The universe's critical density (i.e., critical density of the universe or ρc) is the density of mass across the universe that would leave it flat. The principle of general relativity (Einstein's theory that gravitational force is equivalent to space-time reacting to mass by curving) and the models of the universe based on it (Friedmann models) determine if the universe will "barely" expand forever (which is termed a flat universe, with the expansion of the universe at exactly its escape velocity), or is expanding more than that (an open universe) or will eventually contract (a closed universe), and if a cosmological constant (additional factor) is in play, how it plays into this.
The critical density shifts as the universe ages, i.e., when a distant object is observed, the critical density at the time/place of the object depends on its redshift. However, if gravity is the one force controlling expansion (which is currently believed untrue, the other factor being dark energy) then the density of the universe remains either above or below its critical density, or at the value of the critical density current at that time.
Astrophysics determines the critical density by observation of the universe's expansion and the universe's mass, the latter by direct observation of matter and by observation of apparent local effects of gravity on observed matter. The current estimate for the current critical density is five hydrogen atoms per cubic meter. Actual density of ordinary matter (baryonic mass density) is estimated at 0.2-0.25, but a density including dark matter, dark energy, and other energy (e.g., electromagnetic radiation) is very close to the critical density.
The density parameter of the universe, denoted by Ω, is the density of the universe scaled so that a value of 1 indicates the universe is at the critical density, i.e., Ωc = 1.
The deceleration parameter (q) indicates the universe's acceleration/deceleration of expansion: above zero is a measure of deceleration, zero means expansion is steady, and below zero means the expansion is actually accelerating. The deceleration parameter is defined in terms of the scale factor, "a", and is a (potentially constant) function of time:
a d2a/dt2 q(t) = - ————————— (da/dt)2
If gravity were fully counteracting expansion, the expansion would be decelerating and q would be greater than zero and the universe would eventually contract, presumably resulting the universe returning to a point, a theoretical future event termed the Big Crunch. Deceleration parameter q is defined such that 0.5 indicates a flat universe, i.e., qc = 0.5, which is what would be expected if the universe's density is exactly at its critical density, i.e., Ω = 1. Measurements have revealed acceleration of the expansion with q ≈ -0.55, which has led to the coining of the term dark energy for whatever is counteracting gravity sufficiently to make this happen.