Abstract
We derive the basic equations of the cosmological first-orderpost-Newtonian approximation from the recently formulatedfully nonlinear and exact cosmological perturbation theory in Einstein'sgravity. Apparently the latter, being exact, should include theformer, and here we use this fact as a new derivation of the former.The complete sets of equations in both approaches are presented withoutfixing the temporal gauge conditions so that we can use the gaugechoice as an advantage. Comparisons between the two approaches are made. Both are potentially important in handling relativistic aspects of nonlinearprocesses occurring in cosmological structure formation. We consider an ideal fluid and include the cosmologicalconstant.
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