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.
