This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Deceleration parameter" – news · newspapers · books · scholar · JSTOR (February 2011) (Learn how and when to remove this template message)

Part of a series on
Physical cosmology
Big Bang · Universe Age of the universe Chronology of the universe
Early universe Inflation · Nucleosynthesis Backgrounds Gravitational wave (GWB) Microwave (CMB) · Neutrino (CNB)
Expansion · Future Hubble's law · Redshift Expansion of the universe FLRW metric · Friedmann equations Inhomogeneous cosmology Future of an expanding universe Ultimate fate of the universe
Components · Structure Components Lambda-CDM model Dark energy · Dark matter Structure Shape of the universe Galaxy filament · Galaxy formation Large quasar group Large-scale structure Reionization · Structure formation
Experiments Black Hole Initiative (BHI) BOOMERanG Cosmic Background Explorer (COBE) Dark Energy Survey Planck space observatory Sloan Digital Sky Survey (SDSS) 2dF Galaxy Redshift Survey ("2dF") Wilkinson Microwave Anisotropy Probe (WMAP)
Scientists Aaronson Alfvén Alpher Copernicus de Sitter Dicke Ehlers Einstein Ellis Friedmann Galileo Gamow Guth Hawking Hubble Huygens Kepler Lemaître Mather Newton Penrose Penzias Rubin Schmidt Smoot Suntzeff Sunyaev Tolman Wilson Zeldovich List of cosmologists
Subject history Discovery of cosmic microwave background radiation History of the Big Bang theory Timeline of cosmological theories
Category  Astronomy portal
v t e

The deceleration parameter ${\displaystyle q}$ in cosmology is a dimensionless measure of the cosmic acceleration of the expansion of space in a Friedmann–Lemaître–Robertson–Walker universe. It is defined by:

where ${\displaystyle a}$ is the scale factor of the universe and the dots indicate derivatives by proper time. The expansion of the universe is said to be "accelerating" if ${\displaystyle {\ddot {a}}>0}$ (recent measurements suggest it is), and in this case the deceleration parameter will be negative.^[1] The minus sign and name "deceleration parameter" are historical; at the time of definition ${\displaystyle {\ddot {a}}}$ was expected to be negative, so a minus sign was inserted in the definition to make ${\displaystyle q}$ positive in that case. Since the evidence for the accelerating universe in the 1998–2003 era, it is now believed that ${\displaystyle {\ddot {a}}}$ is positive therefore the present-day value ${\displaystyle q_{0}}$ is negative (though ${\displaystyle q}$ was positive in the past before dark energy became dominant). In general ${\displaystyle q}$ varies with cosmic time, except in a few special cosmological models; the present-day value is denoted ${\displaystyle q_{0}}$.

The Friedmann acceleration equation can be written as

where the sum ${\displaystyle i}$ extends over the different components, matter, radiation and dark energy, ${\displaystyle \rho _{i}}$ is the equivalent mass density of each component, ${\displaystyle p_{i}}$ is its pressure, and ${\displaystyle w_{i}=p_{i}/(\rho _{i}c^{2})}$ is the equation of state for each component. The value of ${\displaystyle w_{i}}$ is 0 for non-relativistic matter (baryons and dark matter), 1/3 for radiation, and −1 for a cosmological constant; for more general dark energy it may differ from −1, in which case it is denoted ${\displaystyle w_{DE}}$ or simply ${\displaystyle w}$.

Defining the critical density as

and the density parameters ${\displaystyle \Omega _{i}\equiv \rho _{i}/\rho _{c}}$, substituting ${\displaystyle \rho _{i}=\Omega _{i}\,\rho _{c}}$ in the acceleration equation gives where the density parameters are at the relevant cosmic epoch. At the present day ${\displaystyle \Omega _{\text{rad}}\sim 10^{-4}}$ is negligible, and if ${\displaystyle w_{DE}=-1}$ (cosmological constant) this simplifies to where the density parameters are present-day values; with Ω_Λ + Ω_m ≈ 1, and Ω_Λ = 0.7 and then Ω_m = 0.3, this evaluates to ${\displaystyle q_{0}\approx -0.55}$ for the parameters estimated from the Planck spacecraft data.^[2] (Note that the CMB, as a high-redshift measurement, does not directly measure ${\displaystyle q_{0}}$; but its value can be inferred by fitting cosmological models to the CMB data, then calculating ${\displaystyle q_{0}}$ from the other measured parameters as above).

The time derivative of the Hubble parameter can be written in terms of the deceleration parameter:

Except in the speculative case of phantom energy (which violates all the energy conditions), all postulated forms of mass-energy yield a deceleration parameter ${\displaystyle q\leqslant -1.}$ Thus, any non-phantom universe should have a decreasing Hubble parameter, except in the case of the distant future of a Lambda-CDM model, where ${\displaystyle q}$ will tend to −1 from above and the Hubble parameter will asymptote to a constant value of ${\displaystyle H_{0}{\sqrt {\Omega _{\Lambda }}}}$.

The above results imply that the universe would be decelerating for any cosmic fluid with equation of state ${\displaystyle w}$ greater than ${\displaystyle -{\tfrac {1}{3}}}$Zdroj:https://en.wikipedia.org?pojem=Deceleration_parameter
Text je dostupný za podmienok Creative Commons Attribution/Share-Alike License 3.0 Unported; prípadne za ďalších podmienok. Podrobnejšie informácie nájdete na stránke Podmienky použitia.

---