Cosmology, cohomology, and compactification

Details Cosmology, cohomology, and compactification Cosmology, cohomology, and compactification

2004-02-24

arxiv.org/abs/gr-qc/0402105v1

Class.Quant.Grav. 21 (2004) L73-L78

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

6 pages, LaTeX

Scientific paper

10.1088/0264-9381/21/11/L02

Ashtekar and Samuel have shown that Bianchi cosmological models with compact spatial sections must be of Bianchi class A. Motivated by general results on the symmetry reduction of variational principles, we show how to extend the Ashtekar-Samuel results to the setting of weakly locally homogeneous spaces as defined, e.g., by Singer and Thurston. In particular, it is shown that any m-dimensional homogeneous space G/K admitting a G-invariant volume form will allow a compact discrete quotient only if the Lie algebra cohomology of G relative to K is non-vanishing at degree m.

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