Update on Minimal Supersymmetric Hybrid Inflation in Light of PLANCK

Abstract

The minimal supersymmetric (or F-term) hybrid inflation is defined by a unique renormalizable superpotential, fixed by a $U(1)$ R-symmetry, and it employs a canonical Kähler potential. The inflationary potential takes into account both radiative and supergravity corrections, as well as an important soft supersymmetry breaking term, with a mass coefficient in the range $(0.1-10)\mathrm{TeV}$. The latter term assists in obtaining a scalar spectral index $n_s$ close to $0.96$, as strongly suggested by the PLANCK and WMAP-9yr measurements. The minimal model predicts that the tensor-to-scalar $r$ is extremely tiny, of order $10^{-12}$, while the spectral index running, $|d{n}_{\mathrm{s}}/d\ln k|\sim 10^{-4}$. If inflation is associated with the breaking of a local $U(1{)}_{B-L}$ symmetry, the corresponding symmetry breaking scale $M$ is $(0.7-1.6)\cdot 10^{15}\mathrm{GeV}$ with $n_{\mathrm{s}}\simeq 0.96$. This scenario is compatible with the bounds on $M$ from cosmic strings, formed at the end of inflation from $B-L$ symmetry breaking. We briefly discuss non-thermal leptogenesis which is readily implemented in this class of models.

Minor corrections regarding the calculation of the tension of the cosmic strings

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