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Ferreiro, A., & Torrenti, F. (2023). Ultraviolet-regularized power spectrum without infrared distortions in cosmological spacetimes. Phys. Lett. B, 840, 137868–6pp.
Abstract: We reexamine the regularization of the two-point function of a scalar field in a Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. Adiabatic regularization provides a set of subtraction terms in momentum space that successfully remove its ultraviolet divergences at coincident points, but can significantly distort the power spectrum at infrared scales, especially for light fields. In this work we propose, by using the intrinsic ambiguities of the renormalization program, a new set of subtraction terms that minimize the distortions for scales k less than or similar to M, with M an arbitrary mass scale. Our method is consistent with local covariance and equivalent to general regularization methods in curved spacetime. We apply our results to the regularization of the power spectrum in de Sitter space: while the adiabatic scheme yields exactly Delta((reg))(phi) = 0 for a massless field, our proposed prescription recovers the standard scale-invariant result Delta((reg))(phi) similar or equal to H-2/(4 pi(2)) at super-horizon scales.
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Ferreiro, A., & Navarro-Salas, J. (2019). Running couplings from adiabatic regularization. Phys. Lett. B, 792, 81–85.
Abstract: We extend the adiabatic regularization method by introducing an arbitrary mass scale μin the construction of the subtraction terms. This allows us to obtain, in a very robust way, the running of the coupling constants by demanding mu-invariance of the effective semiclassical (Maxwell-Einstein) equations. In particular, we get the running of the electric charge of perturbative quantum electrodynamics. Furthermore, the method brings about a renormalization of the cosmological constant and the Newtonian gravitational constant. The running obtained for these dimensionful coupling constants has new relevant (non-logarithmic) contributions, not predicted by dimensional regularization.
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Ferreiro, A., Monin, S., & Torrenti, F. (2024). Physical scale adiabatic regularization in cosmological spacetimes. Phys. Rev. D, 109(4), 045015–16pp.
Abstract: We develop a new regularization method for the stress -energy tensor and the two -point function of free quantum scalar fields propagating in cosmological spacetimes. We proceed by extending the adiabatic regularization scheme with the introduction of two additional mass scales. By setting them to the order of the physical scale of the studied scenario, we obtain ultraviolet -regularized quantities that do not distort the power spectra amplitude at the infrared scales amplified by the expansion of the Universe. This is not ensured by the standard adiabatic approach. We also show how our proposed subtraction terms can be interpreted as a renormalization of coupling constants in the Einstein equations. We finally illustrate our proposed regularization method in two scenarios of cosmological interest: de Sitter inflation and geometric reheating.
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Ferreiro, A., & Pla, S. (2022). Adiabatic regularization and preferred vacuum state for the lambda phi^4 field theory in cosmological spacetimes. Phys. Rev. D, 106(6), 065015–12pp.
Abstract: We extend the method of adiabatic regularization by introducing an arbitrary parameter μfor a scalar field with quartic self-coupling in a Friedmann-Lemaitre-Robertson-Walker spacetime at one-loop order. The subtraction terms constructed from this extended version allow us to define a preferred vacuum state at a fixed time ri 1/4 ri0 for this theory. We compute this vacuum state for two commonly used background fields in cosmology, specially in the context of preheating. We also give a possible prescription for an adequate value for mu.
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Ferreiro, A., Nadal-Gisbert, S., & Navarro-Salas, J. (2021). Renormalization, running couplings, and decoupling for the Yukawa model in a curved spacetime. Phys. Rev. D, 104(2), 025003–8pp.
Abstract: The decoupling of heavy fields as required by the Appelquist-Carazzone theorem plays a fundamental role in the construction of any effective field theory. However, it is not a trivial task to implement a renormalization prescription that produces the expected decoupling of massive fields, and it is even more difficult in curved spacetime. Focused on this idea, we consider the renormalization of the one-loop effective action for the Yukawa interaction with a background scalar field in curved space. We compute the beta functions within a generalized DeWitt-Schwinger subtraction procedure and discuss the decoupling in the running of the coupling constants. For the case of a quantized scalar field, all the beta function exhibit decoupling, including also the gravitational ones. For a quantized Dirac field, decoupling appears almost for all the beta functions. We obtain the anomalous result that the mass of the background scalar field does not decouple.
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