Physics
Scientific paper
Oct 1991
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991phrvd..44.2356k&link_type=abstract
Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 44, Issue 8, 15 October 1991, pp.2356-2368
Physics
12
Scientific paper
Every Bianchi type-IX universe can be interpreted as a closed Friedmann universe on which is superimposed circularly polarized gravitational waves with the longest wavelength that will fit into a closed universe. In this paper, I give a new derivation of this result based on the concept of homogeneous tensor fields on the three-sphere. Every homogeneous symmetric traceless tensor field is shown to be a longest-wavelength three-sphere harmonic. Contrary to previous authors, I show that the wavelength of these gravitational waves is one-half the circumference of the universe. In order to maintain homogeneity, the gravitational waves must all have the same polarization. There are five longest-wavelength modes for each polarization. This interpretation is an exact description that is valid for every Bianchi type-IX universe-it is in no way limited to first-order perturbations of a Friedmann universe.
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