Near scale invariance with modified dispersion relations

We describe a novel mechanism for generating a nearly scale invariant spectrum of adiabatic perturbations during a non-inflationary stage. It relies on a modified dispersion relation that contains higher powers of the spatial momentum of matter perturbations. This dispersion relation leads to the superluminal speeds required to seed a spectrum of super-horizon perturbations (we also explain why superluminal velocities are not a problem in this setting). We implement our mechanism in the context of a massless scalar field in an otherwise perfectly homogeneous universe. The couplings of the field to background scalars and tensors give rise to the required modification of its dispersion relation, and the couplings of the scalar to matter result in an adiabatic primordial spectrum. This work is meant to explicitly illustrate that it is possible to seed nearly scale invariant primordial spectra without inflation, within a conventional expansion history.