Difference between revisions of "Statistical properties of CMB"

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=== Problem 1 ===
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=== Problem 1: kinetic equation ===
 
Construct the differential equation for the photons' distribution function $\varphi(\omega,t)$ in a homogeneous and isotropic Universe.
 
Construct the differential equation for the photons' distribution function $\varphi(\omega,t)$ in a homogeneous and isotropic Universe.
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=== Problem 2 ===
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=== Problem 2: dipole component ===
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.
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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.
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=== Problem 3 ===
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=== Problem 3: annual variations ===
 
Estimate the magnitude of annual variations of CMB anisotropy produced by rotation of the Earth around the Sun.
 
Estimate the magnitude of annual variations of CMB anisotropy produced by rotation of the Earth around the Sun.
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=== Problem 4 ===
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=== 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) by \(\Delta\theta={180^\circ}/{l_{max}}.\)
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Show that the angular resolution $\Delta\theta$ is related to the maximum harmonic $l_{max}$ (in the spherical harmonics decomposition) as
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\[\Delta\theta={180^\circ}/{l_{max}}.\]
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=== Problem 5 ===
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=== 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?
 
Does the measurement of velocity relative to the CMB mean violation of the relativity principle and an attempt to introduce an absolute reference frame?
 
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Revision as of 20:45, 19 November 2012



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?