Difference between revisions of "New Cosmography"

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* (e) $H>0,\; q=0$: expanding, zero deceleration
 
* (e) $H>0,\; q=0$: expanding, zero deceleration
 
* (f) $H<0,\; q=0$: contracting, zero deceleration
 
* (f) $H<0,\; q=0$: contracting, zero deceleration
* (g) $H=0,\; q=0$ : static.</p>
+
* (g) $H=0,\; q=0$ : static.
 +
Of course, generally speaking, both the Hubble parameter and deceleration parameter can change their sign during the evolution. Therefore the evolving Universe can transit from one type to another. It is one of the basic tasks of cosmology to follow this evolution and clarify its causes. There is little doubt that we live in an expanding Universe, and hence only (a), (b), and (e) are possible candidates. Evidences in favor of the fact that the expansion is presently accelerating continuously grows in number and therefore the current dynamics belongs to type (b).</p>
 
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Revision as of 00:00, 2 February 2016

First section of Cosmography


Problem 1

problem id: cs-1

Using the cosmographic parameters introduced above, expand the scale factor into a Taylor series in time.


Problem 2

problem id: cs-2

Using the cosmographic parameters, expand the redshift into a Taylor series in time.


Problem 3

problem id: cs-3

What is the reason for the statement that the cosmological parameters are model-independent?


Problem 4

problem id: cs-4

Obtain the following relations between the deceleration parameter and Hubble's parameter $$q(t)=\frac{d}{dt}(\frac{1}{H})-1;\,\,q(z)=\frac{1+z}{H}\frac{dH}{dz}-1;\,\,q(z)=\frac{d\ln H}{dz}(1+z)-1.$$


Problem 5

problem id: cs-5

Show that the deceleration parameter can be defined by the relation \[q=-\frac{d\dot{a}}{Hda} \]


Problem 6

problem id: cs-6

Classify models of Universe basing on the two cosmographic parameters -- the Hubble parameter and the deceleration parameter.


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