= Radiation-era comoving density mode
{title2=$\Delta_k=A(\sin x/x-\cos x)+B(\cos x/x+\sin x),\quad x=k\eta/\sqrt3$}
For <radiation in cosmology>, the <comoving-gauge density contrast> satisfies $\Delta_k''+(k^2/3-2/\eta^2)\Delta_k=0$. The displayed basis solves it. The first mode is regular and grows as $Ax^2/3$ outside the <sound horizon>; the second diverges as $B/x$ toward the initial singularity. At large $x$, the regular mode approaches $-A\cos x$ and has constant-amplitude acoustic oscillations.
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