Difference between revisions of "Statistical properties of CMB"
(Created page with "3 =Statistical properties of CMB=") |
|||
| Line 1: | Line 1: | ||
[[Category:Cosmic Microwave Background (CMB)|3]] | [[Category:Cosmic Microwave Background (CMB)|3]] | ||
| − | = | + | |
| + | __NOTOC__ | ||
| + | |||
| + | <div id="cmb33"></div> | ||
| + | <div style="border: 1px solid #AAA; padding:5px;"> | ||
| + | === Problem 1 === | ||
| + | Construct the differential equation for the photons' distribution function $\varphi(\omega,t)$ in a homogeneous and isotropic Universe. | ||
| + | <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="cmb18"></div> | ||
| + | <div style="border: 1px solid #AAA; padding:5px;"> | ||
| + | === Problem 1 === | ||
| + | The magnitude of dipole component of anisotropy generated by the Solar system's motion relative to the relic radiation equals $\Delta T_d\simeq3.35mK$. Determine the velocity of the Solar system relative to the relic radiation. | ||
| + | <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="cmb19"></div> | ||
| + | <div style="border: 1px solid #AAA; padding:5px;"> | ||
| + | === Problem 1 === | ||
| + | Estimate the magnitude of annual variations of CMB anisotropy produced by rotation of the Earth around the Sun. | ||
| + | <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="cmb27"></div> | ||
| + | <div style="border: 1px solid #AAA; padding:5px;"> | ||
| + | === Problem 1 === | ||
| + | Show that the angular resolution $\Delta\theta$ is related to the maximum harmonic $l_{max}$ (in the spherical harmonics decomposition) by \(\Delta\theta={180^\circ}/{l_{max}}.\) | ||
| + | <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="cmb38"></div> | ||
| + | <div style="border: 1px solid #AAA; padding:5px;"> | ||
| + | === Problem 1 === | ||
| + | Does the measurement of velocity relative to the CMB mean violation of the relativity principle and an attempt to introduce an absolute reference frame? | ||
| + | <div class="NavFrame collapsed"> | ||
| + | <div class="NavHead">solution</div> | ||
| + | <div style="width:100%;" class="NavContent"> | ||
| + | <p style="text-align: left;"></p> | ||
| + | </div> | ||
| + | </div></div> | ||
Revision as of 20:47, 1 October 2012
Problem 1
Construct the differential equation for the photons' distribution function $\varphi(\omega,t)$ in a homogeneous and isotropic Universe.
Problem 1
The magnitude of dipole component of anisotropy generated by the Solar system's motion relative to the relic radiation equals $\Delta T_d\simeq3.35mK$. Determine the velocity of the Solar system relative to the relic radiation.
Problem 1
Estimate the magnitude of annual variations of CMB anisotropy produced by rotation of the Earth around the Sun.
Problem 1
Show that the angular resolution $\Delta\theta$ is related to the maximum harmonic $l_{max}$ (in the spherical harmonics decomposition) by \(\Delta\theta={180^\circ}/{l_{max}}.\)
Problem 1
Does the measurement of velocity relative to the CMB mean violation of the relativity principle and an attempt to introduce an absolute reference frame?
