<Li> a is the time - dependent cosmic scale factor </Li> <Li> k is the curvature per unit area . </Li> <P> For an observer observing the crest of a light wave at a position r = 0 and time t = t, the crest of the light wave was emitted at a time t = t in the past and a distant position r = R. Integrating over the path in both space and time that the light wave travels yields: </P> <Dl> <Dd> c ∫ t t h e n t n o w d t a = ∫ R 0 d r 1 − k r 2 . (\ displaystyle c \ int _ (t_ (\ mathrm (then))) ^ (t_ (\ mathrm (now))) (\ frac (dt) (a)) \; = \ int _ (R) ^ (0) (\ frac (dr) (\ sqrt (1 - kr ^ (2)))) \, .) </Dd> </Dl>

How does the redshift show galaxies are moving away from us