  Advances in our understanding of the origin, evolution and structure of the
universe have long been driven by cosmological perturbation theory, model
building and effective field theory. In this review, we introduce numerical
relativity as a powerful new complementary tool for fundamental cosmology. To
illustrate its power, we discuss applications of numerical relativity to
studying the robustness of slow contraction and inflation in homogenizing,
isotropizing and flattening the universe beginning from generic unsmooth
initial conditions. In particular, we describe how recent numerical relativity
studies of slow contraction have revealed a novel, non-linear smoothing
mechanism based on ultralocality that challenges the conventional view on what
is required to explain the large-scale homogeneity and isotropy of the
observable universe.
