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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 $2.86\cdot10^{16} {\rm GeV}$, 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 $n_s$ 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, $r\lesssim2.9\cdot10^{-4}$, while the spectral index running, $|dn_{\rm s}/d\ln k|$, 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 $|dn_{\rm s}/d\ln k|\simeq0.006$.