Inflation, Singular Instantons and Eleven Dimensional Cosmology

TL;DR

This paper explores cosmological solutions in eleven-dimensional supergravity with compactified dimensions, analyzing the potential for inflation and instanton solutions, and finding that inflation is not achievable in this model.

Contribution

It derives conditions for inflation and Hawking-Turok instantons in eleven-dimensional supergravity with a squashed compactification.

Findings

Inflation is not possible in the studied model.

The instanton remains singular in eleven dimensions.

Conditions for exponential potentials to admit instantons are established.

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. At early times only one such term is expected to dominate. The condition for an exponential potential to admit inflationary solutions is derived and it is shown 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.