INFLATIONARY INITIAL DATA FOR GENERIC SPATIAL TOPOLOGY

Initial data sets for Einstein's equations with a positive cosmologica l constant which guarantee inflation to the future are constructed. Th e construction is local, allowing pieces to be sewn together to create inflationary initial data with a generic spatial topology. A class of the initial data evolves to have the de Sitter metric locally, but th e resulting spacetime cannot be constructed by performing identificati ons on de Sitter spacetime or subsets of de Sitter spacetime. These so lutions provide a new class of spacetimes which can be used to study t he global effects of inflation. The space of Kantowski-Sachs solutions , which is the evolution of another special class of the initial data, is also considered.