EinsteinVlasov Calculations of Structure Formation
Abstract
We study the dynamics of small inhomogeneities in an expanding universe collapsing to form bound structures using full solutions of the EinsteinVlasov (Nbody) equations. We compare these to standard Newtonian Nbody solutions using quantities defined with respect to fiducial observers in order to bound relativistic effects. We focus on simplified initial conditions containing a limited range of length scales, but vary the inhomogeneities from small magnitude, where the Newtonian and generalrelativistic calculations agree quite well, to large magnitude, where the background metric receives an order one correction. For large inhomogeneities, we find that the collapse of overdensities tends to happen faster in Newtonian calculations relative to fully generalrelativistic ones. Even in this extreme regime, the differences in the spacetime evolution outside the regions of large gravitational potential and velocity are small. For standard cosmological values, we corroborate the robustness of Newtonian Nbody simulations to model large scale perturbations and the related cosmic variance in the local expansion rate.
 Publication:

arXiv eprints
 Pub Date:
 August 2019
 arXiv:
 arXiv:1908.05683
 Bibcode:
 2019arXiv190805683E
 Keywords:

 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 11 pages, 8 figures