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 perturbation equations in two gauge conditions, the zero-shear gauge and the uniform-expansion gauge, exactly reproduce the Newtonian hydrodynamic perturbation equations in the cosmological background; as a consequence, in the same two gauge conditions, the Newtonian hydrodynamic equations are exactly recovered in the Minkowsky background.

12 Pages, appeared in JCAP

References in corpus (2)

• Second order solutions of cosmological perturbation in the matter dominated era
• Cosmological post-Newtonian approximation compared with perturbation theory

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• Newtonian Hydrodynamics with General Relativistic Pressure
• Gravito-magnetic instabilities of Relativistic Magnetohydrodynamics
• Cosmological post-Newtonian equations from nonlinear perturbation theory
• Cosmological Newtonian limit
• Special Relativistic Magnetohydrodynamics with Gravitation
• Cosmological hydrodynamics with relativistic pressure and velocity
• Non-linear power spectra in the synchronous gauge
• Axion cosmology with post-Newtonian corrections