  We discuss cosmological inflation in the minimal Wess-Zumino model with a
single massive chiral supermultiplet. With suitable parameters and assuming a
plausible initial condition at the start of the inflationary epoch, the model
can yield scalar perturbations in the Cosmic Microwave Background (CMB) of the
correct strength with a spectral index n_s ~ 0.96 and a tensor-to-scalar
perturbation ratio r < 0.1, consistent with the Planck CMB data. We also
discuss the possibility of topological inflation within the Wess-Zumino model,
and the possibility of combining it with a seesaw model for neutrino masses.
This would violate R-parity, but at such a low rate that the lightest
supersymmetric particle would have a lifetime long enough to constitute the
astrophysical cold dark matter.
