  We consider an alternative to inflation for the generation of superhorizon
perturbations in the universe in which the speed of sound is faster than the
speed of light. We label such cosmologies, first proposed by Armendariz-Picon,
{\it tachyacoustic}, and explicitly construct examples of non-canonical
Lagrangians which have superluminal sound speed, but which are causally
self-consistent. Such models possess two horizons, a Hubble horizon and an
acoustic horizon, which have independent dynamics. Even in a decelerating
(non-inflationary) background, a nearly scale-invariant spectrum of
perturbations can be generated by quantum perturbations redshifted outside of a
shrinking acoustic horizon. The acoustic horizon can be large or even infinite
at early times, solving the cosmological horizon problem without inflation.
These models do not, however, dynamically solve the cosmological flatness
problem, which must be imposed as a boundary condition. Gravitational wave
modes, which are produced by quantum fluctuations exiting the Hubble horizon,
are not produced.
