Inflation, singular instantons, and eleven dimensional cosmology

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Abstract
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

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