There is something I don't understand about the Hubble "constant" H, as it seems to clump two concepts together that I can't quite unify in my head. On the one side, we have
V = D * H
which means that for a given distance D, there is a certain amount of new space created over time - and H is simply the factor that makes this relationship work. So, for example, say we have two points 1 Mpc apart, this would mean they recede at about 70 km/s away from each other (given our current approximation of H).
Now the thing I can't wrap my head around is that
T = 1 / H
is also the age of the universe. Contrary to claims made on, say, Wikipedia this means that H cannot possibly have been a constant throughout the past 13 billion years, because mathematically 1/H means that H must be continually shrinking as the universe ages.
So if H did start out as some huge value and is now shrinking over time, doesn't this mean the expansion of the universe is slowing down? Because if H is shrinking, I'll get a lower value of V today than I'll get tomorrow. Shouldn't the notation then be more like
V = D * H(t) ?
So which one is it? If 1/H is simply the solution for D=0, how can we use it as the expansion-velocity-per-unit-of-distance at the same time? What's worse, how can literature say H has probably been more or less constant forever and simultaneously assert that 1/H is the current age of the universe? What am I missing?