Shifted <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>μ</mml:mi></mml:math>-hybrid inflation, gravitino dark matter, and observable gravity waves
G. Lazarides, Mansoor Ur Rehman, Qaisar Shafi, Fariha K. Vardag
Abstract
We investigate supersymmetric hybrid inflation in a realistic model based on the gauge symmetry $SU(4{)}_{c}\ifmmode\times\else\texttimes\fi{}SU(2{)}_{L}\ifmmode\times\else\texttimes\fi{}SU(2{)}_{R}$. The minimal supersymmetric standard model (MSSM) $\ensuremath{\mu}$ 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 $SU(4{)}_{c}\ifmmode\times\else\texttimes\fi{}SU(2{)}_{L}\ifmmode\times\else\texttimes\fi{}SU(2{)}_{R}$ symmetry is broken along the inflationary trajectory. The interplay between the (above) $\ensuremath{\mu}$ 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 $r\ensuremath{\sim}{10}^{\ensuremath{-}4}--{10}^{\ensuremath{-}3}$.