Cosmological post-Newtonian expansions to arbitrary order

Abstract

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 =vT/c (0< < 0), where c is the speed of light, and vT is a typical speed of the gravitating fluid. These solutions are shown to exist on a common spacetime slab M [0,T)× 3, and converge as 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 to any specified order with expansion coefficients that satisfy -independent (nonlocal) symmetric hyperbolic equations.