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Pseudoscalar N-flation and axial coupling revisited

We revisit the dynamics of the axial coupling between many N-flatons and an Abelian gauge field, with special attention to its statistically anisotropic signal. The anisotropic power spectrum of curvature perturbations associated to the large wavelength modes of the gauge vector field is generally undetectable, since the anisotropy is confined to small scales. If the gauge field is the electromagnetic field, provided that the number of fields participating in the exponential expansion is large, it could be possible to generate sizable large scale magnetic fields. However, its spectrum is blue, and appreciable power on large scales implies an overly strong field on smaller scales, incompatibly with observations. Furthermore, the anisotropy is also markedly enhanced, and might be at odds with the isotropic observed sky. These aspects further demand that the scale of inflation is kept to a minimum.