One-loop corrections to the primordial tensor spectrum from massless
  isocurvature fields
  We study one-loop corrections to the two-point correlation function of tensor
perturbations in primordial cosmology induced by massless spectator matter
fields. Using the Schwinger-Keldysh formalism in cosmological perturbation
theory, we employ dimensional regularization and cutoff regularization to study
the finite quantum corrections at one-loop arising from isocurvature fields of
the massless scalar, fermion and abelian gauge field which are freely
propagating on the FRW spacetime. For all cases, we find a logarithmic running
of the form $\frac{C}{q^3} \, \frac{H^4}{M^4_p}
  \log \left( \frac{H}{\mu } \right)$ where $C$ is a negative constant related
to the beta function, $H$ is the Hubble parameter at horizon exit and $\mu$ is
the renormalization scale.
