Nearly scale-invariant spectrum of adiabatic fluctuations may be from a very slowly expanding phase of the Universe

In this paper we construct an expanding phase with phantom matter, in which the scale factor expands very slowly but the Hubble parameter increases gradually, and assume that this expanding phase could be matched to our late observational cosmology by the proper mechanism. We obtain the nearly scale-invariant spectrum of adiabatic fluctuations in this scenario; different from the simplest inflation and usual ekpyrotic or cyclic scenario, the tilt of the nearly scale-invariant spectrum in this scenario is blue. Although there exists an uncertainty surrounding the way in which the perturbations propagate through the transition in our scenario, which is dependent on the details of possible “bounce” physics, compared with inflation and the ekpyrotic or cyclic scenario, our work may provide another feasible cosmological scenario generating the nearly scale-invariant perturbation spectrum.