Static Einstein's Universe - Revision history

Cosmo All at 21:10, 2 December 2012

2012-12-02T21:10:19Z

Cosmo All at 21:09, 2 December 2012

2012-12-02T21:09:31Z

Cosmo All: /* Problem 1 */

2012-12-02T21:08:06Z

‎Problem 1

Cosmo All at 21:07, 2 December 2012

2012-12-02T21:07:09Z

Show changes

Cosmo All: Created page with "4"

2012-12-01T13:20:01Z

Created page with "4"

New page

[[Category:Dark Energy|4]]

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 <div id="DE33"></div>
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-=== Problem 1 ===
+=== Problem 10 ===
 Show that the static Einstein's Universe may be realized only in the maximum of the effective potential $V(a)$ of the previous problem.
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 <div id="DE34"></div>
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-=== Problem 1 ===
+=== Problem 11 ===
 Problem [[#DE32]] can be considered in more general setup.<br/>
 Assuming arbitrary values for the contributions of the cosmological constant $\lambda$, matter $\mu$, radiation $\gamma$ and curvature $\varkappa$ respectively, present the first Friedman equation

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 <div id="DE25"></div>
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-=== Problem 1 ===
+=== Problem 2 ===
 Show that the static Einstein's Universe must be closed. Find the total volume and mass of this Universe.
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 <div id="DE26"></div>
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-=== Problem 1 ===
+=== Problem 3 ===
 Find the parameters of static Einstein's Universe filled with cosmological constant and radiation.
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 <div id="DE27"></div>
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-=== Problem 1 ===
+=== Problem 4 ===
 Find the parameters of static Einstein's Universe under the assumption that both matter and radiation are absent.
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 <div id="DE28"></div>
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-=== Problem 1 ===
+=== Problem 5 ===
 Estimate the radius of static Einstein's Universe if the zero-point energy of electromagnetic field is cut off at the classical electron radius.
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-=== Problem 1 ===
+=== Problem 6 ===
 Show that Einstein's Universe is unstable.
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 <div id="DE30"></div>
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-=== Problem 1 ===
+=== Problem 7 ===
 What are the concrete mechanisms that drive the instability of the static Einstein's Universe?
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 <div id="DE31"></div>
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-=== Problem 1 ===
+=== Problem 8 ===
 What is the most unsatisfactory peculiarity of the static Einstein's model of the Universe (besides the instability)?
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 <div id="DE32"></div>
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-=== Problem 1 ===
+=== Problem 9 ===
 Construct the effective one-dimensional potential $V(a)$ for the case of flat Universe filled with non-relativistic matter and dark energy in the form of cosmological constant.
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 File:Diagram.jpg|
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 R=\frac{1}{\sqrt\Lambda}=\frac{\alpha^2M_{Pl}}{(2\pi)^{2/3}
 m_e^2}\simeq31.6\mbox{\it km}.\]
-This is indeed less than the distance to the moon.*
+This is indeed less than the distance to the moon.$^*$
 <br/>
-*It would be more consistent to use the curvature radius of the static de Sitter solution; the result is the same, up to the factor $\sqrt3$.</p>
+$^*$It would be more consistent to use the curvature radius of the static de Sitter solution; the result is the same, up to the factor $\sqrt3$.</p>
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 <div id="DE29"></div>
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 === Problem 1 ===
 Show that Einstein's Universe is unstable.