Gaussian and 1/ Approximations in Semiclassical Cosmology
Jul 12, 198858 pages
Published in:
- Phys.Rev.D 39 (1989) 2234
Report number:
- PRINT-88-0508 (BUENOS-AIRES)
Citations per year
Abstract: (APS)
We study the λφ4 theory and the interacting O(N) model in a curved background using the Gaussian approximation for the former and the large-N approximation for the latter. We obtain the renormalized version of the semiclassical Einstein equations having in mind a future application of these models to investigate the physics of the very early Universe. We show that, while the Gaussian approximation has two different phases, in the large-N limit only one is present. The different features of the two phases are analyzed at the level of the effective field equations. We discuss the initial-value problem and find the initial conditions that make the theory renormalizable. As an example, we study the de Sitter self-consistent solutions of the semiclassical Einstein equations. Finally, for an identically zero mean value of the field we find the evolution equations for the classical field Ω(x)=(λ〈φ2〉)1/2 and the spacetime metric. They are very similar to the ones obtained by replacing the classical potential by the one-loop effective potential in the classical equations but do not have the drawbacks of the one-loop approximation.- FIELD THEORY: SCALAR
- SPACE-TIME
- SYMMETRY: O(N)
- EXPANSION 1/N
- APPROXIMATION: EFFECTIVE POTENTIAL
- Einstein equation
- APPROXIMATION: semiclassical
- TENSOR: ENERGY-MOMENTUM
- RENORMALIZATION: REGULARIZATION
- FIELD THEORY: CRITICAL PHENOMENA
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