Kähler moduli inflation

We show that under general conditions there is at least one natural inflationary direction for the Kähler moduli of type-IIB flux compactifications. This requires a Calabi-Yau 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 Kähler modulus whose only non-vanishing triple-intersection 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 η problem of F-term inflation. In order to obtain COBE-normalised density perturbations, the stabilised volume of the Calabi-Yau must be O(10⁵-10⁷) in string units, and the inflationary scale M_infl ∼ 10¹³ 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.