The cosmological density parameter (Ω) is one of the most used parameters in cosmology. It is dimensionless and expresses the ratio between the actual energy density of the universe and the socalled critical energy density.
Critical energy density is the borderline case between enough energy density to make the universe eventually contract again and too little energy density, causing infinite expansion. The density parameter is therefore:
where ρ is the actual observed density and ρ_{c} is the critical density. Ω has the value that we observe today. In an expanding (or contracting) universe, the density cannot remain constant, e.g., if we consider mass density, it must have been higher in the past of an expanding universe.
Further, energy density does not refer only to mass density  it refers to all forms of energy. The main contributors (in a cosmological sense) are: mass energy, radiation energy and vacuum energy. These components add up in pretty logical way, which is best expressed in terms of the universal expansion factor a, as defined in Part 2 of this miniseries. This gives the density parameter as a function of the expansion factor as:
Does this look logical? Maybe not at a first glance, but actually, it is! Here's why. Mass density varies inversely with the volume of space, i.e., a^{3}  straight engineer's logic.
Radiation density also varies inversely with the volume of space and, in addition to that, it varies inversely with another factor of a, due to the redshift caused by the expansion of the universe  straight cosmologist's logic.
Vacuum energy density does not care about expansion  the more vacuum, the more vacuum energy in a linear fashion  straight quantum theorist's logic.
The scary thing is, according to latest observations, the quantum theorists have got a stake in this, but they cannot agree on the size of their stake!
Relativity 4 Engineers has got some more readily digestible info on all of this weird stuff…

Re: Cosmology Equations Part 3