I've asked this question before, but I don't think I received a good answer, so figured I'd try asking again. How do we know that galaxies are accelerating away from us and not moving at constant speed? People often point to the observation that the further away a galaxy is, the faster it appears to be moving away from us, implying acceleration. However, wouldn't we expect to see the same observation even without any…
The conclusion that the expansion is accelerating was a quite recent result: 1990s, I believe. It's based on careful measurements of supernova explosions of a type with computable intrinsic brightness in increasingly distant galaxies, and the exact pattern seen in their apparent redshifts vs. apparent brightness. It was a shocking discovery when it came out, with two separate teams announcing the result pretty much neck and neck. There's also independent and compatible evidence for acceleration from the exact pattern of variations in the temperature of the cosmic microwave background seen at different points in the sky.