Coupling hybrid inflation to moduli

Abstract

Hybrid inflation can be realized in low energy effective string theory, asdescribed using supergravity. We find that the coupling of moduli toF-term hybrid inflation in supergravity leads to a slope and a curvature for the inflaton potential. Theϵ and η parameters receive contributions at tree and one loop level which are not compatible withslow roll inflation. Furthermore the coupling to the moduli sector can even preventinflation from ending at all. We show that introducing shift symmetries in theinflationary sector and taking the moduli sector to be no-scale removes mostof these problems. If the moduli fields are fixed during inflation, as is usuallyassumed, it appears that viable slow roll inflation can then be obtained with just onefine-tuning of the moduli sector parameters. However, we show this is not a reasonableassumption, and that the small variation of the moduli fields during inflation gives asignificant contribution to the effective inflaton potential. This typically implies thatη≈−6, although it may be possible to obtain smaller values with heavy fine-tuning.