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 $|V&#39;&#39;|\sim V/M^2$, where $V(ϕ)$ 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 $|η|\sim (\mpl/M)^2 > 1$ where $\mpl=(8πG)^{-1/2}$, but inflation requires $|η|<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 $M\ll \mpl$, which makes the problem worse than if $M\sim \mpl$.