= Solution
During <radiation domination>, <conservation of energy> gives $\rho\propto a^{-4}$: dilution contributes $a^{-3}$ and the <cosmological redshift> of each <photon> contributes another $a^{-1}$. Thus $\alpha=4>2$ and $a=A\sqrt t$ in the flat radiation-dominated approximation. The <particle horizon> measured as proper radial distance on a constant-time slice is
$$
\boxed{s_{\rm hor}(t)=a(t)c\int_0^t\frac{dt'}{a(t')}=A\sqrt t\frac{2c\sqrt t}{A}=2ct.}
$$
Every local <comoving observer> measures the <speed of light> to be $c$. However, the spatial separations traversed earlier have expanded by the time the final distance is measured; the present separation from the earliest accessible comoving worldline is not the integral of local path lengths measured at their different traversal times. Indeed $\dot s_{\rm hor}=Hs_{\rm hor}+c=2c$ in this era, explicitly separating <cosmic expansion> from local propagation. Curvature or a later transition to <matter domination> changes the exact formula; $2ct$ is the radiation-dominated result.
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