Abstract
We show that the recently proposed multi-natural inflation can be realized within the framework of 4D ${\cal N}=1$ supergravity. The inflaton potential mainly consists of two sinusoidal potentials that are comparable in size, but have different periodicity with a possible non-zero relative phase. For a sub-Planckian decay constant, the multi-natural inflation model is reduced to axion hilltop inflation. We show that, taking into account the effect of the relative phase, the spectral index can be increased to give a better fit to the Planck results, with respect to the hilltop quartic inflation. We also consider a possible UV completion based on a string-inspired model. Interestingly, the Hubble parameter during inflation is necessarily smaller than the gravitino mass, avoiding possible moduli destabilization. Reheating processes as well as non-thermal leptogenesis are also discussed.
Highlights
To construct a viable inflation model, the inflaton potential should be under good control so as not to break the slow-roll condition and to suppress the inflation scale compared with the the Planck scale
The inflaton potential mainly consists of two sinusoidal potentials that are comparable in size, but have different periodicity with a possible non-zero relative phase
In this model the inflaton potential mainly consists of two sinusoidal functions that are comparable in size, but have different periodicity
Summary
Let us consider a supergravity realization of multi-natural inflation in which an axion plays the role of the inflaton [40]. To this end, we introduce the following Kahler and superpotentials with an axion chiral superfield Φ,. Note that the Kahler potential respects the axionic shift symmetry, φ → φ + const,. We assume that the breaking of the shift symmetry is so weak that the axion mass is hierarchically smaller than the saxion mass. If the saxion mass were comparable to the axion, one would have to follow the multi-field dynamics during inflation. The analysis becomes rather involved, it is possible to realize successful inflation as is the case with racetrack inflation [38, 39]
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