Update on Minimal Supersymmetric Hybrid Inflation in Light of PLANCK

TL;DR

This paper updates minimal supersymmetric hybrid inflation models considering recent PLANCK data, showing they predict a very small tensor-to-scalar ratio and a spectral index close to 0.96, consistent with cosmic string bounds and leptogenesis.

Contribution

It refines the minimal supersymmetric hybrid inflation model by incorporating recent observational constraints and discusses its implications for symmetry breaking scale and leptogenesis.

Findings

Spectral index n_s approximately 0.96

Tensor-to-scalar ratio r around 10^{-12}

Symmetry breaking scale M between 0.7 and 1.6 x 10^{15} GeV

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 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, $|dn_{\rm s}/d\ln k| \sim 10^{-4}$. If inflation is associated with the breaking of a local $U(1)_{B-L}$ symmetry, the corresponding symmetry breaking scale $M$ is $(0.7 - 1.6)\cdot10^{15}~{\rm GeV}$ with $n_{\rm s} \simeq 0.96$. 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.