Linear density modes with polytropic pressure
= Linear density modes with polytropic pressure
In a flat matter-dominated universe with $a\propto t^{2/3}$ and $P\propto\rho^{4/3}$, the squared <sound speed> scales as $t^{-2/3}$. Each comoving Fourier mode then satisfies an <Euler-Cauchy equation>, with gravitational growth at long wavelengths and logarithmic-time acoustic oscillations at short wavelengths.