Anisotropic power spectrum and bispectrum in the f(φ)F2 mechanism

A suitable coupling of the inflaton φ to a vector kinetic term F2 gives frozen and scale invariant vector perturbations. We compute the cosmological perturbations ζ that result from such coupling by taking into account the classical vector field that unavoidably gets generated at large scales during inflation. This generically results in a too-anisotropic power spectrum of ζ. Specifically, the anisotropy exceeds the 1% level (10% level) if inflation lasts ∼5 e-folds (∼50 e-folds) more than the minimal amount required to produce the cosmic microwave background modes. This conclusion applies, among others, to the application of this mechanism for magnetogenesis, for anisotropic inflation, and for the generation of anisotropic perturbations at the end of inflation through a waterfall field coupled to the vector (in this case, the unavoidable contribution that we obtain is effective all throughout inflation, and it is independent of the waterfall field). For a tuned duration of inflation, a 1% (10%) anisotropy in the power spectrum corresponds to an anisotropic bispectrum which is enhanced like the local one in the squeezed limit, and with an effective local f_NL∼3(∼30). More in general, a significant anisotropy of the perturbations may be a natural outcome of all models that sustain higher than 0 spin fields during inflation.