Eliminating the η-problem in SUGRA hybrid inflation with vector backreaction

Abstract

It is shown that, when the inflaton field modulates the gauge kinetic functionof the gauge fields in supergravity realisations of inflation, the dynamicbackreaction leads to a new inflationary attractor solution, in which theinflaton's variation suffers additional impedance. As a result, slow-rollinflation can naturally occur along directions of the scalar potential whichwould be too steep and curved to support it otherwise. This provides a genericsolution to the infamous eta-problem of inflation in supergravity. Moreover,it is shown that, in the new inflationary attractor, the spectral index of thegenerated curvature perturbations is kept mildly red despite eta of orderunity. The above findings are applied to a model of hybrid inflation insupergravity with a generic Kähler potential. The spectral index of thegenerated curvature perturbations is found to be 0.97–0.98, in excellentagreement with observations. The gauge field can play the role of the vectorcurvaton after inflation but observable statistical anisotropy requiressubstantial tuning of the gauge coupling.