Difference between revisions of "New Cosmography"

From Universe in Problems
Jump to: navigation, search
Line 82: Line 82:
 
   <div style="width:100%;" class="NavContent">
 
   <div style="width:100%;" class="NavContent">
 
     <p style="text-align: left;">When the rate of expansion never changes, and $\dot{a}$  is constant, the scaling factor is proportional to time $t$ , and the deceleration term is zero. When the Hubble term is constant, the deceleration term $q$  is also constant and equal to $\mathrm{-}$1, as in the de Sitter and steady-state Universes. In most models of Universes the deceleration term changes in time. One can classify models of Universe on the basis of time dependence of the two parameters. All models can be characterized by whether they expand or contract, and accelerate or decelerate:
 
     <p style="text-align: left;">When the rate of expansion never changes, and $\dot{a}$  is constant, the scaling factor is proportional to time $t$ , and the deceleration term is zero. When the Hubble term is constant, the deceleration term $q$  is also constant and equal to $\mathrm{-}$1, as in the de Sitter and steady-state Universes. In most models of Universes the deceleration term changes in time. One can classify models of Universe on the basis of time dependence of the two parameters. All models can be characterized by whether they expand or contract, and accelerate or decelerate:
* $H>0,\; q>0$ : expanding and decelerating
+
* (a) $H>0,\; q>0$: expanding and decelerating
* $H>0,\; q<0$expanding and accelerating</p>
+
* (b) $H>0,\; q<0$: expanding and accelerating
 +
* (c) $H<0,\; q>0$: contracting and decelerating
 +
* (d) $H<0,\; q<0$: contracting and accelerating
 +
* (e) $H>0,\; q=0$: expanding, zero deceleration
 +
* (f) $H<0,\; q=0$: contracting, zero deceleration
 +
* (g) $H=0,\; q=0$ : static.</p>
 
   </div>
 
   </div>
 
</div></div>
 
</div></div>

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.


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:

Problem

problem id:


Problem

problem id: