= Cosmological bolometric background from conserved sources
{title2=$\mathcal F_0=cLn_0\int a(t)\,dt$}
Normalize the <scale factor> to $a_0=1$. Identical isotropic sources of <bolometric luminosity> $L$ and conserved <comoving number density> $n_0=a^3n$ produce all-sky <radiative flux> $\mathcal F_0=cLn_0\int a(t)\,dt$ in a transparent <FLRW metric>. The <source counts on an FLRW past light cone> and <cosmological flux dimming> cancel the transverse shell-area factor. For arbitrary proper source density the expression is instead $cL\int n(t)a(t)^4dt$. The intensity per <solid angle> is $\mathcal F_0/(4\pi)$. A detector of collecting area $A$ receives power $A\mathcal F_0$ under an all-sky effective-area convention.
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