A Short Course in General Relativity and Cosmology by Reinhard Hentschke & Christian Hölbling

Author:Reinhard Hentschke & Christian Hölbling
Language: eng
Format: epub
ISBN: 9783030463847
Publisher: Springer International Publishing

(7.8)

The universe it describes is homogenous and bounded.

Fig. 7.3A possible time history of the circular universe

A generalisation to three-dimensional space and four-dimensional spacetime is

(7.9)

Note that homogeneity means that a does not depend on position in space and isotropy means that a is the same in every direction. The assumption of both homogeneity and isotropy of the universe is called the cosmological principle. In a perfectly homogeneous and isotropic universe that has no other dynamics, the spatial coordinates of everything it contains stay fixed. The metric (7.9) therefore describes a very special reference frame, which is called comoving. More generally, we can rewrite (7.9) as

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