Relativistic initial conditions for N-body simulations

Abstract

Initial conditions for (Newtonian) cosmological N-body simulations are\nusually set by re-scaling the present-day power spectrum obtained from linear\n(relativistic) Boltzmann codes to the desired initial redshift of the\nsimulation. This back-scaling method can account for the effect of\ninhomogeneous residual thermal radiation at early times, which is absent in the\nNewtonian simulations. We analyse this procedure from a fully relativistic\nperspective, employing the recently-proposed Newtonian motion gauge framework.\nWe find that N-body simulations for LambdaCDM cosmology starting from\nback-scaled initial conditions can be self-consistently embedded in a\nrelativistic space-time with first-order metric potentials calculated using a\nlinear Boltzmann code. This space-time coincides with a simple "N-body gauge"\nfor z<50 for all observable modes. Care must be taken, however, when simulating\nnon-standard cosmologies. As an example, we analyse the back-scaling method in\na cosmology with decaying dark matter, and show that metric perturbations\nbecome large at early times in the back-scaling approach, indicating a\nbreakdown of the perturbative description. We suggest a suitable "forwards\napproach" for such cases.\n