Newtonian versus relativistic cosmology
  We show how the relativistic matter and velocity power spectra behave in
different gauges. We construct a new gauge where both spectra coincide with
Newtonian theory on all scales. However, in this gauge there are geometric
quantities present which do not exist in Newtonian theory, for example the
local variation of the Hubble parameter. Comparing this quantity to second
order Newtonian quantities, we find that Newtonian theory is inaccurate on
scales larger than 10 Mpc. This stresses the importance of relativistic
corrections to Newtonian cosmological N-body simulations on these scales.
