Uniform-separation merger delay-time distribution ($dN/dt\propto t^{-3/4}$)

If a circular compact binary has a gravitational wave coalescence delay $t=B{A}_0^4$ and $dN/d{A}_0$ is constant, then $dN/dt=(dN/d{A}_0)|d{A}_0/dt|\propto t^{-3/4}$. More generally $dN/d{A}_0\propto A_0^{\beta }$ gives a delay-time distribution proportional to $t^{(\beta -3)/4}$. A log-uniform separation distribution instead gives $t^{-1}$.