I was reading Ned Wright's cosmology tutorial ( http://www.astro.ucla.edu/~wright/cosmo_02.htm ), and I'm a bit confused on how to interpret the diagrams featured on that page with respect to Hubble's constant. As I understand, Hubble's constant basically expresses the (pretty much linear) momentary relationship between distance and recessional velocity of far-away objects, such as other superclusters. Judging from the figures on Ned's site (scroll down a bit in that link: they show the expansion of space schematically in space-time diagrams, with our past light cone indicated by red lines), I'd say that Hubble's constant used to be larger in the past. After all, looking at the recessional velocity of objects at a certain fixed distance from 'our' position, this recessional velocity seems to get smaller over the course of time as the universe expands. It could, of course, very well be the case that I'm making some wrong assumptions about those diagrams, but it seems logical to me that linear expansion of space (linear both in space and time) automatically means that Hubble's constant should decrease over time. If it stays constant, we'd be in an exponentially expanding universe, not a linear one. A decrease of Hubble's constant over time would even be compatible with an accelerating expansion (as we are apparently observing to be the case with our universe), that acceleration being within certain limits. Of course we don't have direct observational data on the evolution of Hubble's constant with time (or do we?), but is it generally thought to be decreasing over time? Funny it should be called a 'constant', in that case: constant over space, rather than over time.