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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:

where

and

with

Let us consider a light signal emitted at time t_e and receipt at time t_r let us note respectively z_e and z_r

and

etc the redshifts, " rate of depreciation " of frequencies, etc associated by the formula

at the times t_e and t_r there is the following fundamental formula:

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 d_t(z), luminosity d_l(z) and angular d_a(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)

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: