Signals of inflation in a friendly string landscape

Following Freivogel {\it et al} we consider inflation in a predictive (or`friendly') region of the landscape of string vacua, as modeled byArkani-Hamed, Dimopoulos and Kachru. In such a region the dimensionfulcoefficients of super-renormalizable operators unprotected by symmetries, suchas the vacuum energy and scalar mass-squareds are freely scanned over, and theobjects of study are anthropically or `environmentally' conditioned probabilitydistributions for observables. In this context we study the statisticalpredictions of (inverted) hybrid inflation models, where the properties of theinflaton are probabilistically distributed. We derive the resultingdistributions of observables, including the deviation from flatness$|1-\Omega|$, the spectral index of scalar cosmological perturbations $n_s$(and its scale dependence $dn_s/d\log k$), and the ratio of tensor to scalarperturbations $r$. The environmental bound on the curvature implies a solutionto the $\eta$-problem of inflation with the predicted distribution of $(1-n_s)$indicating values close to current observations. We find a relatively lowprobability ($<3%$) of `just-so' inflation with measurable deviations fromflatness. Intermediate scales of inflation are preferred in these models.Comment: 20 pages, 11 figure