Newtonian limit of fully nonlinear cosmological perturbations in Einstein's gravity

Abstract

We prove that in the infinite speed-of-light limit(i.e., non-relativistic and subhorizon limits),the relativistic fully nonlinear cosmological perturbationequations in two gauge conditions, the zero-shear gauge andthe uniform-expansion gauge, exactly reproduce the Newtonianhydrodynamic perturbation equations in the cosmological background;as a consequence, in the same two gauge conditions, the Newtonianhydrodynamic equations are exactly recovered in the Minkowsky background.