Friedmann–Lemaître–Robertson–Walker metric
The Friedmann - Lemaître - Robertson - Walker ( FLRW ) metric is an exact solution of Einstein's field equations of general relativity and describes a homogeneous, isotropic ( cosmological principle) expansion or just such a contraction of the universe. She is under different combinations of the names of the four scientist Alexander Friedmann, Georges Lemaître, Howard Percy Robertson and Arthur Geoffrey Walker known, eg Friedmann - Robertson - Walker ( FRW) or Robertson - Walker ( RW).
Because it is so easy to calculate, the FLRW metric is used as a first approximation for the cosmological standard Big Bang model of the universe. Because the FLRW homogeneity presupposes, is often falsely claimed that the Big Bang model can not explain the lumpiness of the universe. Models, which will calculate the lumpiness of the universe, expand the FLRW. In 2003, seemed already well understood, the theoretical consequences of different extensions to FLRW. The goal was to bring these to the observations of the COBE and WMAP projects in line.
Formulation
By requiring isotropy yields the Robertson -Walker line element
Where k = 1, 0, -1.
With the substitution x = sin r for k = 1, or x = sinh r for k = -1, the metric can be used as:
Are written;
- C is the vacuum speed of light,
- A ( t) is the scale factor at time t of the universe,
- R is the distance from the moving observer,
- The covariant distance:
- The absolute value of the curvature radius,
- And are.
If one assumes the FLRW metric and a suitable energy -momentum tensor, the Einstein field equations reduce to the Friedmann equations. The solution of the Friedmann equations is the time profile of the scale factor of the FLRW metric.
Fast- FLRW models
All observations in the universe on sufficiently large length scales (ie, larger than the largest identifiable objects in the universe, galaxy clusters ) can be explained well by an almost - FLRW model. An almost - FLRW model follows the FLRW metric, the evolution of matter distribution from primordial fluctuations can be calculated as a small perturbation. In an exact FLRW model there are no clusters of galaxies, stars, or people, because these objects have a higher density than the average of the universe. Nevertheless, it is an almost - FLRW model, for brevity, referred to as the FLRW model ( or FRW model).