Spectrum of Cuscuton Bounce

It has been recently shown that a cosmological bounce model based on Cuscuton gravity does not have any ghosts or curvature instabilities. We explore whether Cuscuton bounce can provide an alternative to inflation for generating near scale-invariant scalar perturbations. While a single field Cuscuton bounce generically produces a strongly blue power spectrum (for a variety of initial/boundary conditions), we demonstrate that scale invariant entropy modes can be generated in a spectator field that starts in adiabatic vacuum, and is kinetically coupled to the primary field. Furthermore, our solution has no singularity, nor requires an ad hoc matching condition. We also study the generation of tensor modes (or gravitational waves) in Cuscuton bounce and show that while they are stable, similar to other bounce models, the produced spectrum is strongly blue and unobservable.