Characteristic Parameters and Scales - Revision history

Igor: /* Problem 10 */

2012-10-13T17:29:31Z

‎Problem 10

2012-10-04T16:40:58Z

‎Problem 2

2012-10-03T20:15:48Z

2012-10-03T20:14:15Z

2012-10-02T10:45:15Z

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[[Category:Standard Cosmological Model|1]]

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 === Problem 10 ===
-Give a qualitative explanation why the age of Universe in SCM is considerably greater than the age of matter dominated Universe (Einstein-de Sitter model).
+Give a qualitative explanation why the age of the Universe in SCM is considerably larger than the age of matter dominated Universe (the Einstein-de Sitter model).
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-	In the Einstein-de Sitter model the expansion is always decelerating, while in the SCM the decelerated expansion turns to the accelerated one. Therefore for a given Hubble constant $H_0$ the preceding value in the Einstein-de Sitter model was greater than that in the SCM, and the average expansion rate was also greater, so the observed size of the Universe was achieved for a shorter time.
+	In the Einstein-de Sitter model the expansion is always decelerating, while in the SCM the decelerated expansion turns to the accelerated one. Therefore for a given Hubble constant $H_0$ the preceding value in the Einstein-de Sitter model was greater than that in the SCM, and the average expansion rate was also greater, so the observed size of the Universe was reached in a smaller period of time.
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-\begin{eqnarray}
+$$
-   N &=& \frac{M}{m_n}=\frac{\frac{4}{3}\pi \left( \frac{c}{H_0} \right)^3\rho }{m_n}=\frac{\frac{4}{3}\pi \alpha \left( \frac{c}{H_0}\right)^3\frac{3H_0^2}{8\pi G}}{m_n}= \\
+   N = \frac{M}{m_n}=\frac{\frac{4}{3}\pi \left( \frac{c}{H_0} \right)^3\rho }{m_n}=\frac{\frac{4}{3}\pi \alpha \left( \frac{c}{H_0}\right)^3\frac{3H_0^2}{8\pi G}}{m_n}=  \frac{1}{2}\alpha \frac{H_0^2}{Gm_n}\left( \frac{c}{H_0} \right)^3=\frac{1}{2}\alpha \frac{M_{Pl}}{m_n}\frac{M_{Pl}c^2}{\hbar H_0}\simeq 10^{80}\quad (\alpha \simeq 0.04)
-   &=& \frac{1}{2}\alpha \frac{H_0^2}{Gm_n}\left( \frac{c}{H_0} \right)^3=\frac{1}{2}\alpha \frac{M_{Pl}}{m_n}\frac{M_{Pl}c^2}{\hbar H_0}\simeq 10^{80}\quad (\alpha \simeq 0.04)
+$$
-\end{eqnarray}
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 === Problem 3 ===
 Find dependence of relative density of dark energy $\Omega_\Lambda$ on the redshift. Plot $\Omega_\Lambda(z)$.

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 === Problem 4 ===
- Estimate total number of stars in the Universe.
+Estimate total number of stars in the Universe.
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