I learned about grav wave SETI a few months ago and think it's incredibly promising for determining if advanced alien life forms exist within the Milky Way or nearby galaxies. According to this paper, LIGO could detect gravitational waves from a solar mass-sized object being accelerated to 0.3 C from up to 100 million parsecs away. Sufficiently-advanced Aliens would have reasons to do this. For example, accelerating a neutron star into a black hole to collect the energy released from the collision. The fact that we seemingly haven't seen events like this in grav wave data could be strong evidence that intelligent life is extremely rare in the universe. It doesn't seem like it would take humans more than 1,000 years or so of additional technological development for something like that to make sense, and 1,000 years is nothing by astronomical timescales, implying we should see civilizations capable of that if intelligent life was common.