Summary formulas for these models of universe
From H O and
given and density of
radiation (of density
today), one builds the
metric for the isotropic universe, universe of radiation and matter (of
density A today with
.
Let us put
The metric is written:
![](img5.gif)
where
and
with
Let us consider a light signal emitted at time te and receipt at
time tr let us note respectively ze and zr
and
etc the redshifts, " rate of depreciation " of frequencies, etc
associated by the formula
at the times te and tr there is the following fundamental formula:
![](img12.gif)
Let us put z the redshift of an observed object, we express according to z
the moment date(z) after the beginning of the universe of the emission of the signal
received today with a redshift of z, the following distances: temporal dt(z),
luminosity dl(z) and angular
da(z) of this object;
the curvature radius R(z), the value of the Hubble parameter H(z),
the densities of matter
and radiation
the deacceleration parameter q(z),
the density parameter
etc (we have the following EXACT FORMULAS)
![](img17.gif)
![](img18.gif)
![](img19.gif)
![](img20.gif)
![](img21.gif)
![](img22.gif)
![](img23.gif)
To obtain the future behavior it is enough to replace 1+ z by
(i.e. to vary z from 0 to -1).
The metric is written then by using z as temporal variable: