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Hartree approximation in curved spacetimes revisited: The effective potential in de Sitter spacetime

Diana L. López Nacir^1,2, Francisco D. Mazzitelli³, and Leonardo G. Trombetta²

¹Abdus Salam International Centre for Theoretical Physics Strada Costiera 11, 34151 Trieste, Italy
²Departamento de Física and IFIBA, FCEyN UBA, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellón I, 1428 Buenos Aires, Argentina
³Centro Atómico Bariloche Comisión Nacional de Energía Atómica, R8402AGP Bariloche, Argentina

Phys. Rev. D 89, 024006 – Published 7 January, 2014

DOI: https://doi.org/10.1103/PhysRevD.89.024006

Abstract

We consider a quantum scalar field with a $λ φ^{4}$ interaction in curved spacetimes. The quantum effects are taken into account nonperturbatively using the Hartree approximation to the two-particle irreducible effective action. Although this approximation has been considered in many previous works, we reconsider it using a consistent nonperturbative renormalization procedure, which we extend to general curved spacetimes. We obtain the renormalized equations for the mean field and for the propagator of the fluctuations, showing explicitly their independence on the arbitrary scale introduced by the regularization scheme. We apply our results to the particular case of de Sitter spacetime and discuss spontaneous symmetry breaking. The results depend strongly on the renormalization procedure.

See Also

Hartree approximation in curved spacetimes revisited. II. The semiclassical Einstein equations and de Sitter self-consistent solutions

Diana L. López Nacir, Francisco D. Mazzitelli, and Leonardo G. Trombetta

Phys. Rev. D 89, 084013 (2014)

Article Text

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