The deflationary universe: An instability of the de Sitter universe

The relevance is discussed of the initial value structure of the cosmological problem for inflationary explanations of its present structure. Existing proofs of the cosmic “no hair” conjecture are found to make use of an unrealistic strong energy condition on the stress tensor of the matter fields not driving the inflation. It is shown by explicit example that the no hair conjecture fails even in isotropic cosmological models if the strong energy conditions is relaxed. A class of exact cosmological models are given which begin in a de Sitter state but subsequently deflate towards the flat Friedman model. Various implications of these examples are discussed.