  The QCD axion solves the strong CP problem and represents an attractive
particle candidate for cold dark matter (CDM). However, quantum fluctuations of
the axion field during inflation easily result in large CDM isocurvature
perturbations that are in conflict with observations of the cosmic microwave
background (CMB). In this paper, we demonstrate how this problem can be solved
in low-scale models of hybrid inflation that may emerge from supersymmetric
grand unified theories. We consider both F-term hybrid inflation (FHI) and
D-term hybrid inflation (DHI) in supergravity, explicitly taking into account
the effect of hidden-sector supersymmetry breaking. We discuss the production
of cosmic strings and show how the soft terms in the scalar potential readily
allow to achieve the correct scalar spectral index. In both cases, we are able
to identify large regions in parameter space that are consistent with all
constraints. In particular, we find that evading the CDM isocurvature
constraint always requires a small Yukawa or gauge coupling of O(10^-3) or
smaller. This translates into upper bounds on the gravitino mass of O(10^5) GeV
in FHI and O(10^9) GeV in DHI. Our results point to interesting scenarios in
well-motivated parameter regions that will be tested in future axion and CMB
experiments.
