grgadget: an N-body TreePM relativistic code for cosmological simulations

We present the merging of the Particle-Mesh (PM) relativistic gevolution code with the TreePM gadget-4 code, with the aim of studying general relativity effects in cosmology. Our code, called grgadget, is able to track the evolution of metric perturbations in the weak field limit by using gevolution's implementation of a relativistic PM in the Poisson gauge. To achieve this, starting from gevolution, we have written a c++ library called libgevolution, which allows a code to access and use the same abstractions and resources that gevolution uses for its PM-only N-body simulations. The code works under the assumption that particle interactions at short distances can be approximated as Newtonian, so that we can combine the forces computed with a Newtonian Tree with those computed with a relativistic PM. The result is a TreePM simulation code that represents metric perturbations at the scales where they are relevant while resolving non-linear structures. We validate our code by closely matching gadget-4 forces, computed with the Tree switched off, with those computed with libgevolution in the Newtonian limit. With grgadget, we obtain a matter power spectrum that is compatible with Newtonian gadget-4 at small scales and contains GR features at large scales that are consistent with results obtained with gevolution. We demonstrate that, due to the better resolution of the highly non-linear regime, the representation of the relativistic fields sampled on the mesh improves with respect to the PM-only simulations.