a Friedmannian background. In this post-Friedmann framework, linear and non-linear relativistic contributions appear at next order. Resumming variables and linearising the equations one recovers first-order relativistic perturbation theory, i.e. the framework is valid on horizon scales and beyond. I will illustrate the first practical application, i.e. the extraction of the frame-dragging gravitomagnetic potential from N-body simulations, and its power spectrum. Similarly, the difference between the two scalar potential, known as "slip" in cosmology, can also in principle be computed, sourced at leading order by purely Newtonian non-linear terms. I will also discuss the relevance of relativistic corrections to the initial conditions in Newtonian simulations that arise at second order in perturbation theory.