Feynman propagators and particle creation in linearly expanding Bianchi type-I universes

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Abstract
Scalar particle creation in the linearly expanding Bianchi type-I universes is studied using the Feynman propagator technique. Explicit expressions for the propagators corresponding to an arbitrary "in" vacuum and the "out" vacuum defined by the WKB positive-frequency solutions are derived. The initial conditions are then singled out by requiring the square integrability of the analytically continued kernels of the propagators considered. It is shown that for each particular model there is only one Riemannian kernel which satisfies this condition. Furthermore, it is proved that all the kernels selected this way admit a well-defined path-integral representation defined on the Riemannian domains of physically allowed values of coordinates. This result confirms the assumption of Chitre and Hartle that the propagator they found in the isotropic model (which is precisely that singled out by the square-integrability condition) can be represented by a path integral defined on the domain to the future of the initial singularity. The initial conditions corresponding to the selected propagators are analyzed. It is shown that they give rise to the creation of pairs with spectrum, which at high energies resembles that of blackbody radiation in one, two, or three directions, depending on the background geometry. Finally, the conceptual and technical problems associated with the complexified spacetime path-integral method, as applied to cosmological models, are discussed.