142 Cosmological models
case, it would show up in multiple images of the same objects [48, 81], identical
circles in the CBR anisotropy pattern across the sky [18], and altered CBR power
spectra predictions [17]. A complete cosmological observational programme
should test for the possibility of such small alternative universe topologies, as
well as determining the fundamental cosmological parameters.
3.8.4 Observations in anisotropic and inhomogeneous models
In anisotropic models, new kinds of observations become possible. First, each of
these relations will be anisotropic and so will vary with direction in the sky. In
particular,
(6) background radiation anisotropies will occur and provide important
information on the global spacetime geometry [100] as well as on local
inhomogeneities [10, 59, 82] and gravitational waves [9];
(7) image distortion effects(strong and weak lensing) are caused by the Weyl
tensor, which in turn is generated by local matter inhomogeneities through
the ‘divE’ equation (3.48).Finally, to fully determine the spacetime geometry [44, 86] we should also
measure
(8) transverse velocities, corresponding to proper motions in the sky. However,
these are so small as to be undetectable and so measurements only give weak
upper limits in this case.To evaluate the limits put on inhomogenity and anisotropy by observations,
one must calculate observational relations predicted in anisotropic and
inhomogenous models.
3.8.4.1 Bianchi observations
One can examine observational relations in the spatially homogeneous class of
models, for example determining predicted Hubble expansion anisotropy, CBR
anisotropy patterns, and nucleosynthesis results in Bianchi universes. These
enable one to put strong limits on the anisotropy of these universe models
since decoupling, and limits on the deviation from FL expansion rates during
nucleosynthesis. However although these analyses put strong limits on the shear
and vorticity in such models today, nevertheless they could have been very
anisotropic at very early times—in particular, before nucleosynthesis—without
violating the observational limits, and they could become anisotropic again at
very late times. Also these limits are derived for specific spatially homogeneous
models of particular Bianchi type, and there are others where they do not apply.
For example, there exist Bianchi models in which rapid oscillations take place in
the shear at late times, and these oscillations prevent a build up of CBR anisotropy,
even though the universe is quite anisotropic at many times.