Different Models of Inflation - Revision history

Cosmo All: /* Problem 11 */

2013-09-20T12:13:00Z

‎Problem 11

Cosmo All: /* Problem 21 */

2013-09-20T12:11:25Z

‎Problem 21

Cosmo All: /* Problem 20 */

2013-09-20T12:11:13Z

‎Problem 20

Cosmo All: /* Problem 13 */

2013-09-20T12:10:31Z

‎Problem 13

Cosmo All at 12:07, 20 September 2013

2013-09-20T12:07:17Z

Show changes

Cosmo All: /* Problem 6 */

2013-09-20T12:00:08Z

‎Problem 6

Cosmo All at 11:59, 20 September 2013

2013-09-20T11:59:48Z

Cosmo All: /* Problem 39 */

2013-09-03T11:17:53Z

‎Problem 39

Cosmo All: /* Problem 38 */

2013-09-03T11:16:43Z

‎Problem 38

Cosmo All at 11:13, 3 September 2013

2013-09-03T11:13:51Z

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 $$\varphi\gg\frac{nM_{Pl}}{4\sqrt{3\pi}},$$
 therefore the slow-roll takes place at field values which are great compared to Planck units.
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 === Problem 1 ===
 Consider inflation with simple power law potential $$V=g\phi^n,$$ and show that there is wide range of scalar field values where classical Einstein equations are applicable and the slow-roll regime is realized too. Assume that the interaction constant $g$ is sufficiently small in Planck units.
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 === Problem 39 ===
-Obtain the value $\eta_\chi$ corresponding to the fast roll down of the field $\chi$ along the potential $V_{eff}(\chi)$ (see the previous problem).
+In what way is the inflation theory related to the solution of the problem: ''why is mathematics so efficient in description of our world and prediction of its evolution?''
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+Consider the following example [A.Linde, arXiv:hep-th/0211048 (2002)]. Assume that inflation is absent. Then the Universe and the reader himself are in stable or meta-stable vacuum state with Planck density $\rho _{Pl} \sim M_{Pl}^4 $. Such Universe is governed by quantum gravity and quantum fluctuations of the space-time are of order of the curvature. It seem that due to the quantum fluctuations our measuring devices (rulers and clocks) are destroyed sooner than we can perform a measurement. Mathematics looses any efficiency, because it is impossible to compare mathematical predictions with the experiment or measurement.
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		+	== Other Types of Inflation ==
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		+	=== Problem 37 ===
		+
		+	Formulate the differences between the models of cold and warm inflation.
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		+	The difference between warm and cold inflation is in the fact that the former is free of separate warming stage. The radiation generation process competes with the inflationary expansion. Realization of inflation requires that the vacuum energy density dominates (in order to create the accelerated expansion). However this condition does not exclude The existence of considerable density of radiation energy during the inflation process. Presence of the radiation during inflation allows to ''smoothen'' the end of inflation and transit to the radiation-dominated epoch without a special warming phase. Such scenario can be realized if vacuum energy density falls down faster than that of radiation, so that at some point a smooth intersection occurs. This enables one to solve the problem of exit from the inflation.
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		+	=== Problem 38 ===
		+
		+	Consider the inflation model of problem \ref{inf_gibrid_1} and obtain the value of $V_{eff}(\chi)$ corresponding to field value $\chi$, at which it starts to roll down to the minimum $\varphi=0$ after the Hubble time $\Delta t \sim H^{-1}(\varphi_c)$ and $\chi = \nu$ after the inflaton reaches the critical value $\varphi_c$.
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		+	Solution text
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		+	=== Problem 39 ===
		+
		+	Obtain the value $\eta_\chi$ corresponding to the fast roll down of the field $\chi$ along the potential $V_{eff}(\chi)$ (see the previous problem).
		+
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		+	<div class="NavHead">solution</div>
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		+	Solution text
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