Abstract : 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 \cdot 10 ^ { 16 } ~ { } { 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 \lesssim 2.9 \cdot 10 ^ { -4 } , while the spectral index running , |dn _ { 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 _ { s } / d \ln k| \simeq 0.006 . PACs numbers : 98.80.Cq , 12.60.Jv