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A suitable coupling of the inflaton phi to a vector kinetic term F^2 givesfrozen and scale invariant vector perturbations. We compute the cosmologicalperturbations zeta that result from such coupling by taking into account theclassical vector field that unavoidably gets generated at large scales duringinflation. This generically results in a too anisotropic power spectrum ofzeta. Specifically, the anisotropy exceeds the 1% level (10% level) ifinflation lasted ~5 e-folds (~50 e-folds) more than the minimal amount requiredto produce the CMB modes. This conclusion applies, among others, to theapplication of this mechanism for magnetogenesis, for anisotropic inflation,and for the generation of anisotropic perturbations at the end of inflationthrough a waterfall field coupled to the vector (in this case, the unavoidablecontribution that we obtain is effective all throughout inflation, and it isindependent of the waterfall field). For a tuned duration of inflation, a 1%(10%) anisotropy in the power spectrum corresponds to an anisotropic bispectrumwhich is enhanced like the local one in the squeezed limit, and with aneffective local f_{NL} ~3 (~30). More in general, a significant anisotropy ofthe perturbations may be a natural outcome of all models that sustain higherthan 0 spin fields during inflation.

The anisotropic power spectrum and bispectrum in the f(phi) F^2 mechanism