  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 is about 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.
