Kähler moduli inflation

Abstract

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 nonvanishing 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(10 5 − 10 7 ) in string units, and the inflationary scale M inf l ∼ 10 13 GeV. We find a robust model independent prediction for the spectral index of 1 − 2 Ne = 0.960 → 0.967, depending on the number of efoldings.

Poly-instanton inflation

“…The different topological origin of the inflaton between our model and the one developed in [14] results in a different canonically normalised inflaton field. This leads to a potential which in our case gives rise to slow-roll in a region much closer to the minimum than in the model of [14] even if in both cases the inflationary potential is generated by non-perturbative effects. This is the reason why in our model string loop corrections are less dangerous and can be shown to be negligible throughout all the inflationary dynamics for rather natural values of the underlying parameters.…”

“…However, as noticed in [15], the model of [14] is plagued by the η-problem since loop corrections dominate over the non-perturbative potential and spoil inflation.…”

“…In section 3 we first show how the poly-instanton corrections to the superpotential can generate a potential for the fibre modulus, and then we study its inflationary applications both analytically and numerically. In the same section we also present a detailed discussion of the η-problem stressing the similarities and the differences of our model with the previous ones developed in [14] and [15], where the inflaton was still a Kähler modulus. We finally conclude in section 4.…”

“…We stress that this was not possible in the model of [14] even if the inflationary potential was still generated by non-perturbative effects, and so had a shape very similar to (3.24). The reason is that in [14] the parameter κ scales with the volume as κ ∼ V 1/2 , so it is large for large values of the volume.…”

Systematics of moduli stabilization, inflationary dynamics and power spectrum

“…: [6,19]). This is somewhat counter-intuitive from the point of view of effective field theory approach, since we are integrating out some of the lighter fields.…”