  We study the dynamical stability of "tachyacoustic" cosmological models, in
which primordial perturbations are generated by a shrinking sound horizon
during a period of decelerating expansion. Such models represent a potential
alternative to inflationary cosmology, but the phase-space behavior of
tachyacoustic solutions has not previously been investigated. We numerically
evaluate the dynamics of two non-canonical Lagrangians, a cuscuton-like
Lagrangian and a Dirac-Born-Infeld Lagrangian, which generate a scale-invariant
spectrum of perturbations. We show that the power-law background solutions in
both cases are dynamical attractors.
