Abstract

Much of our current understanding of the early universe is based on cosmological solutions to the Einstein field equations, which by construction are spatially homogeneous. For example, studying the resulting ordinary system of differential equations leads to the widely accepted interpretation that our universe started with a big bang. An open question, however, is whether the homogeneous reduction is valid: are the features (specifically long-time asymptotics) of the cosmological solutions preserved if a small amount of inhomogeneity is added to the evolution? In this talk I will provide a quite introduction to the problem, survey some historical and recent positive answers to this question. Then, I will discuss how, under different sets of hypotheses, the question may be given a negative answer, through a joint work with Shih-Fang Yeh.