Inflationary initial data for generic spatial topology

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Abstract
Initial data sets for Einstein's equations with a positive cosmological constant which guarantee inflation to the future are constructed. The 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 the resulting spacetime cannot be constructed by performing identifications on de Sitter spacetime or subsets of de Sitter spacetime. These solutions provide a new class of spacetimes which can be used to study the 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.