Extras - Revision history

Igor at 21:08, 19 November 2012

2012-11-19T21:08:53Z

Cosmo All: /* Problem 1 */

2012-10-01T21:27:59Z

‎Problem 1

Cosmo All at 21:24, 1 October 2012

2012-10-01T21:24:31Z

Cosmo All: Created page with "6 =Extras="

2012-09-25T00:12:29Z

Created page with "6 =Extras="

New page

[[Category:Cosmic Microwave Background (CMB)|6]]
=Extras=

@@ Line 6: / Line 6: @@
 <div id="cmb2"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 1 ===
+=== Problem 1: Gamov, 1953 ===
-In year 1953 the article "Extended Universe and creation of Galactics" by G.A. Gamov was published.<br/>
+The paper "Extended Universe and creation of Galactics" by G.A. Gamov was published in 1953.<br/>
-In that paper Gamov took two numbers - the age of the world and average density of matter in the Universe - and basing on them he determined the third number: the temperature of the relic radiation (cosmic microwave background). Try to repeat the scientific feat of Gamov.
+In that paper Gamov took two numbers - the age of the world and average density of matter in the Universe - and basing on them he determined the third number: the temperature of the relic radiation (cosmic microwave background). Try to repeat this scientific feat of Gamov.
 <div class="NavFrame collapsed">
    <div class="NavHead">solution</div>
    <div style="width:100%;" class="NavContent">
-     <p style="text-align: left;">Gamov considered the simplest variant of cosmological dynamics---the inertial regime of the expansion of Universe: \( R \propto t,\ v = const.
+     <p style="text-align: left;">Gamov considered the simplest variant of cosmological dynamics---the inertial regime of the expansion of the Universe: \( R \propto t,\ v = const.
-\) Density of homogeneous Universe, filled by non-relativistic matter, is
+\) Density of homogeneous Universe filled by non-relativistic matter is
 \[\rho _m  = \frac{M}{(4/3\pi )R^3 } = \rho _m (t_0 )\left(
 \frac{t_0}{t} \right)^3.
 \]
-Gamov used the following numerical numbers for current age of Universe and the matter density respectively:
+Gamov used the following numerical values for the current age of the Universe and matter density respectively:
 \( t_0  \simeq 3\cdot^10^9\mbox{years},
 \rho _m (t_0 ) \simeq 10^{-30} \mbox{g/cm}^3.\) Energy density in the radiation dominated Universe is
@@ Line 25: / Line 25: @@
 Then Gamov used the condition $\rho _r (t^*) = \rho _m (t^*)$ to find the moment of time when radiation-dominated epoch changed to matter-dominated one:
   \(
-t^*  \simeq 73\cdot10^6\ \mbox{years}\) Then he made use of the Stephan-Boltzmann law to determine the temperature in the joining point, i.e. at the time moment $t^*$ , \( T(t^*) = 320K.\) It is left only to use the condition $aT = const,$ in order to convert the temperature for the present time to obtain the following
+t^*  \simeq 73\cdot10^6\ \mbox{years}\) Then he made use of the Stephan-Boltzmann law to determine the temperature at the matching point, i.e. at the moment $t^*$ , \( T(t^*) = 320K.\) Then he only heeded to use the condition $aT = const,$ in order to convert the temperature for the present time to obtain
   \[
 T(t_0 ) = T\left( {t^*} \right)\frac{t^*}{t_0 }  \simeq 7K.

@@ Line 14: / Line 14: @@
      <p style="text-align: left;">Gamov considered the simplest variant of cosmological dynamics---the inertial regime of the expansion of Universe: \( R \propto t,\ v = const.
 \) Density of homogeneous Universe, filled by non-relativistic matter, is
-\[
+\[\rho _m  = \frac{M}{(4/3\pi )R^3 } = \rho _m (t_0 )\left(
-\rho _m  = \frac{M}{{(4/3\pi )R^3 }} = \rho _m (t_0 )\left(
+\frac{t_0}{t} \right)^3.
-{\frac{{t_0 }}{t}} \right)^3.
 \]
 Gamov used the following numerical numbers for current age of Universe and the matter density respectively:
 \( t_0  \simeq 3\cdot^10^9\mbox{years},
-\rho _m (t_0 ) \simeq 10^{-30} \mbox{\it g/cm}^3.\) Energy density in the radiation dominated Universe is
+\rho _m (t_0 ) \simeq 10^{-30} \mbox{g/cm}^3.\) Energy density in the radiation dominated Universe is
 \[
-\rho _r  = \frac{3}{{32\pi Gt^2 }}.
+\rho _r  = \frac{3}{32\pi Gt^2 }.
 \]
 Then Gamov used the condition $\rho _r (t^*) = \rho _m (t^*)$ to find the moment of time when radiation-dominated epoch changed to matter-dominated one:
@@ Line 28: / Line 27: @@
 t^*  \simeq 73\cdot10^6\ \mbox{years}\) Then he made use of the Stephan-Boltzmann law to determine the temperature in the joining point, i.e. at the time moment $t^*$ , \( T(t^*) = 320K.\) It is left only to use the condition $aT = const,$ in order to convert the temperature for the present time to obtain the following
   \[
-T(t_0 ) = T\left( {t^*} \right){\frac{{t^*}}{{t_0 }}}  \simeq 7K.
+T(t_0 ) = T\left( {t^*} \right)\frac{t^*}{t_0 }  \simeq 7K.
 \]

← Older revision		Revision as of 21:24, 1 October 2012
Line 1:		Line 1:
	[[Category:Cosmic Microwave Background (CMB)\|6]]		[[Category:Cosmic Microwave Background (CMB)\|6]]
−	=~~Extras~~=	+
		+
		+
		+
		+	<div id="cmb2"></div>
		+	<div style="border: 1px solid #AAA; padding:5px;">
		+	=== Problem 1 ===
		+	In year 1953 the article "Extended Universe and creation of Galactics" by G.A. Gamov was published.<br/>
		+	In that paper Gamov took two numbers - the age of the world and average density of matter in the Universe - and basing on them he determined the third number: the temperature of the relic radiation (cosmic microwave background). Try to repeat the scientific feat of Gamov.
		+	<div class="NavFrame collapsed">
		+	<div class="NavHead">solution</div>
		+	<div style="width:100%;" class="NavContent">
		+	<p style="text-align: left;">Gamov considered the simplest variant of cosmological dynamics---the inertial regime of the expansion of Universe: \( R \propto t,\ v = const.
		+	\) Density of homogeneous Universe, filled by non-relativistic matter, is
		+	\[
		+	\rho _m = \frac{M}{{(4/3\pi )R^3 }} = \rho _m (t_0 )\left(
		+	{\frac{{t_0 }}{t}} \right)^3.
		+	\]
		+	Gamov used the following numerical numbers for current age of Universe and the matter density respectively:
		+	\( t_0 \simeq 3\cdot^10^9\mbox{years},
		+	\rho _m (t_0 ) \simeq 10^{-30} \mbox{\it g/cm}^3.\) Energy density in the radiation dominated Universe is
		+	\[
		+	\rho _r = \frac{3}{{32\pi Gt^2 }}.
		+	\]
		+	Then Gamov used the condition $\rho _r (t^) = \rho _m (t^)$ to find the moment of time when radiation-dominated epoch changed to matter-dominated one:
		+	\(
		+	t^* \simeq 73\cdot10^6\ \mbox{years}\) Then he made use of the Stephan-Boltzmann law to determine the temperature in the joining point, i.e. at the time moment $t^$ , \( T(t^) = 320K.\) It is left only to use the condition $aT = const,$ in order to convert the temperature for the present time to obtain the following
		+	\[
		+	T(t_0 ) = T\left( {t^} \right){\frac{{t^}}{{t_0 }}} \simeq 7K.
		+	\]
		+
		+	"Is it possible to take two asymptotes, join them and determine the CMB temperature? The answer is, firstly, it is impossible, and secondly, Gamov did it already long ago." (A.D. Chernin)</p>
		+	</div>
		+	</div></div>