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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 lambda > 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 rho0 or density parameter Omega0

pressure p0

age of the universe.

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

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

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