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{Mcong [0,T)times mathbb {T}^3}, and converge as esearrow 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.