### 3. MODELS OF THE UNIVERSE

**3.1 Basic concepts**
In view of the complexity of the subject universe there seems to be no
other approach but the adoption of simple models and attempts at their
falsification, in which case other simple models will have to be
substituted. So far, tests have not yet excluded models based on the

- cosmological principle (isotropy and homogeneity) (from 1916 onwards,
see below)

- Einstein's general theory of relativity
(1916)

- Friedmann's concept of a *time-dependent* scale factor
(1922)

- Friedmann's metric, with the time coordinate *orthogonal* to the three
space coordinates, and constant sign of curvature
(1922, positive
curvature,
1924 negative
curvature)

- Heckmann's extension to zero curvature and display of a series of
models with *k* = +1, 0, -1 and > 0, = 0, < 0
(1931,
1932)

- Tolman's (1929)
and Robertson's
(1929)
derivation of a Friedmann
metric entirely from the assumption of homogeneity and isotropy, and
the final formulation of the metric by
Walker (1936).

Within the above concepts, cosmology tries to derive numerical values
for the

Hubble constant *H*_{0}

acceleration parameter *q*_{0}

curvature parameter *k*

matter density _{0} or density parameter _{0}

pressure *p*_{0}

age of the universe.

A successful method for the independent derivation of the cosmological
constant has not yet been
applied ^{(3)}.

^{3} In the early literature, the
designation is more
frequently used than . When
no confusion with wavelength
is possible, the original designation was kept in the present quotations
and discussions.