The Trans-Planckian problem in Tachyacoustic Cosmology

We study Tachyacoustic models of cosmology, for which a scale-invariant perturbation spectrum is generated via superluminal sound speed instead of accelerated expansion, as in the case of inflation. We derive two bounds on the size of acoustic horizon which constrain the duration of tachyacoustic evolution, and therefore generation of primordial perturbations. We show that existing models cannot solve the horizon problem without violating the condition that all physical scales -- such as the Hubble parameter, the pressure, and the length scale at which quantum modes freeze out and become classical -- be sub-Planckian.