1. The Hubble Parameter
The Hubble parameter is the normalized rate of expansion:
Note that the Hubble parameter is not a constant! It changes with time. The Hubble constant is the Hubble parameter measured today -- we denote its value by H0. Best estimates are in the range of H0 = 65-75 km/s/Mpc. (ASTR 222 recommended value = 72)
Also note you will often see the parameter h, particularly in distance-dependant quantities (for example, 30h-1 Mpc). This is usually defined by h=H0/100.
Look at the Friedmann equation:
Rewriting this using the Hubble parameter, and for now set Lambda=0:
The Universe is flat if k=0, or if it has a critical mass density (in the absence of lamba) of
We define the matter density parameter as
Best measurements for Omega-matter are about 0.25 - 0.3, meaning the universe cannot have spatial flatness based on mass alone.
3. The "dark energy"