Kahler moduli inflation

We show that under general conditions there is at least one natural inflationary direction for the Kahler moduli of type-IIB flux compactifications. This requires a CalabiYau which has h(2,1) > h(1,1) > 2 and for which the structure of the scalar potential is as in the recently found exponentially large volume compactifications. We also need - although these conditions may be relaxed - at least one Kahler modulus whose only non-vanishing tripleintersection is with itself and which appears by itself in the non-perturbative superpotential. Slow-roll inflation then occurs without a fine tuning of parameters, evading the eta problem of F-term inflation. In order to obtain COBE-normalised density perturbations, the stabilised volume of the Calabi-Yau must be O(10(5) - 10(7)) in string units, and the inflationary scale M-infl similar to 10(13) GeV. We find a robust model independent prediction for the spectral index of 1 - 2/N-e = 0.960 -> 0.967, depending on the number of efoldings.