= Solution
For $\Omega_m=1$ the preceding result reduces to $\kappa=\Omega_b C_H[(1+z_{\rm re})^{3/2}-1]$. Using $C_H=0.032$ and $\Omega_b=0.05$ gives
$$
\boxed{z_{\rm re}=(1+625)^{2/3}-1\simeq72.2\qquad(\kappa=1).}
$$
At fixed $H_0$ and $\Omega_b$, a lower matter density lowers $H(z)$ relative to the flat dust value at positive redshift. The same <Electron> density then persists for a longer scattering time, increasing the <optical depth>. Hence the <reionization> redshift giving unit depth is lower in an open universe.
In the high-redshift matter regime the scaling is $1+z_{\rm re}\propto\Omega_m^{1/3}$ at fixed <optical depth>; for $\Omega_m=0.3$ this suggests a redshift near fifty rather than seventy. This comparison holds the baryon density fixed, not the baryon fraction $\Omega_b/\Omega_m$, and is not an estimate of the actual observed <reionization> epoch.
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