Cosmological Parameters

Before going further, it is useful to define some of the cosmological parameters in the Friedmann equation (and elsewhere).

1. The Hubble Parameter

The Hubble parameter is the normalized rate of expansion:

Note that the Hubble parameter is not a constant! The Hubble constant is the Hubble parameter measured today -- we denote its value by H0. Current estimates are in the range of H0 = 65-75 km/s/Mpc -- we will discuss these efforts in more detail later.

Also note you will often see the parameter h, particularly in distance-dependant quantities (for example, 75h-1 Mpc). This is usually defined by h=H0/100.

2. The Matter Density Parameter.
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 density of

We define the matter density parameter as

Best measurements for Om are about 0.25 - 0.35


 3. The "dark energy" density parameter

We can express a similar density parameter for lambda again by using the Friedmann equation and setting rhom=0. We then get

Best measurements for OL are about 0.65-0.75

4. "Total Omega"

What is Omega if the Universe is flat? What is Omega if the Universe is accelerating?

5. The deceleration parameter

Not used as often any more, describes the de/acceleration rate of the Universe's expansion: