Density parameter

In cosmology, the density parameters ( symbols ) indicate the distribution of the total density of the universe over various forms of matter and energy . They determine the geometry and the development of the universe, especially the temporal course of its expansion . ${\displaystyle \Omega _{(+{\text{Index}})}}$

definition

The actual mean density (mass per unit volume) is divided by the critical density , giving a dimensionless quantity ${\displaystyle \rho }$ ${\displaystyle \rho _{\mathrm {c} }}$

${\displaystyle \Omega _{\mathrm {tot} }={\frac {\rho }{\rho _{\mathrm {c} }}}}$.

receives. The index for total characterizes the total density, which is composed of the density of matter and energy. The critical density is the density at which the universe is flat : ${\displaystyle {}_{\mathrm {tot} }}$

${\displaystyle \rho _{\mathrm {c} }={\frac {3H_{0}^{2}}{8\pi G}}\simeq 8{,}5\cdot 10^{-27}\,{\frac {\mathrm {kg} }{\mathrm {m} ^{3}}}.}$

It is

• ${\displaystyle H_{0}}$the current Hubble parameter and
• ${\displaystyle G}$the gravitational constant .

In general, the density parameters change over time. An exception is the exact value . Usually the values ​​of the density parameters are given at the present time. ${\displaystyle \Omega _{\mathrm {tot} }=1}$

Influence on the geometry of the universe

possible geometries of the universe as a function of the total matter and energy density here as a designated ${\displaystyle \Omega _{0}}$

The spatial geometry of the universe is determined by the total density of matter and energy : ${\displaystyle \Omega _{\mathrm {tot} }}$

Overall density	geometry
${\displaystyle \Omega _{\mathrm {tot} }>1}$	spherical
${\displaystyle \Omega _{\mathrm {tot} }=1}$	flat
${\displaystyle \Omega _{\mathrm {tot} }<1}$	hyperbolic

The density parameters can be determined very precisely by observing temperature fluctuations in the cosmological background radiation and other astronomical observations. The current measurements (especially by the WMAP and Planck satellites) result in the context of the standard model of cosmology ( isotropic and homogeneous universe, dynamics described by the Friedmann equations ) for the total density of the universe:

${\displaystyle \Omega _{\mathrm {tot} }=1{,}0005\pm 0{,}0065}$

In terms of measurement accuracy , the universe appears flat.

Share of this total density:

• The largest part of the universe consists of dark energy with negative pressure (see also cosmological constant ). ${\displaystyle \Omega _{\Lambda }=0{,}685\pm 0{,}013}$
• The second largest part consists of matter , ${\displaystyle \Omega _{\mathrm {M} }=0{,}315\pm 0{,}013}$
  • whereby the predominant part consists of dark matter and
  • ordinary baryonic matter only contributes. ${\displaystyle \Omega _{\mathrm {b} }=0{,}0489\pm 0{,}00062}$
• Also worth mentioning is electromagnetic radiation , whose contribution today is with

${\displaystyle \Omega _{\mathrm {rad} }={\frac {\rho _{\rm {rad}}}{\rho _{\rm {c}}}}\approx 5{,}5\cdot 10^{-5}}$

but is very small. It is

${\displaystyle \rho _{\rm {rad}}={\frac {8\pi ^{5}k_{\rm {B}}^{4}T^{4}}{15c^{5}h^{3}}}\approx 4{,}64\cdot 10^{-31}\,{\rm {kg/m^{3}}}}$

the radiation density of the microwave background radiation, and the temperature of the background radiation , the Boltzmann constant and the Planck's constant . ${\displaystyle T=2{,}725\,{\rm {K}}}$ ${\displaystyle k_{\rm {B}}}$ ${\displaystyle h}$

See also

• Inflation (cosmology)
• general theory of relativity
• Lambda CDM model

Individual evidence

1. ↑ Planck Mission 2013 Volume XVI, page 42, column 2