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

TL;DR

This paper analyzes the anisotropic effects in the power spectrum and bispectrum caused by a specific inflaton coupling to a vector field, highlighting the unavoidable anisotropy levels and their implications for inflationary models.

Contribution

It provides a detailed calculation of the anisotropic perturbations resulting from the f(phi) F^2 mechanism, showing the unavoidable anisotropy levels during inflation and their observational consequences.

Findings

Anisotropy exceeds 1% for ~5 e-folds of inflation beyond minimal.

Anisotropic bispectrum can be enhanced with local f_NL ~3.

Unavoidable vector field contributions affect various inflationary scenarios.

Abstract

A suitable coupling of the inflaton phi to a vector kinetic term F^2 gives frozen and scale invariant vector perturbations. We compute the cosmological perturbations zeta 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 zeta. Specifically, the anisotropy exceeds the 1% level (10% level) if inflation lasted ~5 e-folds (~50 e-folds) more than the minimal amount required to produce the CMB 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.