The Hubble Constant and the Expansion of the Universe

[madness]

The Hubble constant v = Hd tells us recessional velocity of galaxies is proportional to distance. But distance is equivalent to looking back in time. So what we are seeing is the recessional velocities of galaxies at different times in the universe? This surely can't be right, because for an expanding universe, recessional velocity should be proportional to physical distance, not time.

 

[Chalnoth]

The Hubble constant v = Hd tells us recessional velocity of galaxies is proportional to distance. But distance is equivalent to looking back in time. So what we are seeing is the recessional velocities of galaxies at different times in the universe? This surely can't be right, because for an expanding universe, recessional velocity should be proportional to physical distance, not time.

The above equation only holds when you have a constant expansion rate. When the expansion rate changes with time, you have to use an integral.