= Solution
For an <Einstein-de Sitter universe>, the <Hubble parameter> is $H(z)=H_0(1+z)^{3/2}$. The <comoving particle horizon> becomes
$$
r_h(z)=\frac c{H_0}\int_z^\infty(1+z')^{-3/2}\,dz'
=\frac c{H_0}\left[-2(1+z')^{-1/2}\right]_z^\infty.
$$
Thus
$$
\boxed{r_h(z)=\frac{2c}{H_0\sqrt{1+z}}.}
$$
It tends to zero towards the initial singularity and increases without bound as $z\to-1$ in the infinite future. At the present time it is $2c/H_0=3ct_0$, since the <Einstein-de Sitter universe> has age $t_0=2/(3H_0)$.
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