As cosmological parameters we consider parameters which define the present and past structure of the Universe. Principal parameters are: the Hubble constant, which characterises the expansion speed of the Universe; the age and acceleration parameter of the Universe; densities of main constituents of the Universe: baryonic matter, dark matter and dark energy; and parameters, which define the amplitude and shape of the power spectrum of galaxies and matter. Cosmological parameters and descriptive functions can be used to test various scenarios of structure evolution.
The Hubble constant, h, can be estimated by several methods: through the ladder of various distance estimators from star clusters to cepheids in nearby galaxies, through the light curves of medium-distant supernovae, or using several physical methods (gravitational lensing, Sunyaev-Zeldovich-effect). Summaries of recent determinations are given in [41, 47]. A mean value of recent determinations is h = 0.65 ± 0.07.
The baryon density can be determined most accurately from observations
of the deuterium, helium and lithium abundances in combination with
the nucleosynthesis constrains. The best available result is
bh2
= 0.019 ± 0.002
[11].
The total density of matter,
tot =
m +
v,
determines the position of the first Doppler peak of the angular
spectrum of CMB temperature fluctuations; here
m and
v are the densities
of matter and dark (vacuum) energy,
respectively. Recent observations show that the maximum of the first
Doppler peak lies at
l 
200
[17,
30]. This
indicates that
tot
1. Since this is the
theoretically preferred value, I assume in the following that
tot = 1.
There exist a number of methods to estimate the density of matter,
m =
b +
c +
n, where
b,
c, and
n are the densities
of baryonic matter, cold
dark matter (CDM), and hot dark matter (HDM), respectively. The
luminosity-distance method, used in the distant supernova project,
yields
m = 0.28 ± 0.05
[43,
45]. Another
method is based on X-ray data on clusters of galaxies, which gives the
fraction of gas in clusters, fgas =
b /
m. If
compared to the density of the baryonic matter one gets the estimate
of the total density,
m =
0.31 ± 0.05(h / 0.65)-1/3
[39].
A third method is
based on the geometry of the
Universe. Observations show the presence of a dominant scale,
l0 = 130 ± 10 h-1 Mpc, in the
distribution of high-density regions
[8,
21,
20].
A similar phenomenon is observed in the
distribution of Lyman-break galaxies
[9]
at high redshift,
z 3. We can assume
that this scale is primordial and co-moves
with the expansion; in other words - it can be used as a standard
ruler. The relation between redshift difference and linear comoving
separation depends on the density parameter of the Universe; for a
closed universe one gets a density estimate
m = 0.4 ± 0.1.
The same method was applied for the distribution of quasars by Roukema
& Mamon [46]
with the result