Higher-dimensional homogeneous cosmological models.

Details Higher-dimensional homogeneous cosmological models. Higher-dimensional homogeneous cosmological models.

Nov 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990achph..63..965h&link_type=abstract

Helvetica Physica Acta, Vol. 63, No. 8, p. 965 - 1067

Mathematics

Logic

1

Cosmological Models: Singularities

Scientific paper

The author studies the structure of the field equations for higher-dimensional homogeneous cosmological models and discusses the behavior of their solutions close to the initial singularity. First it is shown that the application of the ADM-formalism to the finite dimensional situation of homogeneous cosmology yields a Hamiltonian system only if the underlying Lie group is unimodular. Otherwise, to obtain the correct field equations, one has to introduce constraint forces perpendicular to the cotangent bundle with respect to the de Witt metric. Using coordinates similar to the Jacobi coordinates of classical mechanics, the author generalizes the (3+1)-dimensional time-dependent Hamiltonian description to an arbitrary number of spatial dimensions. Subsequently he shows how to eliminate the explicit time-dependence and derives an autonomous system for the anisotropy coordinates.

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