Moretti, F., Bombacigno, F., & Montani, G. (2021). The Role of Longitudinal Polarizations in Horndeski and Macroscopic Gravity: Introducing Gravitational Plasmas. Universe, 7(12), 496–28pp.
Abstract: We discuss some general and relevant features of longitudinal gravitational modes in Horndeski gravity and their interaction with matter media. Adopting a gauge-invariant formulation, we clarify how massive scalar and vector fields can induce additional transverse and longitudinal excitations, resulting in breathing, vector, and longitudinal polarizations. We review, then, the interaction of standard gravitational waves with a molecular medium, outlining the emergence of effective massive gravitons, induced by the net quadrupole moment due to molecule deformation. Finally, we investigate the interaction of the massive mode in Horndeski gravity with a noncollisional medium, showing that Landau damping phenomenon can occur in the gravitational sector as well. That allows us to introduce the concept of “gravitational plasma”, where inertial forces associated with the background field play the role of cold ions in electromagnetic plasma.
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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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Borja, E. F., Garay, I., & Vidotto, F. (2012). Learning about Quantum Gravity with a Couple of Nodes. Symmetry Integr. Geom., 8, 015–44pp.
Abstract: Loop Quantum Gravity provides a natural truncation of the infinite degrees of freedom of gravity, obtained by studying the theory on a given finite graph. We review this procedure and we present the construction of the canonical theory on a simple graph, formed by only two nodes. We review the U(N) framework, which provides a powerful tool for the canonical study of this model, and a formulation of the system based on spinors. We consider also the covariant theory, which permits to derive the model from a more complex formulation, paying special attention to the cosmological interpretation of the theory.
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Afonso, V. I., Olmo, G. J., & Rubiera-Garcia, D. (2017). Scalar geons in Born-Infeld gravity. J. Cosmol. Astropart. Phys., 08(8), 031–35pp.
Abstract: The existence of static, spherically symmetric, self-gravitating scalar field solutions in the context of Born-Infeld gravity is explored. Upon a combination of analytical approximations and numerical methods, the equations for a free scalar field (without a potential term) are solved, verifying that the solutions recover the predictions of General Relativity far from the center but finding important new effects in the central regions. We find two classes of objects depending on the ratio between the Schwarzschild radius and a length scale associated to the Born-Infeld theory: massive solutions have a wormhole structure, with their throat at r = 2 M, while for the lighter configurations the topology is Euclidean. The total energy density of these solutions exhibits a solitonic profile with a maximum peaked away from the center, and located at the throat whenever a wormhole exists. The geodesic structure and curvature invariants are analyzed for the various configurations considered.
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Creminelli, P., Loayza, N., Serra, F., Trincherini, E., & Trombetta, L. G. (2020). Hairy black-holes in shift-symmetric theories. J. High Energy Phys., 08(8), 045–24pp.
Abstract: Scalar hair of black holes in theories with a shift symmetry are constrained by the no-hair theorem of Hui and Nicolis, assuming spherical symmetry, time-independence of the scalar field and asymptotic flatness. The most studied counterexample is a linear coupling of the scalar with the Gauss-Bonnet invariant. However, in this case the norm of the shift-symmetry current J(2) diverges at the horizon casting doubts on whether the solution is physically sound. We show that this is not an issue since J(2) is not a scalar quantity, since J(mu) is not a diffinvariant current in the presence of Gauss-Bonnet. The same theory can be written in Horndeski form with a non-analytic function G(5)similar to log X . In this case the shift-symmetry current is diff-invariant, but contains powers of X in the denominator, so that its divergence at the horizon is again immaterial. We confirm that other hairy solutions in the presence of non-analytic Horndeski functions are pathological, featuring divergences of physical quantities as soon as one departs from time-independence and spherical symmetry. We generalise the no-hair theorem to Beyond Horndeski and DHOST theories, showing that the coupling with Gauss-Bonnet is necessary to have hair.
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