An M Theory Solution to the Strong CP Problem and Constraints on the Axiverse

We give an explicit realization of the "String Axiverse" discussed in Arvanitaki et. al \cite{Arvanitaki:2009fg} by extending our previous results on moduli stabilization in $M$ theory to include axions. We extend the analysis of \cite{Arvanitaki:2009fg} to allow for high scale inflation that leads to a moduli dominated pre-BBN Universe. We demonstrate that an axion which solves the strong-CP problem naturally arises and that both the axion decay constants and GUT scale can consistently be around $2\times 10^{16}$ GeV with a much smaller fine tuning than is usually expected. Constraints on the Axiverse from cosmological observations, namely isocurvature perturbations and tensor modes are described. Extending work of Fox et. al \cite{Fox:2004kb}, we note that {\it the observation of tensor modes at Planck will falsify the Axiverse completely.} Finally we note that Axiverse models whose lightest axion has mass of order $10^{-15}$ eV and with decay constants of order $5\times 10^{14}$ GeV require no (anthropic) fine-tuning, though standard unification at $10^{16}$ GeV is difficult to accommodate