The BICEP2/Keck+PLANCK joint analysis of the e??μ-model polarization and polarization by foreground dust sets an upper bound on the tensor-to-scalar ratio of e?‘?0.05 & 0.12 at 95% CL. The popular Starorbinsky model Higgs-inflation or the conformally equivalent Higgs-inflation model allow low e?‘? values (a??10a?’3). We survey the generalizations of the Starobinskya€“Higgs models which would allow larger values (e?‘? a?? 0.1). The Starobinskya€“Higgs inflation models require an exponential potential which can be naturally derived from SUGRA models. We show that a variation of the no-scale SUGRA model can give rise to the generalized Starobinsky models which give large e?‘?. We also examine non-standard boundary conditions which would allow a large deviation of the tensor spectral index from the slow roll values and propose that the presence of a thermal component in the tensor spectrum arises from Gibbonsa€“Hawking temperature of the de-Sitter space.
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