Inflation , Singular Instantons and Eleven Dimensional Cosmology

We investigate cosmological solutions of eleven dimensional supergravity compactified on a squashed seven manifold. The effective action for the four dimensional theory contains scalar fields describing the size and squashing of the compactifying space. The potential for these fields consists of a sum of exponential terms. We derive a criterion for an exponential potential to give rise to inflation and demonstrate that inflation is not possible in our model. The criterion for an exponential potential to admit a Hawking-Turok instanton is also derived. It is shown that the instanton remains singular in eleven dimensions. Typeset using REVTEX ∗email: [email protected] †email: [email protected]