Difference between revisions of "New oleg"
(Created page with " <div id=""></div> <div style="border: 1px solid #AAA; padding:5px;"> '''Problem 1''' <p style= "color: #999;font-size: 11px">problem id: </p> <div class="NavFrame collapsed...") |
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'''Problem 1''' | '''Problem 1''' | ||
<p style= "color: #999;font-size: 11px">problem id: </p> | <p style= "color: #999;font-size: 11px">problem id: </p> | ||
| − | + | Let us consider a very simple model with the following conservation equations: | |
| + | \begin{equation}\label{conserv_Qm} | ||
| + | \dot{\rho_{dm}}+3H\rho_{dm}=Q, | ||
| + | \end{equation} | ||
| + | \begin{equation}\label{conserv_Qe} | ||
| + | \dot{\rho_{de}}+3H\rho_{de}(1+w)=-Q, | ||
| + | \end{equation} | ||
| + | where $Q=3H\delta\rho_{dm}$ is the source of interaction and $w$ is the state equation parameter for dark energy. The positive small coupling constant $\delta$ will eventually characterize how evolution of the matter energy density | ||
| + | \begin{equation}\label{rho-m1} | ||
| + | \rho_{dm}= \rho_{dm0}a^{-3(1-\delta)}, | ||
| + | \end{equation} | ||
| + | will deviate from the standard case ($\rho_{m0}$ is the present value of $\rho_m$). | ||
<div class="NavFrame collapsed"> | <div class="NavFrame collapsed"> | ||
<div class="NavHead">solution</div> | <div class="NavHead">solution</div> | ||
Revision as of 21:39, 9 April 2015
Problem 1
problem id:
Let us consider a very simple model with the following conservation equations: \begin{equation}\label{conserv_Qm} \dot{\rho_{dm}}+3H\rho_{dm}=Q, \end{equation} \begin{equation}\label{conserv_Qe} \dot{\rho_{de}}+3H\rho_{de}(1+w)=-Q, \end{equation} where $Q=3H\delta\rho_{dm}$ is the source of interaction and $w$ is the state equation parameter for dark energy. The positive small coupling constant $\delta$ will eventually characterize how evolution of the matter energy density \begin{equation}\label{rho-m1} \rho_{dm}= \rho_{dm0}a^{-3(1-\delta)}, \end{equation} will deviate from the standard case ($\rho_{m0}$ is the present value of $\rho_m$).
Problem 2
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Problem 3
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Problem 4
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Problem 5
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Problem 6
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