Modern constraints on F-term SUSY hybrid inflation models

Abstract

We study modifications of supersymmetric hybrid inflation, which continues to be one of the most popular inflationary models. The seminal formulation considered the VG+Δ V potential, in which one can show that [special characters ommitted] , which indicates that the breaking scale M ∼ 1016 GeV. This is a non-trivial fact, and provides a clue the group may be a Grand Unified Theory (GUT). Inspired by this, we consider inflating while constraining the breaking scale M at the MSSM gauge coupling unification scale, 2.86 × 1016 GeV. We show that one can inflate successfully; in particular, we use non-minimal Kähler to achieve, for the recent Planck bounds 0.945 < ns < 0.975, r ≈ 3 × 10-4 in the case where V is bounded from below, and r ≈ 1 × 10-2 where this condition is relaxed. Unfortunately, GUTs tend to predict topological defects. To ameliorate this problem, we consider the addition of a Planck-suppressed term which gives rise to shifted inflation, where one inflates in a similar way except that ||[straight phi]|| ≠ 0. We show that one can inflate successfully; one achieves similar results as in the standard case, including the large r solutions particular to non-minimal Kähler contributions. We achieve r ≈ 0.02, which is similar to the non-minimal standard case. Finally, we consider a generalization of the model to include Planck-suppressed R-symmetry violation, parametrized by α. One can generate masses more naturally in MSSM by treating R-symmetry as approximate, and we discover that, keeping to the standard inflationary track ||[straight phi]|| = 0, the effect is to raise r in the preferred ns range by about four orders of magnitude as compared with the standard case, for α ≈ 10-9 . By considering α ≈ 10-7 , one can achieve r ≈ 10 -4 . This is fairly remarkable in that it is done with only minimal Kähler.