Smooth Cosmologies from M-Theory

We review two ways in which smooth cosmological evolution between two de Sitter phases can be obtained from M/string-theory. Firstly, we perform a hyperbolic reduction of massive type IIA* theory to D = 6 N = (1, 1) SU (2) × U (1) gauged de Sitter supergravity, which supports smooth cosmological evolution between dS₄ × S² and a dS₆-type geometry. Secondly, we obtain four-dimensional de Sitter gravity with SU(2) Yang-Mills gauge fields from a hyperbolic reduction of standard eleven-dimensional supergravity. The four-dimensional theory supports smooth cosmological evolution between dS₂ × S² and a dS₄-type geometry. Although time-dependent, these solutions arise from a first-order system via a superpotential construction. For appropriate choices of charges, these solutions describe an expanding universe whose expansion rate is significantly larger in the past than in the future, as required for an inflationary model.