Cosmo All at 21:22, 24 February 2014

2014-02-24T21:22:31Z

Show changes

Cosmo All at 11:31, 18 February 2014

2014-02-18T11:31:59Z

Cosmo All at 11:20, 18 February 2014

2014-02-18T11:20:18Z

Show changes

Cosmo All: Created page with "2"

2014-02-11T11:13:34Z

Created page with "2"

New page

[[Category:Perturbation theory in cosmology|2]]

@@ Line 33: / Line 33: @@
 <div id="per12"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 1 ===
+=== Problem 2 ===
 <p style= "color: #999;font-size: 11px">problem id: per12</p>
 Determine the dependence of density fluctuations on scale factor in the flat Universe when
@@ Line 51: / Line 51: @@
 <div id="per13"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 1 ===
+=== Problem 3 ===
 <p style= "color: #999;font-size: 11px">problem id: per13</p>
 Determine the dependence of density fluctuations on time in the closed Universe with $k=1$.
@@ Line 64: / Line 64: @@
 <div id="per14"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 1 ===
+=== Problem 4 ===
 <p style= "color: #999;font-size: 11px">problem id: per14</p>
 Determine the dependence of density fluctuations on time in the open Universe with $k=-1$.
@@ Line 80: / Line 80: @@
 <div id="per18"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 1 ===
+=== Problem 5 ===
 <p style= "color: #999;font-size: 11px">problem id: per18</p>
 The inhomogeneities in matter distribution in the Universe generate perturbations of different kinds. In linear approximation these perturbations do not interact with each other and evolve independently. Construct the classifications of perturbations.
@@ Line 122: / Line 122: @@
 <div id="per19"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 1 ===
+=== Problem 6 ===
 <p style= "color: #999;font-size: 11px">problem id: per19</p>
 Determine the number of independent functions required for description of perturbations, considered in the previous problem.
@@ Line 139: / Line 139: @@
 <div id="per20ntenzor"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 1 ===
+=== Problem 7 ===
 <p style= "color: #999;font-size: 11px">problem id: per20ntenzor</p>
 Assuming, that in the Universe with metrics
@@ Line 170: / Line 170: @@
 <div id="per21ntenzor"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 1 ===
+=== Problem 8 ===
 <p style= "color: #999;font-size: 11px">problem id: per21ntenzor</p>
 Demonstrate, that spatial velocity $v^i$ from previous problem is physical.
@@ Line 193: / Line 193: @@
 <div id="per22ntenzor"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 1 ===
+=== Problem 9 ===
 <p style= "color: #999;font-size: 11px">problem id: per22ntenzor</p>
 Using the results of two previous problems, calculate the components of energy--momentum tensor perturbation $\delta T^\mu_\nu$, which is induced by the perturbations of density and pressure $$\widetilde{\rho}=\rho+\delta \rho, ~  \widetilde{p}=p+\delta p,$$ where $\rho,p$ are their background values.
@@ Line 215: / Line 215: @@
 <div id="per23ntenzor"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 1 ===
+=== Problem 10 ===
 <p style= "color: #999;font-size: 11px">problem id: per23ntenzor</p>
 Obtain the equations of covariant convervation in linear approximation in components of tensor perturbations $h_{\mu\nu}$. Use the gauge $h_{0i}=0$ for simplicity.
@@ Line 236: / Line 236: @@
 <div id="per20"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 1 ===
+=== Problem 11 ===
 <p style= "color: #999;font-size: 11px">problem id: per20</p>
 In the first order of $h_{ik}$ calculate the components of energy--momentum tensor for the Universe. filled with ideal fluid with equation of state$p=w\rho$ and metrics \eqref{met_ten_per}
@@ Line 274: / Line 274: @@
 <div id="per21"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 1 ===
+=== Problem 12 ===
 <p style= "color: #999;font-size: 11px">problem id: per21</p>
 In linear approximation determine the transformation of metrics $g_{\mu\nu}$, which is generated by the space transformation $x^\alpha\rightarrow \tilde{x}^\alpha=x^\alpha+\xi^\alpha$, where $\xi^\alpha$ is infinitesimal scalar function.
@@ Line 305: / Line 305: @@
 <div id="per22"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 1 ===
+=== Problem 13 ===
 <p style= "color: #999;font-size: 11px">problem id: per22</p>
 Using the results of previous problem determine the transformation of metrics, generated by the transformation $x^\alpha\rightarrow \tilde{x}^\alpha=x^\alpha+\xi^\alpha$. Here the four--vector  $\xi^\alpha=(\xi^0,\xi^i)$ satisfies the condition $\xi^i=\xi^i_\bot+\zeta^i$, $\xi^i_\bot$ is a three--vector with zero divergence ($\xi^i_{\bot,i}=0$) and $\zeta^i$ is a scalar function.
@@ Line 331: / Line 331: @@
 <div id="per22_1"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
-=== Problem 1 ===
+=== Problem 14 ===
 <p style= "color: #999;font-size: 11px">problem id: per22_1</p>
 Demonstrate, that non--uniform flat Friedman metrics

Introduction to relativistic theory of small perturbations - Revision history

Cosmo All at 21:22, 24 February 2014

Cosmo All at 11:31, 18 February 2014

Cosmo All at 11:20, 18 February 2014

Cosmo All: Created page with "2"