Update on Minimal Supersymmetric Hybrid Inflation in Light of PLANCK

Understand

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 K\"{a}hler 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 $(0.1 - 10)~{\rm TeV}$.
• 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, $|dn_{\rm s}/d\ln k| \sim 10^{-4}$.