= Adiabatic radiation-era cold-dark-matter transfer solution
{title2=$\delta_C=K F(x),\quad x=k\tau/\sqrt3$}
In a radiation-dominated background with comoving <cold dark matter>, neglect its contribution to gravity but retain the radiation perturbation. The regular <adiabatic initial conditions> select $F(x)=\int_0^x(1-\cos t)dt/t+\sin x/x-(1-\cos x)/x^2-1/2$. It obeys $x^2F^{(4)}+5xF^{(3)}+x^2F''+xF'=0$, with $F\sim x^2/8$ at zero and $F\sim\ln x+\gamma-1/2$ at infinity. The accompanying radiation contrast is $K[-2\cos x+4\sin x/x-4(1-\cos x)/x^2]/3$. This exact leading-radiation solution explains the transition from common superhorizon growth to acoustic radiation oscillations and logarithmic matter growth.
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