We show how successful supersymmetric hybrid inflation is realized in realistic models where the resolution of the minimal supersymmetric standard model \mu problem is intimately linked with axion physics .
The scalar fields that accompany the axion , such as the saxion , are closely monitored during and after inflation to ensure that the axion isocurvature perturbations lie below the observational limits .
The scalar spectral index n _ { s } \simeq 0.96 - 0.97 , while the tensor-to-scalar ratio r , a canonical measure of gravity waves , lies well below the observable range in our example .
The axion domain walls are inflated away , and depending on the axion decay constant f _ { a } and the magnitude of the \mu parameter , the axions and/or the lightest supersymmetric particle compose the dark matter in the universe .
Non-thermal leptogenesis is naturally implemented in this class of models .