= Superhorizon radiation-era entropy integration constants
{title2=$S=\delta_r-\tfrac43\delta_c=S_0+S_1\tau$}
In the leading <radiation domination> limit, neglect $k^2\delta_r$ and the matter contribution to gravity. The radiation equation gives $S''=0$. Substitution into $\delta_c''+\delta_c'/\tau=3\delta_r/\tau^2$ gives
$$
\delta_c=C_g\tau^2+C_d\tau^{-2}-\frac34S_0-S_1\tau,\qquad
\delta_r=\frac43C_g\tau^2+\frac43C_d\tau^{-2}-\frac13S_1\tau.
$$
Thus <adiabatic initial conditions> select both $S_0=0$ and $S_1=0$, leaving the growing and decaying power-law modes. The four constants describe the leading supplied coupled system; regularity and additional initial <Einstein field equations> constraints can further restrict their physical interpretation.
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