= Solution
The physical <particle horizon> is
$$
d_H(t)=a(t)\int_0^t\frac{c\,dt'}{a(t')}.
$$
For an <Einstein-de Sitter universe>, $a(t)\propto t^{2/3}$, so
$$
d_H(t_0)=t_0^{2/3}c\int_0^{t_0}t'^{-2/3} dt'=3ct_0.
$$
Since $H_0=2/(3t_0)$,
$$
\boxed{d_H(t_0)=\frac{2c}{H_0}.}
$$
The <horizon problem> is that widely separated regions of the observed universe have nearly identical conditions even though, in a decelerating standard Big Bang history, their past light cones do not overlap early enough to establish causal thermal equilibrium.
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