The scale of inflation in the landscape

We determine the frequency of regions of small-field inflation in the Wigner landscape as an approximation to random supergravities/type IIB flux compactifications. We show that small-field inflation occurs exponentially more often than large-field inflation. The power of primordial gravitational waves from inflation is generically tied to the scale of inflation. As for small-field models this is below observational reach, their exponential enhancement seems to indicate a tendency towards small tensor-to-scalar ratio r. However, cosmologically viable inflationary regions must provide for a successful exit from inflation into a meta-stable dS minimum. Hence future work will need to determine the ‘graceful exit likelihood’ before any statement about the statistically expected level of tensor modes r is possible.