Observable non-gaussianity from gauge field production in slow roll inflation, and a challenging connection with magnetogenesis

In any realistic particle physics model of inflation, the inflaton can be expected to couple to other fields. We consider a model with a dilaton-like coupling between a U(1) gauge field and a scalar inflaton. We show that this coupling can result in observable non-gaussianity, even in the conventional regime where inflation is supported by a single scalar slowly rolling on a smooth potential: the time dependent inflaton condensate leads to amplification of the large-scale gauge field fluctuations, which can feed-back into the scalar/tensor cosmological perturbations. In the squeezed limit, the resulting bispectrum is close to the local one, but it shows a sizable and characteristic quadrupolar dependence on the angle between the shorter and the larger modes in the correlation. Observable non-gaussianity is obtained in a regime where perturbation theory is under control. If the gauge field is identified with the electromagnetic field, the model that we study is a realization of the magnetogenesis idea originally proposed by Ratra, and widely studied. This identification (which is not necessary for the non-gaussianity production) is however problematic in light of a strong coupling problem already noted in the literature.