General conditions for scale-invariant perturbations in an expanding   universe
  We investigate the general properties of expanding cosmological models which generate scale-invariant curvature perturbations in the presence of a variable speed of sound. We show that in an expanding universe, generation of a super-Hubble, nearly scale-invariant spectrum of perturbations over a range of wavelengths consistent with observation requires at least one of three conditions: (1) accelerating expansion, (2) a speed of sound faster than the speed of light, or (3) super-Planckian energy density. 
Ghazal Geshnizjani, William H. Kinney, Azadeh Moradinezhad Dizgah   (Univ. at Buffalo, SUNY)
astro-ph.CO