Abstract
We investigate supersymmetric hybrid inflation in a realistic model based on the gauge symmetry $SU(4)_c \times SU(2)_L \times SU(2)_R$. The minimal supersymmetric standard model (MSSM) $\mu$ term arises, following Dvali, Lazarides, and Shafi, from the coupling of the MSSM electroweak doublets to a gauge singlet superfield which plays an essential role in inflation. The primordial monopoles are inflated away by arranging that the $SU(4)_c \times SU(2)_L \times SU(2)_R$ symmetry is broken along the inflationary trajectory. The interplay between the (above) $\mu$ coupling, the gravitino mass, and the reheating following inflation is discussed in detail. We explore regions of the parameter space that yield gravitino dark matter and observable gravity waves with the tensor-to-scalar ratio $r \sim 10^{-4}-10^{-3}$.
Highlights
In its simplest form supersymmetric (SUSY) hybrid inflation [1,2] is associated with a gauge symmetry breaking G → H, and it employs a minimal renormalizable superpotential W and a canonical Kähler potential K
We have implemented a version of SUSY hybrid inflation in SUð4Þc × SUð2ÞL × SUð2ÞR, a well motivated extension of the standard model (SM)
The minimal supersymmetric standard model (MSSM) μ term arises, following Dvali, Lazarides, and Shafi, from the coupling of the electroweak doublets to a gauge singlet superfield playing an essential role in inflation, which takes place along a shifted flat direction
Summary
In its simplest form supersymmetric (SUSY) hybrid inflation [1,2] is associated with a gauge symmetry breaking G → H, and it employs a minimal renormalizable superpotential W and a canonical Kähler potential K. [15,16] for generating the minimal supersymmetric standard model (MSSM) μ term, and we exploit shifted hybrid inflation to overcome the monopole problem We implement this scenario using both minimal and nonminimal Kähler potentials and address in both cases important issues related to the gravitino problem [17]. Trying to reconcile supergravity and cosmic inflation, one runs into the so-called η problem, which arises as the effective inflationary potential is quite steep This leads to large inflaton masses on the order of the Hubble parameter H, and the slow-roll conditions are violated. The lifetime is (see Fig. 1 of Ref. [41])
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