On the accuracy of N-body simulations at very large scales

Understand

We examine the deviation of Cold Dark Matter particle trajectories from the Newtonian result as the size of the region under study becomes comparable to or exceeds the particle horizon.

• To first order in the gravitational potential, the general relativistic result coincides with the Zel'dovich approximation and hence the Newtonian prediction on all scales.
• At second order, General Relativity predicts corrections which overtake the corresponding second order Newtonian terms above a certain scale of the order of the Hubble radius.
• However, since second order corrections are very much suppressed on such scales, we conclude that simulations which exceed the particle horizon but use Newtonian equations to evolve the particles, reproduce the correct trajectories very well.