I heard on the TED Radio Hour that the LIGO team was able to make an independent measurement of the Hubble constant and the increasing expansion rate of the universe when they detected the gravitational waves coming from a neutron star collision. How does measuring those waves tell you about the expansion rate of the universe?
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The distance to a merging binary gravitational wave source can be independently determined. See How were the solar masses and distance of the GW150914 merger event calculated from the signal? For this reason, they have been dubbed "standard sirens".
If the source of the gravitational waves is then also traced to a particular galaxy (as it was in the case of the recent merging neutron star source) then that galaxy's distance is determined by the gravitational wave distance.
The Hubble constant can then be estimated from the ratio of that galaxy's redshift velocity to its distance, and hence the "expansion rate of the universe".
The original paper is by Abbott et al. (2017), who find a relatively weak constraint of $H_0 = 70.0^{+12}_{-8}$ km s$^{-1}$/Mpc, which
is consistent with existing measurements, while being completely independent of them
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1$\begingroup$ Oh I see so it's more of an independent distance measurement that they didn't have before. Sort of a kin to the the standard candles of type 1A supernovae where you know the intrinsic brightness so you can extrapolate the distance. In the linked question, they can estimate the mass of the system from the phase of the signal. Then they can measure the amplitude and work backwards to the distance. Once you've got the distance, you can work out the Hubble constant independent of other standard candles. Cool! $\endgroup$– JohnCommented Feb 15, 2018 at 18:41
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$\begingroup$ @John Yes, they have become known as standard sirens. $\endgroup$– ProfRobCommented Feb 15, 2018 at 21:20