Difference between revisions of "Statistical properties of CMB"
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[[Category:Cosmic Microwave Background (CMB)|3]] | [[Category:Cosmic Microwave Background (CMB)|3]] | ||
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| + | __TOC__ | ||
| + | |||
| + | <div id="cmb33"></div> | ||
| + | <div style="border: 1px solid #AAA; padding:5px;"> | ||
| + | === Problem 1: kinetic equation === | ||
| + | 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 2: dipole component === | ||
| + | The magnitude of the 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 3: annual variations === | ||
| + | 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 4: characteristic harmonic number === | ||
| + | Show that the angular resolution $\Delta\theta$ is related to the maximum harmonic $l_{max}$ (in the spherical harmonics decomposition) as | ||
| + | \[\Delta\theta={180^\circ}/{l_{max}}.\] | ||
| + | <!--<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 5: relativity === | ||
| + | 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> | ||
Latest revision as of 20:45, 19 November 2012
Contents
Problem 1: kinetic equation
Construct the differential equation for the photons' distribution function $\varphi(\omega,t)$ in a homogeneous and isotropic Universe.
Problem 2: dipole component
The magnitude of the 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 3: annual variations
Estimate the magnitude of annual variations of CMB anisotropy produced by rotation of the Earth around the Sun.
Problem 4: characteristic harmonic number
Show that the angular resolution $\Delta\theta$ is related to the maximum harmonic $l_{max}$ (in the spherical harmonics decomposition) as \[\Delta\theta={180^\circ}/{l_{max}}.\]
Problem 5: relativity
Does the measurement of velocity relative to the CMB mean violation of the relativity principle and an attempt to introduce an absolute reference frame?
