Parametric Resonance of Entropy Perturbations in Massless Preheating
  Here, we revisit the question of possible preheating of entropy modes in a two field model with a massless inflaton coupled to a matter scalar field. Using a perturbative approximation to the covariant method we demonstrate that there is indeed a parametric instability of the entropy mode which then at second order leads to exponential growth of the curvature fluctuation on super-Hubble scale. Back-reaction effects shut off the induced curvature fluctuations, but possibly not early enough to prevent phenomenological problems. This confirms previous results obtained using different methods and resolves a controversy in the literature. 
Hossein Bazrafshan Moghaddam, Robert H. Brandenberger, Yi-Fu Cai,   Elisa G. M. Ferreira
astro-ph.CO gr-qc hep-ph hep-th