Difference between revisions of "New Cosmography"

From Universe in Problems
Jump to: navigation, search
Line 103: Line 103:
  
  
<div id=""></div>
+
<div id="cs-8"></div>
 
<div style="border: 1px solid #AAA; padding:5px;">
 
<div style="border: 1px solid #AAA; padding:5px;">
 
'''Problem '''
 
'''Problem '''
<p style= "color: #999;font-size: 11px">problem id: </p>
+
<p style= "color: #999;font-size: 11px">problem id: cs-8</p>
 
+
Show that for the deceleration parameter the following relation holds:
 +
$$q(a)=-\left(1+\frac{dH/dt}{H^2}right)-\left(1+\frac{adH/da}{H}\right)$$
 
<div class="NavFrame collapsed">
 
<div class="NavFrame collapsed">
 
   <div class="NavHead">solution</div>
 
   <div class="NavHead">solution</div>
Line 114: Line 115:
 
   </div>
 
   </div>
 
</div></div>
 
</div></div>
 +
  
 
<div id=""></div>
 
<div id=""></div>

Revision as of 21:18, 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 \[q=-\frac{d\dot{a}}{Hda} \]


Problem 6

problem id: cs-6

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


Problem 7

problem id: cs-7

Show that the deceleration parameter $q$ can be presented in the form $$q(x)=\frac{\dot{H}(x)}{H(x)}x-1;\,\,x=1+z$$


Problem

problem id: cs-8

Show that for the deceleration parameter the following relation holds: $$q(a)=-\left(1+\frac{dH/dt}{H^2}right)-\left(1+\frac{adH/da}{H}\right)$$


Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id:

Problem

problem id:


Problem

problem id: