General relativistic 'screening' in cosmological simulations
  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. We demonstrate that it is thus possible to carry out N-body
simulations in the Newtonian gauge by replacing Poisson's equation with this
Helmholtz equation, involving a trivial change in the Green's function kernel.
Our results also motivate a simple, approximate (but very accurate) gauge
transformation - $\delta_{\rm N}(\mathbf{k}) \approx \delta_{\rm
sim}(\mathbf{k})\times (k^2+\ell^{-2})/k^2$ - to convert the density field
$\delta_{\rm sim}$ of standard collisionless N-body simulations (initialised in
the comoving synchronous gauge) into the Newtonian gauge density $\delta_{\rm
N}$ at arbitrary times. A similar conversion can also be written in terms of
particle positions. Our results can be interpreted in terms of a Jeans
stability criterion induced by the expansion of the Universe. The appearance of
the screening scale $\ell$ in the evolution of $\psi$, in particular, leads to
a natural resolution of the 'Jeans swindle' in the presence of super-horizon
modes.
