Non-renormalizable terms and M theory during inflation

Abstract

Inflation is well known to be difficult in the context of supergravity, if the potential is dominated by the $F$ term. Non-renormalizable terms generically give $|V^{\prime \prime }|\sim V/M^2$, where $V(\varphi )$ is the inflaton potential and $M$ is the scale above which the effective field theory under consideration is supposed to break down. This is equivalent to $|\eta |\sim (\text{mpl}/M{)}^2>1$ where $\text{mpl}=(8\pi G{)}^{-1/2}$, but inflation requires $|\eta |<0.1$. I here point out that all of the above applies also if the $D$ term dominates, with the crucial difference that the generic result is now easily avoided by imposing a discrete symmetry. I also point out that if extra spacetime dimensions appear well below the Planck scale, as in a recent M-theory model, one expects $M\ll \text{mpl}$, which makes the problem worse than if $M\sim \text{mpl}$.

Comments: 9 pages latex. Significant change flagged by 3rd footnote