Difference between revisions of "Peculiarity of dynamics of scalar field coupled to dark matter"
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[[Category:Interactions in the Dark Sector|6]] | [[Category:Interactions in the Dark Sector|6]] | ||
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__NOTOC__ | __NOTOC__ | ||
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+ | = Interacting quintessence model = | ||
+ | Given that the quintessence field and the dark matter have unknown physical natures, there seem to be no a priori reasons to exclude a coupling between the two components. Let us consider a two-component system (scalar field $\varphi$ + dark matter) with the energy density and pressure | ||
+ | \[\rho=\rho_\varphi+\rho_{dm},\quad p=p_\varphi+p_{dm}\] | ||
+ | (we do not exclude the possibility of warm DM ($p_{dm}\ne0$).) | ||
+ | If some interaction exists between the scalar field and DM, then | ||
+ | \[\dot\rho_{dm}+3H(\rho_{dm}+p_{dm})=Q\] | ||
+ | \[\dot\rho_\varphi+3H(\rho_\varphi+p_\varphi)=-Q.\] | ||
+ | Using the effective pressures $\Pi_\varphi$ and $\Pi_{dm}$, | ||
+ | \[Q=-3H\Pi_{dm}=3H\Pi_\varphi\] | ||
+ | one can transit to the system | ||
+ | \begin{align} | ||
+ | \nonumber | ||
+ | \dot\rho_{dm}+3H(\rho_{dm}+p_{dm}+\Pi_{dm}) & =0,\\ | ||
+ | \nonumber | ||
+ | \dot\rho_\varphi+3H(\rho_\varphi+p_\varphi+\Pi_\varphi) & =0. | ||
+ | \end{align} | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
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+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
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+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
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+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
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+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
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+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
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+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
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+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
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+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
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+ | <div class="NavHead">solution</div> | ||
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+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
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+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
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+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
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+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
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+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
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+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
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+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
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+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
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+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
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+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
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+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
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+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
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+ | <div class="NavHead">solution</div> | ||
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+ | </div> | ||
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+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
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+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
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+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
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+ | <div class="NavHead">solution</div> | ||
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+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
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+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
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+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
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+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
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+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
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+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
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+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
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+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
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+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
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+ | <div style="width:100%;" class="NavContent"> | ||
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+ | <div style="width:100%;" class="NavContent"> | ||
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+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
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+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
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+ | <div style="width:100%;" class="NavContent"> | ||
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+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
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+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
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+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
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+ | <div style="width:100%;" class="NavContent"> | ||
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+ | </div> | ||
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+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
+ | <div style="border: 1px solid #AAA; padding:5px;"> | ||
+ | === Problem 1 === | ||
+ | |||
+ | <div class="NavFrame collapsed"> | ||
+ | <div class="NavHead">solution</div> | ||
+ | <div style="width:100%;" class="NavContent"> | ||
+ | <p style="text-align: left;"></p> | ||
+ | </div> | ||
+ | </div></div> | ||
+ | |||
+ | |||
+ | |||
+ | <div id=""></div> | ||
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Revision as of 11:38, 8 November 2013
Interacting quintessence model
Given that the quintessence field and the dark matter have unknown physical natures, there seem to be no a priori reasons to exclude a coupling between the two components. Let us consider a two-component system (scalar field $\varphi$ + dark matter) with the energy density and pressure \[\rho=\rho_\varphi+\rho_{dm},\quad p=p_\varphi+p_{dm}\] (we do not exclude the possibility of warm DM ($p_{dm}\ne0$).) If some interaction exists between the scalar field and DM, then \[\dot\rho_{dm}+3H(\rho_{dm}+p_{dm})=Q\] \[\dot\rho_\varphi+3H(\rho_\varphi+p_\varphi)=-Q.\] Using the effective pressures $\Pi_\varphi$ and $\Pi_{dm}$, \[Q=-3H\Pi_{dm}=3H\Pi_\varphi\] one can transit to the system \begin{align} \nonumber \dot\rho_{dm}+3H(\rho_{dm}+p_{dm}+\Pi_{dm}) & =0,\\ \nonumber \dot\rho_\varphi+3H(\rho_\varphi+p_\varphi+\Pi_\varphi) & =0. \end{align}
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