Relativistic numerical cosmology with Silent Universes

Relativistic numerical cosmology is most often based either on the exact solutions of the Einstein equations, or perturbation theory, or weak-field limit, or the BSSN formalism. The Silent Universe provides an alternative approach to investigate relativistic evolution of cosmological systems. The silent universe is based on the solution of the Einstein equations in 1+3 comoving coordinates with additional constraints imposed. These constraints include: the gravitational field is sourced by dust and cosmological constant only, both rotation and magnetic part of the Weyl tensor vanish, and the shear is diagnosable. This paper describes the code simsilun (free software distributed under the terms of the reposi General Public License), which implements the equations of the Silent Universe. The paper also discusses applications of the Silent Universe and it uses the Millennium simulation to set up the initial conditions for the code simsilun. The simulation obtained this way consists of 16,777,216 worldlines, which are evolved from z=80 to z=0. Initially, the mean evolution (averaged over the whole domain) follows the evolution of the background $\Lambda$CDM model. However, once the evolution of cosmic structures becomes nonlinear, the spatial curvature evolves from $\Omega_K =0$ to $\Omega_K \approx 0.1$ at the present day. The emergence of the spatial curvature is associated with $\Omega_M$ and $\Omega_\Lambda$ being smaller by approximately 0.05 compared to the $\Lambda$CDM.