Dilatons, flatness, and the cosmological constant

Symmetries that exist for some theories when considering small perturbations around some special backgrounds, which include flat but not de Sitter space and, among cosmological solutions spatially flat but generally not k=1 Robertson-Walker solutions, are studied. The models examined include theories of nonconformally coupled massless fields, Brans-Dicke theories, and some supergravity theories with a dilaton field. The uses and possible consequences of these symmetries, among them the fact that they should help define the quantum vacuum in certain cosmologies, are discussed. Possible mechanisms which may solve the cosmological and flatness problems in which these symmetries play a role are also discussed.