Difference between revisions of "New Cosmography"

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<p style= "color: #999;font-size: 11px">problem id: cs-5</p>
 
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Show that the deceleration parameter can be defined by the relation \[q=-\frac{d\dot{a}}{Hda} \]
 
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     <p style="text-align: left;">\[q=-\frac{d\dot{a}}{Hda} =-\frac{\ddot{a}dt}{Hda} =-\frac{\ddot{a}}{aH^{2} }  .\]
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It corresponds to the standard definition of the deceleration parameter
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\[q-\frac{\ddot{a}}{aH^{2} }  .\]</p>
 
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Revision as of 23:56, 1 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 \[q=-\frac{d\dot{a}}{Hda} \]


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