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Delhom, A., Mariz, T., Nascimento, J. R., Olmo, G. J., Petrov, A. Y., & Porfirio, P. J. (2022). Spontaneous Lorentz symmetry breaking and one-loop effective action in the metric-affine bumblebee gravity. J. Cosmol. Astropart. Phys., 07(7), 018–27pp.
Abstract: The metric-affine bumblebee model in the presence of fermionic matter minimally coupled to the connection is studied. We show that the model admits an Einstein frame representation in which the matter sector is described by a non-minimal Dirac action without any analogy in the literature. Such non-minimal terms involve unconventional couplings between the bumblebee and the fermion field. We then rewrite the quadratic fermion action in the Einstein frame in the basis of 16 Dirac matrices in order to identify the coefficients for Lorentz/CPT violation in all orders of the non-minimal coupling xi. The exact result for the fermionic determinant in the Einstein frame, including all orders in xi, is also provided. We demonstrate that the axial contributions are at least of second order in the perturbative expansion of xi. Furthermore, we compute the one-loop effective potential within the weak field approximation.
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Araujo Filho, A. A., Nascimento, J. R., Petrov, A. Y., & Porfírio, P. J. (2023). Vacuum solution within a metric-affine bumblebee gravity. Phys. Rev. D, 108(8), 085010–13pp.
Abstract: We consider a metric-affine extension to the gravitational sector of the Standard Model extension for the Lorentz-violating coefficients u and s(mu nu). The general results, which are applied to a specific model called metric-affine bumblebee gravity, are obtained. A Schwarzschild-like solution, incorporating effects of the Lorentz symmetry breaking through the coefficient X = xi b(2), is found. Furthermore, a complete study of the geodesic trajectories of particles is accomplished in this background, emphasizing the departure from general relativity. We also compute the advance of Mercury's perihelion and the deflection of light within the context of the weak-field approximation, and we verify that there exist two new contributions ascribed to the Lorentz symmetry breaking. As a phenomenological application, we compare our theoretical results with observational data in order to estimate the coefficient X.
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