Conformal energy-momentum tensor in curved spacetime: Adiabatic regularization and renormalization
- 15 December 1974
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 10 (12), 3905-3924
- https://doi.org/10.1103/physrevd.10.3905
Abstract
In preparation for an investigation of whether field-theoretic effects helped to make the early universe become isotropic, we seek to determine the physical (divergence-free) energy-momentum tensor through which the geometry of spacetime is influenced by a quantized scalar field with conformal ("new improved") coupling to the metric. The cosmological models studied are the Kasner-like (type I) metrics (homogeneous, spatially flat, nonrotating, but anisotropic), and also the isotropic Robertson-Walker metrics. The methods employed have previously been expounded in the context of a minimally coupled scalar field and a Robertson-Walker metric. Three divergent leading terms are extracted from an adiabatic expansion of the formal expressions for the expectation values of the energy density and pressures. In the Kasner case a slight reshuffling of the leading terms in the energy density displays all divergences to be proportional to either the metric tensor or a second-order curvature tensor which vanishes when the spacetime is isotropic; hence a finite energy-momentum tensor remains after renormalization of the cosmological constant and one other coupling constant in a generalized Einstein equation. In the Robertson-Walker cases, because of conformal flatness, there is no divergence beyond the usual quartically divergent constant vacuum energy; when the mass is not zero, however, a finite renormalization of the gravitational constant is suggested. The correctness of the methods is tested by considering a coordinate system in which flat spacetime assumes the form of a Kasner universe: The adiabatic definition of particle number and vacuum, which is basic to our expansion and renormalization methods, is seen to be consistent with the usual flat-space concepts.Keywords
This publication has 15 references indexed in Scilit:
- Renormalization in the theory of a quantized scalar field interacting with a robertson-walker spacetimeAnnals of Physics, 1974
- Scalar waves in the mixmaster universe. II. Particle creationPhysical Review D, 1974
- Adiabatic regularization of the energy-momentum tensor of a quantized field in homogeneous spacesPhysical Review D, 1974
- Gravitation and the new improved energy-momentum tensorJournal of Mathematical Physics, 1973
- Quantized Scalar Fields in a Closed Anisotropic UniversePhysical Review D, 1973
- Conformal Energy-Momentum Tensor in Riemannian Space-TimePhysical Review D, 1973
- The mathematical problem of reflection solved by an extension of the WKB methodJournal of Mathematical Physics, 1973
- A new improved energy-momentum tensorAnnals of Physics, 1970
- Quantized Fields and Particle Creation in Expanding Universes. IPhysical Review B, 1969
- Geometrical Theorems on Einstein's Cosmological EquationsAmerican Journal of Mathematics, 1921