Did the LIGO gravitational waves originate from primordial black holes?

Pardon. That should have been \( = M_{\textrm{chirp}}^{-5/8} \left( t_0 - t \right)^{-11/8}\) and is fixed now.

 

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Flaky system with frequent disconnects -> complete reinstall from scratch -> back in a few days. More then.

 

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Using units where \(c = G = M = 1\) and a fixed 1:1 ratio between the masses, we get a much simpler answer, but of course lose any dependence on M.
Let \(f = \tilde{f} \frac{c^3}{GM}, \; t = \tilde{t} \frac{GM}{c^3}, \; M_{\textrm{chirp}}^5 = \mu^3 M^2, \; \mu = \frac{1}{4} M\).
Then \(\tilde{f} \frac{c^3}{GM} = \frac{1}{8 \pi} \left( 20^3 \left( \frac{c^3}{GM} \right)^5 \right)^{1/8} \left( \frac{GM}{c^3} \left( \tilde{t}_0 - \tilde{t} \right) \right)^{-3/8} \)
or
\( \tilde{f} = \frac{1}{8 \pi} \left( \frac{20}{ \tilde{t}_0 - \tilde{t} } \right)^{3/8} \)
for an orbit angular frequency of
\( \tilde{\Omega} = \frac{1}{8} \left( \frac{20}{ \tilde{t}_0 - \tilde{t} } \right)^{3/8} \) which closely compares with figure 11 of https://arxiv.org/abs/gr-qc/0602026v2

 

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The conclusion comments in https://arxiv.org/abs/gr-qc/0602026v2 I agree with. Best left at that probably.