The discussion focuses on the differences between Bianchi models and Kantowski-Sachs models within the context of cosmology. Participants explore the mathematical definitions and properties of these models, particularly their symmetry groups and characteristics of homogeneity and isotropy.
There is some agreement on the definitions and properties of the models, but there is also disagreement regarding the characterization of the spaces as homogeneous and isotropic versus homogeneous and anisotropic. The discussion remains unresolved on this point.
Participants express uncertainty about the definitions and implications of the symmetry groups, and there are unresolved aspects regarding the classification of the models.
Yes, I meant ANisotropic, in both places!utku said:
Thanks!The number of parameters in a group is the number of variables you need to specify to pick out a particular group element. For example the usual group of 3-d rotations acting on a sphere S - you can rotate the North pole P into any other point Q on the sphere, and you must give the latitude and longitude of Q - that's two parameters. But after doing that, you can still rotate through some angle ψ about Q, keeping Q fixed. That's a total of three parameters. And the group action on S is multiply transitive - since ψ can be anything, there are many group elements that map P into Q.utku said: