Fermionic Isocurvature Perturbations
  Isocurvature perturbations in the inflationary literature typically involve
quantum fluctuations of bosonic field degrees of freedom. In this work, we
consider isocurvature perturbations from fermionic quantum fluctuations during
inflation. When a stable massive fermion is coupled to a non-conformal sector
different from the scalar metric perturbations, observably large amplitude
scale invariant isocurvature perturbations can be generated. In addition to the
computation of the isocurvature two-point function, an estimate of the local
non-Gaussianities is also given and found to be promising for observations in a
corner of the parameter space. The results provide a new class of cosmological
probes for theories with stable massive fermions. On the technical side, we
explicitly renormalize the composite operator in curved spacetime and show that
gravitational Ward identities play an important role in suppressing certain
contributions to the fermionic isocurvature perturbations.
