= Open dust bolometric background integral
{title2=$\mathcal F_0=\dfrac{cLn_0\Omega_0^2}{4H_0(1-\Omega_0)^{5/2}}J(u_0)$}
For an <open matter-dominated Friedmann solution>, put $u=H_0\sqrt{1-\Omega_0}\,\tau$, $a=\Omega_0(\cosh u-1)/[2(1-\Omega_0)]$ and $\cosh u_0=2/\Omega_0-1$. The <cosmological bolometric background from conserved sources> has $J(u)=\sinh(2u)/4-2\sinh u+3u/2$, since $J'=(\cosh u-1)^2$ and $dt=a\,du/[H_0\sqrt{1-\Omega_0}]$. At fixed $H_0$, the limit $\Omega_0\to0$ is $cLn_0/(2H_0)$, whereas the <Einstein-de Sitter universe> gives $2cLn_0/(5H_0)$. Keeping the cosmic age fixed instead reverses this ordering: the two values are respectively $cLn_0t_0/2$ and $3cLn_0t_0/5$.
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