A Minisuperspace Example: The Gowdy $T^3$ Cosmology

The Gowdy $T^3$ inhomogeneous cosmology is an exact vacuum solution of Einstein's equations representing gravitational waves propagating in an expanding closed universe. As shown by Berger, it provides an example showing graviton pair creation as a quantum effect near the initial singularity, together with the reaction this induces in the cosmological expansion. The truncated quantization given here by superspace methods develops the "single residual constraint" quantization method proposed by Moncrief. The quantum wave equation is soluble by separation of variables, and shows that graviton number is a concept unsuited to the description of the initial (velocity-dominated) singularity. Thus a good description of the pair creation occurring in even this soluble model has not yet been developed.