Ermis Mitsou - October 6, 2016
A numerical relativity scheme for cosmological simulations
We present a new 3+1 integration scheme of full General Relativity for N-body/fluid
cosmological simulations. Standard numerical relativity schemes have two features that
make them unsuitable for this task: the presence of a growing linear mode in the matter
fluid, which affects the numerical robustness, and the diffeomorphism constraints that
are incompatible with the ad-hoc particle-to-mesh operations or potential modifications
emulating baryonic processes. We circumvent these problems by noting that, in the
presence of a fluid which permeates all of space, one can reduce the gravity/fluid
system to a set of totally deconstrained evolution equations for the 3-metric and
extrinsic curvature alone. Then, with the appropriate choice of gauge, all evolving
fields have strictly damped linear perturbations and the robustness test is passed on
an FLRW background. We derive our equations through some action, so that it is
straightforward to include extra matter content.