GRAMSES: a new route to general relativistic $N$-body simulations in cosmology. Part I. Methodology and code description

Understand

We present GRAMSES, a new pipeline for nonlinear cosmological $N$-body simulations in General Relativity (GR).

• This code adopts the Arnowitt-Deser-Misner (ADM) formalism of GR, with constant mean curvature and minimum distortion gauge fixings, which provides a fully nonlinear and background independent framework for relativistic cosmology.
• Employing a fully constrained formulation, the Einstein equations are reduced to a set of ten elliptical equations which are solved using multigrid relaxation with adaptive mesh refinements (AMR), and three hyperbolic equations for the evolution of tensor degrees of freedom.
• The current version of GRAMSES neglects the latter by using the conformal flatness approximation, which allows it to compute the two scalar and two vector degrees of freedom of the metric.