1.2. The Hubble Parameter h

Determining the Hubble constant, H0, requires that we have a way of getting the distance to galaxies independently of their redshifts. The history of determining the extragalactic distance scale is in itself a fascinating subject (Rowan-Robinson, 1986) and even today there is considerable uncertainty. There seems to be two distinct bodies of opinion, one clustering its estimates of H0 around 50 km s-1 Mpc-1 and the other around 80 km s-1 Mpc-1. We shall absorb this ignorance into a "Hubble parameter" h defined so that

So all distances quoted will contain the quantity h, and the reader is invited to substitute her/his favourite value.

It is probably safer in practise to use radial velocity to express distances. This reflects the Hubble law and so when we say a galaxy is at a distance of 30h-1 Mpc. we could equally well say it is at a distance of 3000 km s-1. This is fine, but it may look a bit strange to say that a void has a diameter of 5000 km s-1, or to say that the galaxy clustering correlation function drops to unity on a scale of 500 km s-1. The present value of the Hubble Constant, H0, and the density parameter, 0, together determine the present age of the universe. In the case of an 0 < 1 universe:

It is certain that there should not be any objects older than this in the Universe, so determining ages is an important way of constraining the values of H0 and 0. It seems that the oldest known stellar systems for which we can determine ages have ages in excess of 16 Gyr. (Sandage and Cacciari, 1990). If we accept this value, then we see that an 0 = 1 universe is always too young unless H0 is considerably lower than any of the values so far put forward. An open universe with 0 < 0.1 can work provided H0 is at the lower end of the suggested range of values.

What are we to make of this? That neither age determinations of star clusters nor the extragalactic distance scale can be relied on, with the latter probably being the most uncertain. Introducing a cosmological constant would of course help.