Cosmo All at 22:07, 2 March 2015

2015-03-02T22:07:21Z

Cosmo All at 17:37, 23 February 2015

2015-02-23T17:37:52Z

Cosmo All at 17:35, 23 February 2015

2015-02-23T17:35:17Z

Cosmo All: Created page with "

'''Problem 1'''
problem id: 1301_1
Show that for a spa..."

2015-02-23T17:34:57Z

Created page with " <div id="1301_1"></div> <div style="border: 1px solid #AAA; padding:5px;"> '''Problem 1''' <p style= "color: #999;font-size: 11px">problem id: 1301_1</p> Show that for a spa..."

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      <p style="text-align: left;">\[\frac{\ddot a}{a}=-\frac{4\pi G}{3}\rho(1+3w).\]
-In the flat case \[\rho=\frac{3}{8\pi G}H^2\] and \[q=-\frac{\dot a}{aH^2}=\frac12(1+3w).\]</p>
+In the flat case \[\rho=\frac{3}{8\pi G}H^2\] and \[q=-\frac{\ddot a}{aH^2}=\frac12(1+3w).\]</p>
    </div>
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    <div style="width:100%;" class="NavContent">
      <p style="text-align: left;">\[\frac{\ddot a}{a}=-\frac{4\pi G}{3}\rho(1+3w).\]
-Substitution \[\rho=\frac{3}{8\pi G}\left(H^2+\frac k{a^2}\right)\] gives \[q=-\frac{\dot a}{aH^2}=\frac12(1+3w)\left(1+\frac k{a^2H^2}\right).\]</p>
+Substitution \[\rho=\frac{3}{8\pi G}\left(H^2+\frac k{a^2}\right)\] gives \[q=-\frac{\ddot a}{aH^2}=\frac12(1+3w)\left(1+\frac k{a^2H^2}\right).\]</p>
    </div>
 </div></div>
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    <div style="width:100%;" class="NavContent">
      <p style="text-align: left;">In this case
-\[q=-\frac{\dot a}{aH^2}=\frac12(1+3\frac p\rho)\left(1+\frac k{a^2H^2}\right) =\] \[=\frac12\left[1+3\frac p\rho\left(1+\frac k{a^2H^2}\right)\right]+\frac k{2a^2H^2},\]
+\[q=-\frac{\ddot a}{aH^2}=\frac12(1+3\frac p\rho)\left(1+\frac k{a^2H^2}\right) =\] \[=\frac12\left[1+3\frac p\rho\left(1+\frac k{a^2H^2}\right)\right]+\frac k{2a^2H^2},\]
 \[1+\frac k{a^2H^2}=\sum\limits_i\Omega_i,\quad\frac p\rho=\frac{\sum\limits_iw_i\Omega_i}{\sum\limits_i\Omega_i},\]
 \[q=\frac12\left(1+3\sum\limits_i\Omega_i\right)+\frac k{2a^2H^2}.\]

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Category:Deceleration Parameter - Revision history

Cosmo All at 22:07, 2 March 2015

Cosmo All at 17:37, 23 February 2015

Cosmo All at 17:35, 23 February 2015

Cosmo All: Created page with " '''Problem 1''' problem id: 1301_1 Show that for a spa..."

Cosmo All: Created page with "

'''Problem 1'''
problem id: 1301_1
Show that for a spa..."