MODERN COSMOLOGY

Models and symmetries 127 Thedimension r of the group of symmetriesof a space of dimensionnis r=s+q(translations plus rotations) ...

128 Cosmological models Ta b l e 3. 1. Classification of cosmological models (with(μ+p)> 0 )by isotropy and homogeneity. Dim ...

Models and symmetries 129 not a viable cosmology because it has no redshifts, but it laid the foundation for the discovery of th ...

130 Cosmological models 3.5.2.3 Spatially inhomogeneous universes These models haves≤2. TheLRS cases(q= 1 ⇒s= 2 ,r= 3 )are the s ...

Friedmann–Lemaˆıtre models 131 the Raychaudhuri equation (3.34): 3 S ̈ S =−^12 (μ+ 3 p)+λ (3.83) and the Friedmann equation (3.4 ...

132 Cosmological models FL models can occur even ifk =0ork =− 1 ,for example with a toroidal topology [27]. These universes can ...

Bianchi universes (s= 3 ) 133 3.7.1 Constructing Bianchi universes The approach of Ellis and MacCallum [45]) uses an orthonormal ...

134 Cosmological models Ta b l e 3. 2. Canonical structure constants for different Bianchi types. The parameter h=a^2 /n 2 n 3. ...

Bianchi universes (s= 3 ) 135 theσαβ). This also simplifies other quantities (for example the choice of a shear eigenframe will ...

136 Cosmological models equation forH, namely (3.91), decouples from the remaining equations (3.92) and (3.93). Thus the DE (3.9 ...

Bianchi universes (s= 3 ) 137 In this case the parameterH 0 is no longer essential, since it can be set to unity by a translatio ...

138 Cosmological models evolution patterns very difficult to follow. It is better to keep them separate, but to learn to identif ...

Observations and horizons 139 Bianchi evolution theorem 2.In each set of Bianchi models of a type admitting intermediate isotrop ...

140 Cosmological models (1) theredshift, basically a time-dilation effect for all measurements of the source (determined by the ...

Observations and horizons 141 hence via the Hawking–Penrose singularity theorems, leads to the prediction of the existence of a ...

142 Cosmological models case, it would show up in multiple images of the same objects [48, 81], identical circles in the CBR ani ...

Observations and horizons 143 3.8.4.2 Inhomogeneity and observations Similarly, one can examine observational relations in speci ...

144 Cosmological models with spatial homogeneity; but once we take evolution into account, we can fit almost any observational r ...

Observations and horizons 145 so there is no reason to think they are very different. Nevertheless, in the end this argument res ...

146 Cosmological models in another 50 Hubble times), so late-time anisotropic modes which are presently negligble could come to ...