Issues on Generating Primordial Anisotropies at the End of Inflation

TL;DR

This paper analyzes whether primordial anisotropies can be generated at the end of inflation in gauge-field–based models, focusing on a charged hybrid inflation setup. Using the δN formalism, it derives the end-of-inflation contribution to the curvature perturbation and shows that anisotropies are exponentially suppressed on cosmological scales due to the gauge field’s exponential evolution and the need for the re-scaled perturbation to be frozen. The results reveal that, in a FRW background, end-of-inflation anisotropies are unobservable, with anisotropic contributions to the power spectrum and bispectrum remaining negligible (the latter with f_NL anisotropic components suppressed by factors like e^{7–8N_*}). The authors argue this is a generic feature of FRW backgrounds for such gauge-field models and highlight that observable anisotropies may only appear if the background is explicitly anisotropic (e.g., Bianchi I).

Abstract

We revisit the idea of generating primordial anisotropies at the end of inflation in models of inflation with gauge fields. To be specific we consider the charged hybrid inflation model where the waterfall field is charged under a U(1) gauge field so the surface of end of inflation is controlled both by inflaton and the gauge fields. Using delta N formalism properly we find that the anisotropies generated at the end of inflation from the gauge field fluctuations are exponentially suppressed on cosmological scales. This is because the gauge field evolves exponentially during inflation while in order to generate appreciable anisotropies at the end of inflation the spectator gauge field has to be frozen and scale invariant. We argue that this is a generic feature, that is, one can not generate observable anisotropies at the end of inflation within an FRW background.