del Rio, A., Navarro-Salas, J., & Torrenti, F. (2014). Renormalized stress-energy tensor for spin-1/2 fields in expanding universes. Phys. Rev. D, 90(8), 084017–15pp.
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.
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Agullo, I., Landete, A., & Navarro-Salas, J. (2014). Electric-magnetic duality and renormalization in curved spacetimes. Phys. Rev. D, 90(12), 124067–7pp.
Abstract: We point out that the duality symmetry of free electromagnetism does not hold in the quantum theory if an arbitrary classical gravitational background is present. The symmetry breaks in the process of renormalization, as also happens with conformal invariance. We show that a similar duality anomaly appears for a massless scalar field in 1 + 1 dimensions.
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del Rio, A., & Navarro-Salas, J. (2015). Equivalence of adiabatic and DeWitt-Schwinger renormalization schemes. Phys. Rev. D, 91(6), 064031–14pp.
Abstract: We prove that adiabatic regularization and DeWitt-Schwinger point-splitting provide the same result when renormalizing expectation values of the stress-energy tensor for spin-1/2 fields. This generalizes the equivalence found for scalar fields, which is here recovered in a different way. We also argue that the coincidence limit of the DeWitt-Schwinger proper time expansion of the two-point function agrees exactly with the analogous expansion defined by the adiabatic regularization method at any order (for both scalar and spin-1/2 fields). We also illustrate the power of the adiabatic method to compute higher order DeWitt coefficients in Friedmann-Lemaitre-Robertson-Walker Universes.
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Agullo, I., del Rio, A., & Navarro-Salas, J. (2017). Electromagnetic Duality Anomaly in Curved Spacetimes. Phys. Rev. Lett., 118(11), 111301–5pp.
Abstract: The source-free Maxwell action is invariant under electric-magnetic duality rotations in arbitrary spacetimes. This leads to a conserved classical Noether charge. We show that this conservation law is broken at the quantum level in the presence of a background classical gravitational field with a nontrivial Chern-Pontryagin invariant, in parallel with the chiral anomaly for massless Dirac fermions. Among the physical consequences, the net polarization of the quantum electromagnetic field is not conserved.
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del Rio, A., Ferreiro, A., Navarro-Salas, J., & Torrenti, F. (2017). Adiabatic regularization with a Yukawa interaction. Phys. Rev. D, 95(10), 105003–19pp.
Abstract: We extend the adiabatic regularization method for an expanding universe to include the Yukawa interaction between quantized Dirac fermions and a homogeneous background scalar field. We give explicit expressions for the renormalized expectation values of the stress-energy tensor < T-mu nu > and the bilinear <(psi) over bar psi > in a spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. These are basic ingredients in the semiclassical field equations of fermionic matter in curved spacetime interacting with a background scalar field. The ultraviolet subtracting terms of the adiabatic regularization can be naturally interpreted as coming from appropriate counterterms of the background fields. We fix the required covariant counterterms. To test our approach we determine the contribution of the Yukawa interaction to the conformal anomaly in the massless limit and show its consistency with the heat-kernel method using the effective action.
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