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Arrechea, J., Delhom, A., & Jimenez-Cano, A. (2021). Inconsistencies in four-dimensional Einstein-Gauss-Bonnet gravity. Chin. Phys. C, 45(1), 013107–8pp.
Abstract: We attempt to clarify several aspects concerning the recently presented four-dimensional Einstein-Gauss-Bonnet gravity. We argue that the limiting procedure outlined in [Phys. Rev. Lett. 124, 081301 (2020)] generally involves ill-defined terms in the four dimensional field equations. Potential ways to circumvent this issue are discussed, alongside remarks regarding specific solutions of the theory. We prove that, although linear perturbations are well behaved around maximally symmetric backgrounds, the equations for second-order perturbations are ill-defined even around a Minkowskian background. Additionally, we perform a detailed analysis of the spherically symmetric solutions and find that the central curvature singularity can be reached within a finite proper time.
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Beltran Jimenez, J., de Andres, D., & Delhom, A. (2020). Anisotropic deformations in a class of projectively-invariant metric-affine theories of gravity. Class. Quantum Gravity, 37(22), 225013–25pp.
Abstract: Among the general class of metric-affine theories of gravity, there is a special class conformed by those endowed with a projective symmetry. Perhaps the simplest manner to realise this symmetry is by constructing the action in terms of the symmetric part of the Ricci tensor. In these theories, the connection can be solved algebraically in terms of a metric that relates to the spacetime metric by means of the so-called deformation matrix that is given in terms of the matter fields. In most phenomenological applications, this deformation matrix is assumed to inherit the symmetries of the matter sector so that in the presence of an isotropic energy-momentum tensor, it respects isotropy. In this work we discuss this condition and, in particular, we show how the deformation matrix can be anisotropic even in the presence of isotropic sources due to the non-linear nature of the equations. Remarkably, we find that Eddington-inspired-Born-Infeld (EiBI) theories do not admit anisotropic deformations, but more general theories do. However, we find that the anisotropic branches of solutions are generally prone to a pathological physical behaviour.
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Beltran Jimenez, J., & Delhom, A. (2019). Ghosts in metric-affine higher order curvature gravity. Eur. Phys. J. C, 79(8), 656–7pp.
Abstract: We disprove the widespread belief that higher order curvature theories of gravity in the metric-affine formalism are generally ghost-free. This is clarified by considering a sub-class of theories constructed only with the Ricci tensor and showing that the non-projectively invariant sector propagates ghost-like degrees of freedom. We also explain how these pathologies can be avoided either by imposing a projective symmetry or additional constraints in the gravity sector. Our results put forward that higher order curvature gravity theories generally remain pathological in the metric-affine (and hybrid) formalisms and highlight the key importance of the projective symmetry and/or additional constraints for their physical viability and, by extension, of general metric-affine theories.
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Delhom, A., Lobo, I. P., Olmo, G. J., & Romero, C. (2019). A generalized Weyl structure with arbitrary non-metricity. Eur. Phys. J. C, 79(10), 878–9pp.
Abstract: A Weyl structure is usually defined by an equivalence class of pairs (g, omega) related by Weyl transformations, which preserve the relation del g = omega circle times g, where g and omega denote the metric tensor and a 1-form field. An equivalent way of defining such a structure is as an equivalence class of conformally related metrics with a unique affine connection Gamma((omega)), which is invariant under Weyl transformations. In a standard Weyl structure, this unique connection is assumed to be torsion-free and have vectorial non-metricity. This second view allows us to present two different generalizations of standard Weyl structures. The first one relies on conformal symmetry while allowing for a general non-metricity tensor, and the other comes from extending the symmetry to arbitrary (disformal) transformations of the metric.
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Delhom, A., Miralles, V., & Peñuelas, A. (2020). Effective interactions in Ricci-Based Gravity below the non-metricity scale. Eur. Phys. J. C, 80(4), 340–14pp.
Abstract: We show how minimally-coupled matter fields of arbitrary spin, when coupled to Ricci-based gravity theories, develop non-trivial effective interactions that can be treated perturbatively only below a characteristic high-energy scale . We then use this interactions to set bounds on the high-energy scale that controls departures of Ricci-Based Gravity theories from General Relativity. Particularly, for Eddington-inspired Born-Infeld gravity we obtain the strong bound vertical bar kappa vertical bar<10(-26)m(5)kg(-1)s(-2).
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Delhom, A., Lobo, I. P., Olmo, G. J., & Romero, C. (2020). Conformally invariant proper time with general non-metricity. Eur. Phys. J. C, 80(5), 415–11pp.
Abstract: We show that the definition of proper time for Weyl-invariant space-times given by Perlick naturally extends to spaces with arbitrary non-metricity. We then discuss the relation between this generalized proper time and the Ehlers-Pirani-Schild definition of time when there is arbitrary non-metricity. Then we show how this generalized proper time suffers from a second clock effect. Assuming that muons are a device to measure this proper time, we constrain the non-metricity tensor on Earth's surface and then elaborate on the feasibility of such assumption.
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Beltran Jimenez, J., & Delhom, A. (2020). Instabilities in metric-affine theories of gravity with higher order curvature terms. Eur. Phys. J. C, 80(6), 585–27pp.
Abstract: We discuss the presence of ghostly instabilities for metric-affine theories constructed with higher order curvature terms. We mainly focus on theories containing only the Ricci tensor and show the crucial role played by the projective symmetry. The pathological modes arise from the absence of a pure kinetic term for the projective mode and the non-minimal coupling of a 2-form field contained in the connection, and which can be related to the antisymmetric part of the metric in non-symmetric gravity theories. The couplings to matter are considered at length and cannot be used to render the theories stable. We discuss different procedures to avoid the ghosts by adding additional constraints. We finally argue how these pathologies are expected to be present in general metric-affine theories unless much care is taken in their construction.
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Delhom, A. (2020). Minimal coupling in presence of non-metricity and torsion. Eur. Phys. J. C, 80(8), 728–17pp.
Abstract: We deal with the question of what it means to define a minimal coupling prescription in presence of torsion and/or non-metricity, carefully explaining while the naive substitution partial derivative -> del introduces extra couplings between the matter fields and the connection that can be regarded as non-minimal in presence of torsion and/or non-metricity. We will also investigate whether minimal coupling prescriptions at the level of the action (MCPL) or at the level of field equations (MCPF) lead to different dynamics. To that end, we will first write the Euler-Lagrange equations for matter fields in terms of the covariant derivatives of a general non-Riemannian space, and derivate the form of the associated Noether currents and charges. Then we will see that if the minimal coupling prescriptions is applied as we discuss, for spin 0 and 1 fields the results of MCPL and MCPF are equivalent, while for spin 1/2 fields there is a difference if one applies the MCPF or the MCPL, since the former leads to charge violation.
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Delhom, A., Nascimento, J. R., Olmo, G. J., Petrov, A. Y., & Porfirio, P. J. (2021). Metric-affine bumblebee gravity: classical aspects. Eur. Phys. J. C, 81(4), 287–10pp.
Abstract: We consider the metric-affine formulation of bumblebee gravity, derive the field equations, and show that the connection can be written as Levi-Civita of a disformally related metric in which the bumblebee field determines the disformal part. As a consequence, the bumblebee field gets coupled to all the other matter fields present in the theory, potentially leading to nontrivial phenomenological effects. To explore this issue we compute the post-Minkowskian, weak-field limit and study the resulting effective theory. In this scenario, we couple scalar and spinorial matter to the effective metric, and then we explore the physical properties of the VEV of the bumblebee field, focusing mainly on the dispersion relations and the stability of the resulting effective theory.
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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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