We should also be on the lookout for things which don't belong, like discrepancies in isotope abundances which may be evidence of alien technology in distant geological time, or things which are missing. Where did all of those magnetic monopoles which should have been created in the Big Bang go, anyway? Or maybe they've moved on to some other, richer domain in the universe. According to the consensus model of cosmology, we have no idea whatsoever what more than 95% of the universe is made of. Maybe they've transcended their juvenile baryonic origins and decamped to the greener fields we call, in our ignorance, “dark matter” and “dark energy”. While we're pointing antennas at obsolete stars in the sky, maybe they're already here (and everywhere else), not as UFOs or alien invaders, but super-intelligences made of structures which interact only gravitationally with the thin scum of baryonic matter on top of the rich ocean of the universe. Maybe their galactic Internet traffic is already tickling the mirrors of our gravitational wave detectors at intensities we can't hope to detect with our crude technologies.