= Solution
After the decay products dominate the background, <radiation domination> gives $\rho_r\propto a^{-4}$. Neglecting curvature and vacuum terms, the <Friedmann equation> implies $\dot a/a=C/a^2$, so $a\propto(t-t_B)^{1/2}$ and
$$
\boxed{H=\frac1{2(t-t_B)}.}
$$
The displayed $1/(2t)$ form uses a cosmic-time origin with $t_B=0$. After a late transition the extrapolated radiation-era origin need not be the original Big Bang; this time shift does not change the growth law.
For the remaining pressureless matter, neglect its self-gravity to leading order in $\rho_m/\rho_r$. Its <density contrast> obeys $\ddot\delta+(t-t_B)^{-1}\dot\delta=0$. Using the conserved <expansion-weighted derivative of a passive density perturbation> gives
$$
\boxed{\delta(t)=C_1+C_2\log\!\left(\frac{t-t_B}{t_*-t_B}\right)
=A+B\log a(t).}
$$
Thus <logarithmic growth of matter perturbations during radiation domination> replaces the static exponential growth and the matter-era $t^{2/3}$ growth. The expansion persists while its dominant radiation component supplies little sustained clustering in this pressureless test-component approximation. The residual matter can eventually become important again because $\rho_m/\rho_r\propto a$; the approximation is for the radiation-dominated interval. The equation is not a pressureless growth equation for the relativistic decay products themselves, whose pressure and, when a fluid description applies, <radiation acoustic oscillations> must be retained.
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