Cosmological Newtonian Limits on Large Scales

This thesis is about the rigid cosmological Newtonian limits on large time and space scales and answers the following fundamental question: On what space and time scales can Newtonian cosmological simulations be trusted to approximate relativistic cosmologies? We will resolve this question with small initial data and the positive cosmological constant condition, and answer it on large spacetime scales and establish, under suitable assumptions, the existence of realistic inhomogeneous cosmological solutions that (1) admit a foliation by spacelike (i.e. constant time) hypersurfaces diffeomorphic to R^3, (2) exist globally to the future, (3) can be approximated to arbitrary precision uniformly to the future by a Newtonian solution, and (4) represent non-linear perturbations of a FLRW fluid solution.