Cosmological Post-Newtonian Expansions to Arbitrary Order

We prove the existence of a large class of one parameter families of solutions to the Einstein-Euler equations that depend on the singular parameter e = v_T/c{\epsilon=v_T/c} (0 < e < e₀){(0< \epsilon < \epsilon_0)}, where c is the speed of light, and v _T is a typical speed of the gravitating fluid. These solutions are shown to exist on a common spacetime slab M @ 0,T)×\mathbb T³{M\cong 0,T)\times \mathbb {T}^3}, and converge as e\searrow 0{\epsilon \searrow 0} to a solution of the cosmological Poisson-Euler equations of Newtonian gravity. Moreover, we establish that these solutions can be expanded in the parameter e{\epsilon} to any specified order with expansion coefficients that satisfy e{\epsilon}-independent (nonlocal) symmetric hyperbolic equations.