Negative-w barotropic-fluid gradient instability ($c_s^2=w<0$)

A propagating adiabatic fluid with the constant closure $p=w\rho$ has $c_s^2=dp/d\rho =w$. For $-1<w<0$, a short-wavelength Fourier perturbation obeys ${\omega }^2\simeq w{k}_{\mathrm{phys}}^2<0$, producing gradient growth. This does not exclude a negative-pressure perfect-fluid stress tensor with nonadiabatic pressure response, or a canonical scalar with rest-frame sound speed one. A cosmological constant has no independent propagating fluid density mode.

// Target: cosmology.bigb