Exact spectrum of scalar field perturbations in a radiation deformed   closed de Sitter universe
  We observe that the equation of motion for a free scalar field in a closed universe with radiation and a positive cosmological constant is given by Lam\'e's equation. Computing the exact power spectrum of scalar field perturbations, the presence of both curvature and radiation produces a red tilt weakly dependent on the amount of radiation. 
Sash Sarangi, Koenraad Schalm, Gary Shiu, Jan Pieter van der Schaar