3. MODELS OF THE UNIVERSE

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 H₀

acceleration parameter q₀

curvature parameter k

matter density ₀ or density parameter ₀

pressure p₀

age of the universe.

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