|
|
| Line 1: |
Line 1: |
| {{Refimprove|date=February 2011}}
| | The writer's name is Andera and she thinks it sounds fairly good. Kentucky is where I've usually been residing. Invoicing is my profession. Playing badminton is a thing that he is completely addicted to.<br><br>Check out my web site; psychics online ([http://kjhkkb.net/xe/notice/374835 Related Home Page]) |
| {{Cosmology}}
| |
| The '''deceleration parameter ''<math>\! q</math>''''' in cosmology is a [[dimensionless]] measure of the '''cosmic acceleration''' of the expansion of space in a [[Friedmann–Lemaître–Robertson–Walker metric|Friedmann–Lemaître–Robertson–Walker universe]]. It is defined by: | |
| :<math>q \ \stackrel{\mathrm{def}}{=}\ -\frac{\ddot{a} a }{\dot{a}^2}</math>
| |
| where <math>\! a</math> is the [[Scale factor (cosmology)|scale factor of the universe]] and the dots indicate derivatives by [[proper time]]. The expansion of the universe is said to be "accelerating" if <math>\ddot{a}</math> is positive (recent measurements suggest it is), and in this case the deceleration parameter will be negative.<ref>{{cite book | last = Jones | first = Mark H. | coauthors = Robert J. Lambourne | title = An Introduction to Galaxies and Cosmology | publisher =Cambridge University Press | date= 2004 | page = [http://books.google.com/books?id=36K1PfetZegC&lpg=PP1&pg=PA244#v=onepage&q&f=false 244] | isbn = 978-0-521-83738-5 }}</ref> The minus sign and name "deceleration parameter" are historical; at the time of definition <math>\! q</math> was thought to be positive, now it is believed to be negative. | |
| | |
| The [[Friedmann equations|Friedmann acceleration equation]] can be written as
| |
| :<math>3\frac{\ddot{a}}{a} =-4 \pi G (\rho+3p)=-4\pi G(1+3w)\rho, </math>
| |
| where <math>\! \rho</math> is the energy density of the universe, <math>\! p</math> is its pressure, and <math>\! w</math> is the [[Equation of state (cosmology)|equation of state]] of the universe.
| |
| | |
| This can be rewritten as
| |
| :<math>q=\frac{1}{2}(1+3w)\left(1+K/(aH)^2\right)</math> | |
| by using the first Friedmann equation, where <math>\! H</math> is the [[Hubble parameter]] and <math>\! K=1,0</math> or <math>\! -1</math> depending on whether the universe is [[shape of the universe|hyperspherical]], [[shape of the universe|flat]] or [[shape of the universe|hyperbolic]] respectively.
| |
| | |
| The derivative of the [[Hubble parameter]] can be written in terms of the deceleration parameter:
| |
| :<math>\frac{\dot{H}}{H^2}=-(1+q).</math>
| |
| Except in the speculative case of [[phantom energy]] (which violates all the energy conditions), all postulated forms of matter yield a deceleration parameter <math>\! q \ge -1</math>. Thus, any ''expanding'' universe should have a decreasing Hubble parameter and the local expansion of space is always slowing (or, in the case of a cosmological constant, proceeds at a constant rate, as in [[de Sitter space]]).
| |
| | |
| Observations of the [[cosmic microwave background]] demonstrate that the universe is very nearly flat, so:
| |
| :<math>q=\frac{1}{2}(1+3w)</math>
| |
| This implies that the universe is decelerating for any cosmic fluid with equation of state <math>\! w</math> greater than <math>\! -1/3</math> (any fluid satisfying the [[strong energy condition]] does so, as does any form of matter present in the [[Standard Model]], but excluding inflation). However observations of distant [[type Ia supernova]]e indicate that <math>\! q</math> is negative; the expansion of the universe is accelerating. This is an indication that the gravitational attraction of matter, on the cosmological scale, is more than counteracted by negative pressure [[dark energy]], in the form of either [[Quintessence (physics)|quintessence]] or a positive [[cosmological constant]].
| |
| | |
| Before the first indications of an accelerating universe, in 1998, it was thought that the universe was dominated by dust with negligible equation of state, <math>\! w \approx 0</math>. This had suggested that the deceleration parameter was equal to one half; the experimental effort to confirm this prediction led to the discovery of possible acceleration...
| |
| | |
| ==References==
| |
| {{reflist}}
| |
| | |
| [[Category:Physical cosmology]]
| |
The writer's name is Andera and she thinks it sounds fairly good. Kentucky is where I've usually been residing. Invoicing is my profession. Playing badminton is a thing that he is completely addicted to.
Check out my web site; psychics online (Related Home Page)