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Using appropriate harmonics, we study the future asymptotic behavior ofmassless scalar fields on a class of cosmological vacuum spacetimes. Thespatial manifold is assumed to be a circle bundle over a higher genus surfacewith a locally homogeneous metric. Such a manifold corresponds to theSL(2,R)-geometry (Bianchi VIII type) or the H^2 x R-geometry (Bianchi IIItype). After a technical preparation including an introduction of suitableharmonics for the circle-fibered Bianchi VIII to separate variables, we derivesystems of ordinary differential equations for the scalar field. We presentfuture asymptotic solutions for these equations in a special case, and findthat there is a close similarity with those on the circle-fibered Bianchi IIIspacetime. We discuss implications of this similarity, especially to(gravitational) linear perturbations. We also point out that this similaritycan be explained by the "fiber term dominated behavior" of the two models.Comment: 23 pages, no figures, to be published in Class. Quant. Gravi

Scalar fields on SL (2, R ) and H 2 R geometric spacetimes and linear perturbations

Scalar fields on SL (2, R ) and H ² R geometric spacetimes and linear perturbations