Upper bound on the tensor-to-scalar ratio in GUT-scale supersymmetric hybrid inflation

We explore the upper bound on the tensor-to-scalar ratio r   in supersymmetric (F-term) hybrid inflation models with the gauge symmetry breaking scale set equal to the value 2.86⋅1016 GeV2.86⋅1016 GeV, as dictated by the unification of the MSSM gauge couplings. We employ a unique renormalizable superpotential and a quasi-canonical Kähler potential, and the scalar spectral index nsns is required to lie within the two-sigma interval from the central value found by the Planck satellite. In a sizable region of the parameter space the potential along the inflationary trajectory is a monotonically increasing function of the inflaton, and for this case, r≲2.9⋅10−4r≲2.9⋅10−4, while the spectral index running, |dns/dln⁡k||dns/dln⁡k|, can be as large as 0.01. Ignoring higher order terms which ensure the boundedness of the potential for large values of the inflaton, the upper bound on r   is significantly larger, of order 0.01, for subplanckian values of the inflaton, and |dns/dln⁡k|≃0.006|dns/dln⁡k|≃0.006.