### Critical Density

**(ρ**_{c}, Critical Density of the Universe)
(density of the universe which leaves it flat)

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 (a **Flat Universe**,
with space's expansion 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.,
**Ω**_{c} = 1.

The **Deceleration Parameter** (**q**) indicates the
universe's acceleration/deceleration of expansion and
a deceleration parameter of .5 indicates
a flat universe, i.e., **q**_{c} = .5. The
deceleration parameter is a function of time, defined in terms
of the Scale Factor, "a":

a d^{2}a/dt^{2}
q(t) = —————————
(da/dt)^{2}

(*astrophysics,cosmology,measure*)
https://en.wikipedia.org/wiki/Friedmann_equations#Density_parameter

**Referenced by:**

Astronomical Quantities

Cluster Radius

Lambda-CDM model (ΛCDM)

Mass Density

Virial Theorem

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