critical density

The universe's critical density (i.e., critical density of the universe or ρ_c) 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 alternately, it is expanding more than that (an open universe) or thirdly, it will eventually contract (a closed universe). Other factors, e.g., a cosmological constant, may exist and affect this characteristic of the universe.

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 were the only force controlling expansion (which is currently believed untrue, an additional factor being what is termed dark energy), then as time passes, the density of the universe would remain above, on, or below the critical density of the point in 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 about the mass of five hydrogen atoms per cubic meter. The actual density of ordinary matter (baryonic mass density) is estimated to be 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 term density parameter, denoted by Ω, indicates a measure of the density scaled so that a value of 1 indicates the universe's critical density. Ω₀ indicates the density parameter of the current universe (I presume "0" means at present, i.e., zero lookback time, in the manner that H₀ indicates the Hubble parameter's value at present). Ω_c is sometimes used for the density parameter that matches the critical density, i.e., 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 (possibly constant) function of time:

         a d2a/dt2
q(t) = - —————————
         (da/dt)2

Deceleration parameter q is defined such that 0.5 indicates a flat universe, i.e., q_c = 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.