# Difference between revisions of "New Cosmography"

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: $$q(a)=-\left(1+\frac{dH/dt}{H^2}\right)-\left(1+\frac{adH/da}{H}\right)$$

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