Statistical properties of CMB - Revision history

Igor at 20:45, 19 November 2012

2012-11-19T20:45:43Z

Igor at 20:45, 19 November 2012

2012-11-19T20:45:15Z

Cosmo All at 20:47, 1 October 2012

2012-10-01T20:47:56Z

Cosmo All at 20:47, 1 October 2012

2012-10-01T20:47:11Z

Cosmo All: Created page with "3 =Statistical properties of CMB="

2012-09-25T00:12:36Z

Created page with "3 =Statistical properties of CMB="

New page

[[Category:Cosmic Microwave Background (CMB)|3]]
=Statistical properties of CMB=

@@ Line 1: / Line 1: @@
 [[Category:Cosmic Microwave Background (CMB)|3]]
-__NOTOC__
+__TOC__
 <div id="cmb33"></div>
@@ Line 60: / Line 60: @@
 === 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="NavFrame collapsed">
    <div class="NavHead">solution</div>
    <div style="width:100%;" class="NavContent">
      <p style="text-align: left;"></p>
    </div>
-</div></div>
+</div>--></div>

@@ Line 5: / Line 5: @@
 <div id="cmb33"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 1 ===
+=== 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="NavFrame collapsed">
    <div class="NavHead">solution</div>
    <div style="width:100%;" class="NavContent">
      <p style="text-align: left;"></p>
    </div>
-</div></div>
+</div>--></div>
@@ Line 18: / Line 18: @@
 <div id="cmb18"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 2 ===
+=== 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.
+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="NavFrame collapsed">
    <div class="NavHead">solution</div>
    <div style="width:100%;" class="NavContent">
      <p style="text-align: left;"></p>
    </div>
-</div></div>
+</div>--></div>
@@ Line 31: / Line 31: @@
 <div id="cmb19"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 3 ===
+=== 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="NavFrame collapsed">
    <div class="NavHead">solution</div>
    <div style="width:100%;" class="NavContent">
      <p style="text-align: left;"></p>
    </div>
-</div></div>
+</div>--></div>
@@ Line 44: / Line 44: @@
 <div id="cmb27"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 4 ===
+=== 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 \(\Delta\theta={180^\circ}/{l_{max}}.\)
+Show that the angular resolution $\Delta\theta$ is related to the maximum harmonic $l_{max}$ (in the spherical harmonics decomposition) as
-<div class="NavFrame collapsed">
+\[\Delta\theta={180^\circ}/{l_{max}}.\]
    <div class="NavHead">solution</div>
    <div style="width:100%;" class="NavContent">
      <p style="text-align: left;"></p>
    </div>
-</div></div>
+</div>--></div>
@@ Line 57: / Line 58: @@
 <div id="cmb38"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 5 ===
+=== 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">

@@ Line 18: / Line 18: @@
 <div id="cmb18"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 1 ===
+=== Problem 2 ===
 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">
@@ Line 31: / Line 31: @@
 <div id="cmb19"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 1 ===
+=== Problem 3 ===
 Estimate the magnitude of annual variations of CMB anisotropy produced by rotation of the Earth around the Sun.
 <div class="NavFrame collapsed">
@@ Line 44: / Line 44: @@
 <div id="cmb27"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 1 ===
+=== Problem 4 ===
 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">
@@ Line 57: / Line 57: @@
 <div id="cmb38"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 1 ===
+=== Problem 5 ===
 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">

← Older revision		Revision as of 20:47, 1 October 2012
Line 1:		Line 1:
	[[Category:Cosmic Microwave Background (CMB)\|3]]		[[Category:Cosmic Microwave Background (CMB)\|3]]
−	=~~Statistical properties~~ of CMB=	+
		+	__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>