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Ferreiro, A., & Navarro-Salas, J. (2020). Running gravitational couplings, decoupling, and curved spacetime renormalization. Phys. Rev. D, 102(4), 045021–6pp.
Abstract: We propose to slightly generalize the DeWitt-Schwinger adiabatic renormalization subtractions in curved space to include an arbitrary renornialization mass scale mu. The new predicted running for the gravitational couplings are fully consistent with decoupling of heavy massive fields. This is a somewhat improvement with respect to the more standard treatment of minimal (DeWitt-Schwinger) subtractions via dimensional regularization. We also show how the vacuum metamorphosis model emerges from the running couplings.
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Landete, A., Navarro-Salas, J., & Torrenti, F. (2013). Adiabatic regularization for spin-1/2 fields. Phys. Rev. D, 88(6), 061501–5pp.
Abstract: We extend the adiabatic regularization method to spin-1/2 fields. The ansatz for the adiabatic expansion for fermionic modes differs significantly from the WKB-type template that works for scalar modes. We give explicit expressions for the first adiabatic orders and analyze particle creation in de Sitter spacetime. As for scalar fields, the adiabatic method can be distinguished by its capability to overcome the UV divergences of the particle number operator. We also test the consistency of the extended method by working out the conformal and axial anomalies for a Dirac field in a Friedmann-Lemaitre-Robertson-Walker spacetime, in exact agreement with those obtained from other renormalization prescriptions. We finally show its power by computing the renormalized stress-energy tensor for Dirac fermions in de Sitter space.
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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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Navarro-Salas, J., & Pla, S. (2021). (F, G)-summed form of the QED effective action. Phys. Rev. D, 103(8), L081702–7pp.
Abstract: We conjecture that the proper-time series expansion of the one-loop effective Lagrangian of quantum electrodynamics can be summed in all terms containing the field-strength invariants F = 1/4F F-mu nu(mu nu) (x), G = 1/4 (F) over tilde F-mu nu(mu nu) (x), including those also possessing derivatives of the electromagnetic field strength. This partial resummation is exactly encapsulated in a factor with the same form as the Heisenberg-Euler Lagrangian density, except that now the electric and magnetic fields can depend arbitrarily on spacetime coordinates. We provide strong evidence for this conjecture, which is proved to sixth order in the proper time. Furthermore, and as a byproduct, we generate some solvable electromagnetic backgrounds. We also discuss the implications for a generalization of the Schwinger formula for pair production induced by nonconstant electric fields. Finally, we briefly outline the extension of these results in the presence of gravity.
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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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del Rio, A., & Navarro-Salas, J. (2014). Spacetime correlators of perturbations in slow-roll de Sitter inflation. Phys. Rev. D, 89(8), 084037–7pp.
Abstract: Two-point correlators and self-correlators of primordial perturbations in quasi-de Sitter spacetime backgrounds are considered. For large separations two-point correlators exhibit nearly scale invariance, while for short distances self-correlators need standard renormalization. We study the deformation of two-point correlators to smoothly match the self-correlators at coincidence. The corresponding angular power spectrum is evaluated in the Sachs-Wolfe regime of low multipoles. Scale invariance is maintained, but the amplitude of C(l)could change in a nontrivial way.
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Navarro-Salas, J. (2024). Black holes, conformal symmetry, and fundamental fields. Class. Quantum Gravity, 41(8), 085003–14pp.
Abstract: Cosmic censorship protects the outside world from black hole singularities and paves the way for assigning entropy to gravity at the event horizons. We point out a tension between cosmic censorship and the quantum backreacted geometry of Schwarzschild black holes, induced by vacuum polarization and driven by the conformal anomaly. A similar tension appears for the Weyl curvature hypothesis at the Big Bang singularity. We argue that the requirement of exact conformal symmetry resolves both conflicts and has major implications for constraining the set of fundamental constituents of the Standard Model.
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Beltran-Palau, P., Ferreiro, A., Navarro-Salas, J., & Pla, S. (2019). Breaking of adiabatic invariance in the creation of particles by electromagnetic backgrounds. Phys. Rev. D, 100(8), 085014–12pp.
Abstract: Particles are spontaneously created from the vacuum by time-varying gravitational or electromagnetic backgrounds. It has been proven that the particle number operator in an expanding universe is an adiabatic invariant. In this paper we show that, in some special cases, the expected adiabatic invariance of the particle number fails in presence of electromagnetic backgrounds. In order to do this, we consider as a prototype a Sauter-type electric pulse. Furthermore, we also show a close relation between the breaking of the adiabatic invariance and the emergence of the axial anomaly.
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Nadal-Gisbert, S., Navarro-Salas, J., & Pla, S. (2023). Low-energy states and CPT invariance at the big bang. Phys. Rev. D, 107(8), 085018–16pp.
Abstract: In this paper, we analyze the quantum vacuum in a radiation-dominated and CPT -invariant universe by further imposing the quantum states to be ultraviolet regular i.e., satisfying the Hadamard/adiabatic condition. For scalar fields, this is enforced by constructing the vacuum via the states of low-energy proposal. For spin -12 fields, we extend this proposal for a FLRW spacetime and apply it for the radiation-dominated and CPT -invariant universe. We focus on minimizing the smeared energy density around the big bang and give strong evidence that the resulting states satisfy the Hadamard/adiabatic condition. These states are then self -consistent candidates as effective big bang quantum vacuum from the field theory perspective.
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Beltran-Palau, P., del Rio, A., & Navarro-Salas, J. (2023). Quantum corrections to the Schwarzschild metric from vacuum polarization. Phys. Rev. D, 107(8), 085023–15pp.
Abstract: We explore static and spherically symmetric solutions of the 4-dimensional semiclassical Einstein's equations using the quantum vacuum polarization of a conformal field as a source. These solutions may be of interest for the study of exotic compact objects (ECOs). The full backreaction problem is addressed by solving the semiclassical Tolman-Oppenheimer-Volkoff (TOV) equations making use of effective equations of state inspired by the trace anomaly and an extra simplifying and reasonable assumption. We combine analytical and numerical techniques to solve the resulting differential equations, both perturbatively and nonperturbatively in h. In all cases the solution is similar to the Schwarzschild metric up p ffiffito the vicinity of the classical horizon r = 2M. However, at r = 2M + epsilon, with epsilon similar to O(root h), we find a coordinate singularity. In the case of matching with a static star, this leads to an upper bound in the compactness, and sets a constraint on the family of stable ECOs. We also study the corrections that the quantum-vacuum polarization induces on the propagation of waves, and discuss the implications. For the pure vacuum case, we can further extend the solution by using appropriate coordinates until we reach another singular point, where this time a null curvature singularity arises and prevents extending beyond. This picture qualitatively agrees with the results obtained in the effective two-dimensional approach, and reinforces the latter as a reasonable method.
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