Fibre inflation: observable gravity waves from IIB string compactifications

Abstract

We introduce a simple string model of inflation, inwhich the inflaton field can take trans-Planckian values whiledriving a period of slow-roll inflation. This leads naturally to arealisation of large field inflation, inasmuch as the inflationaryepoch is well described by the single-field scalar potential V = V0(3−4e−φ̂/(3)1/2). Remarkably, fora broad class of vacua all adjustable parameters enter onlythrough the overall coefficient V0, and in particular do notenter into the slow-roll parameters. Consequently these aredetermined purely by the number of e -foldings, Ne, and so arenot independent: ε ≃ 3⁄2η2. This impliessimilar relations among observables like the primordialscalar-to-tensor amplitude, r, and the scalar spectral tilt,ns: r ≃ 6(ns−1)2. Ne is itself moremodel-dependent since it depends partly on the post-inflationaryreheat history. In a simple reheating scenario a reheatingtemperature of Trh ≃ 109 GeV gives Ne ≃ 58,corresponding to ns ≃ 0.970 and r ≃ 0.005, withinreach of future observations. The model is an example of a classthat arises naturally in the context of type IIB stringcompactifications with large-volume moduli stabilisation, andtakes advantage of the generic existence there of Kähler moduliwhose dominant appearance in the scalar potential arises fromstring loop corrections to the Kähler potential. The inflatonfield is a combination of Kähler moduli of a K3-fiberedCalabi-Yau manifold. We believe there are likely to be a greatnumber of models in this class—``high-fibre models''—in whichthe inflaton starts off far enough up the fibre to produceobservably large primordial gravity waves.