General relativistic 'screening' in cosmological simulations

Understand

We revisit the issue of interpreting the results of large volume cosmological simulations in the context of large scale general relativistic effects.

• We look for simple modifications to the nonlinear evolution of the gravitational potential $\psi$ that lead on large scales to the correct, fully relativistic description of density perturbations in the Newtonian gauge.
• We note that the relativistic constraint equation for $\psi$ can be cast as a diffusion equation, with a diffusion length scale determined by the expansion of the Universe.
• Exploiting the weak time evolution of $\psi$ in all regimes of interest, this equation can be further accurately approximated as a Helmholtz equation, with an effective relativistic 'screening' scale $\ell$ related to the Hubble radius.