|The Hubble Constant|
The first interesting parameter is the current expansion rate, or the Hubble constant H0. When we look at galaxies around us, the speed at which they are moving away from us is proportional to their distance from us. This is known as "Hubble's Law" and can be written as
The recession speed, v, can be determined from the shift in wavelength of the galaxy's light. As a galaxy moves away from us, its light is shifted to longer wavelengths; the faster it moves away, the more the light is shifted. This shift is known as the redshift (called "z") and can be determined by taking a spectrum of the galaxy. So the more "redshifted" the galaxy is, the further away it is.
To solve for the Hubble constant, though, we need to also know exactly how far away the galaxy is. This is the hard part, and has been a major stumbling block in determining the Hubble constant. There are several different ways to measure the distances to galaxies, for example using the brightness of variable stars, or correlations between a galaxy's luminosity and the speed at which it rotates, but all the methods have different levels of uncertainty.
Once we know both the distance and recession speed of a galaxy, we can solve for the expansion rate. We do this for large samples of galaxies to reduce the uncertainties in the calculation, and as our distances get better, our constraint on the Hubble constant gets better. For a long time in the 1970s and 1980s, the Hubble constant was only poorly constrained, in the range 50 km/s/Mpc < H0 < 100 km/s/Mpc. Now, however, most estimates place it in the range 60 km/s/Mpc < H0 < 70 km/s/Mpc.