Renormalized stress-energy tensor for spin-1/2 fields in expanding universes

Adrian del Rio, Jose Navarro-Salas, and Francisco Torrenti
Phys. Rev. D 90, 084017 – Published 13 October 2014

Abstract

We provide an explicit expression for the renormalized expectation value of the stress-energy tensor of a spin-1/2 field in a spatially flat Friedmann-Lemaitre-Robertson-Walker universe. Its computation is based on the extension of the adiabatic regularization method to fermion fields introduced recently in the literature. The tensor is given in terms of UV-finite integrals in momentum space, which involve the mode functions that define the quantum state. As illustrative examples of the method efficiency, we see how to compute the renormalized energy density and pressure in two interesting cosmological scenarios: a de Sitter spacetime and a radiation-dominated universe. In the second case, we explicitly show that the late-time renormalized stress-energy tensor behaves as that of classical cold matter. We also check that, if we obtain the adiabatic expansion of the scalar field mode functions with a similar procedure to the one used for fermions, we recover the well-known WKB-type expansion.

  • Received 18 July 2014

DOI:https://doi.org/10.1103/PhysRevD.90.084017

© 2014 American Physical Society

Authors & Affiliations

Adrian del Rio1,*, Jose Navarro-Salas1,†, and Francisco Torrenti2,‡

  • 1Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Facultad de Fisica, Universidad de Valencia, Burjassot, 46100 Valencia, Spain
  • 2Instituto de Fisica Teorica UAM/CSIC, Universidad Autonoma de Madrid, Cantoblanco, 28049 Madrid, Spain

  • *adrian.rio@uv.es
  • jnavarro@ific.uv.es
  • f.torrenti@csic.es

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Issue

Vol. 90, Iss. 8 — 15 October 2014

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