COSMOLOGICAL MODEL WITH GRAVITATIONAL AND SCALAR WAVES

Gowdy's vacuum three-torus universe, which was recently the subject of a detailed investigation by Berger and Misner, is generalized by incorporating a minimally coupled massless scalar field. We construct the general solution and consider some particular cases, one of which reduces to the Taub-Tabenski solution. The asymptotic behavior is found (i) in the vicinity of the initial singularity (ii) in the high-frequency limit. It is shown that in both asymptotic cases the behavior of the present solution is significantly different from that of the vacuum solution. The high-frequency limit is shown to be a new exact solution of Einstein's equations with the energy-momentum tensor corresponding to a spatially homogeneous massless scalar field plus a null fluid. Finally, the full model is used to generate a new solution of coupled gravitational-conformal scalar field equations. © 1979 The American Physical Society.