Cosmological post-Newtonian equations from nonlinear perturbation theory

Abstract

We derive the basic equations of the cosmological first-order post-Newtonian approximation from the recently formulated fully nonlinear and exact cosmological perturbation theory in Einstein's gravity. Apparently the latter, being exact, should include the former, and here we use this fact as a new derivation of the former. The complete sets of equations in both approaches are presented without fixing the temporal gauge conditions so that we can use the gauge choice as an advantage. Comparisons between the two approaches are made. Both are potentially important in handling relativistic aspects of nonlinear processes occurring in cosmological structure formation. We consider an ideal fluid and include the cosmological constant.

16 pages, no figure

References in corpus (4)

• The New Horizon Run Cosmological N-Body Simulations
• Fully nonlinear and exact perturbations of the Friedmann world model
• Newtonian limit of fully nonlinear cosmological perturbations in Einstein's gravity
• Cosmological post-Newtonian approximation compared with perturbation theory

Cited by in corpus (6)

• Special relativistic hydrodynamics with gravitation
• Newtonian Hydrodynamics with General Relativistic Pressure
• Special Relativistic Magnetohydrodynamics with Gravitation
• Cosmological hydrodynamics with relativistic pressure and velocity
• Axion cosmology with post-Newtonian corrections
• Newtonian, post-Newtonian and Relativistic Cosmological Perturbation Theory