| 1. |
- Beltran Jimenez, Jose, et al.
(författare)
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Coincident general relativity
- 2018
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Ingår i: Physical Review D. - : American Physical Society. - 2470-0010 .- 2470-0029. ; 98:4
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Tidskriftsartikel (refereegranskat)abstract
- The metric-affine variational principle is applied to generate teleparallel and symmetric teleparallel theories of gravity. From the latter we discover an exceptional class which is consistent with a vanishing affine connection. Based on this remarkable property, this work proposes a simpler geometrical formulation of general relativity that is oblivious to the affine spacetime structure, thus fundamentally depriving gravity of any inertial character. The resulting theory is described by the Hilbert action purged from the boundary term and is more robustly underpinned by the spin-2 field theory, where an extra symmetry is now manifest, possibly related to the double-copy structure of the gravity amplitudes. This construction also provides a novel starting point for modified gravity theories, and the paper presents new and simple generalizations where analytical self-accelerating cosmological solutions arise naturally in the early-and late-time Universe.
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| 2. |
- Beltran Jimenez, Jose, et al.
(författare)
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Cosmology in f (Q) geometry
- 2020
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Ingår i: Physical Review D. - : American Physical Society (APS). - 1550-7998 .- 1550-2368. ; 101:10
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Tidskriftsartikel (refereegranskat)abstract
- The universal character of the gravitational interaction provided by the equivalence principle motivates a geometrical description of gravity. The standard formulation of general relativity a la Einstein attributes gravity to the spacetime curvature, to which we have grown accustomed. However, this perception has masked the fact that two alternative, though equivalent, formulations of general relativity in flat spacetimes exist, where gravity can be fully ascribed either to torsion or to nonmetricity. The latter allows a simpler geometrical formulation of general relativity that is oblivious to the affine spacetime structure. Generalizations along this line permit us to generate teleparallel and symmetric teleparallel theories of gravity with exceptional properties. In this work we explore modified gravity theories based on nonlinear extensions of the nonmetricity scalar. After presenting some general properties and briefly studying some interesting background cosmologies (including accelerating solutions with relevance for inflation and dark energy), we analyze the behavior of the cosmological perturbations. Tensor perturbations feature a rescaling of the corresponding Newton's constant, while vector perturbations do not contribute in the absence of vector sources. In the scalar sector we find two additional propagating modes, hinting that f(Q) theories introduce, at least, 2 additional degrees of freedom. These scalar modes disappear around maximally symmetric backgrounds because of the appearance of an accidental residual gauge symmetry corresponding to a restricted diffeomorphism. We finally discuss the potential strong coupling problems of these maximally symmetric backgrounds caused by the discontinuity in the number of propagating modes.
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| 3. |
- Beltran Jimenez, Jose, et al.
(författare)
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Teleparallel Palatini theories
- 2018
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Ingår i: Journal of Cosmology and Astroparticle Physics. - : Institute of Physics Publishing (IOPP). - 1475-7516. ; :8
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Tidskriftsartikel (refereegranskat)abstract
- The Palatini formalism, which assumes the metric and the affine connection as independent variables, is developed for gravitational theories in flat geometries. We focus on two particularly interesting scenarios. First, we fix the connection to be metric compatible, as done in the usual teleparallel theories, but we follow a completely covariant approach by imposing the constraints with suitable Lagrange multipliers. For a general quadratic theory we show how torsion naturally propagates and we reproduce the Teleparallel Equivalent of General Relativity as a particular quadratic action that features an additional Lorentz symmetry. We then study the much less explored theories formulated in a geometry with neither curvature nor torsion, so that all the geometrical information is encoded in the non-metricity. We discuss how this geometrical framework leads to a purely inertial connection that can thus be completely removed by a coordinate gauge choice, the coincident gauge. From the quadratic theory we recover a simpler formulation of General Relativity in the form of the Einstein action, which enjoys an enhanced symmetry that reduces to a second linearised diffeomorphism at linear order. More general theories in both geometries can be formulated consistently by taking into account the inertial connection and the associated additional degrees of freedom. As immediate applications, the new cosmological equations and their Newtonian limit are considered, where the role of the lapse in the consistency of the equations is clarified, and the Schwarzschild black hole entropy is computed by evaluating the corresponding Euclidean action. We discuss how the boundary terms in the usual formulation of General Relativity are related to different choices of coordinates in its coincident version and show that in isotropic coordinates the Euclidean action is finite without the need to introduce boundary or normalisation terms. Finally, we discuss the double-copy structure of the gravity amplitudes and the bootstrapping of gravity within the framework of coincident General Relativity.
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| 4. |
- Beltran Jimenez, Jose, et al.
(författare)
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The canonical frame of purified gravity
- 2019
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Ingår i: International Journal of Modern Physics D. - : World Scientific Publishing Co. Pte Ltd. - 0218-2718. ; 28:14
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Tidskriftsartikel (refereegranskat)abstract
- In the recently introduced gauge theory of translations, dubbed Coincident General Relativity (CGR), gravity is described with neither torsion nor curvature in the spacetime affine geometry. The action of the theory enjoys an enhanced symmetry and avoids the second derivatives that appear in the conventional Einstein-Hilbert action. While it implies the equivalent classical dynamics, the improved action principle can make a difference in considerations of energetics, thermodynamics and quantum theory. This paper reports on possible progress in those three aspects of gravity theory. In the so-called purified gravity, (1) energy-momentum is described locally by a conserved, symmetric tensor, (2) the Euclidean path integral is convergent without the addition of boundary or regulating terms and (3) it is possible to identify a canonical frame for quantization.
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| 5. |
- Beltran Jimenez, Jose, et al.
(författare)
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The Geometrical Trinity of Gravity
- 2019
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Ingår i: Universe. - : MDPI. - 2218-1997. ; 5:7
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Tidskriftsartikel (refereegranskat)abstract
- The geometrical nature of gravity emerges from the universality dictated by the equivalence principle. In the usual formulation of General Relativity, the geometrisation of the gravitational interaction is performed in terms of the spacetime curvature, which is now the standard interpretation of gravity. However, this is not the only possibility. In these notes, we discuss two alternative, though equivalent, formulations of General Relativity in flat spacetimes, in which gravity is fully ascribed either to torsion or to non-metricity, thus putting forward the existence of three seemingly unrelated representations of the same underlying theory. Based on these three alternative formulations of General Relativity, we then discuss some extensions.
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| 6. |
- Jimenez, Jose Beltran, et al.
(författare)
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Extended Gauss-Bonnet gravities in Weyl geometry
- 2014
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Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 31:13, s. 135002-
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we consider an extended Gauss-Bonnet gravity theory in arbitrary dimensions and in a space provided with a Weyl connection, which is torsion-free but non-metric-compatible, the non-metricity tensor being determined by a vector field. The action considered consists of the usual Einstein-Hilbert action plus all the terms quadratic in the curvature that reduce to the usual Gauss-Bonnet term for vanishing Weyl connection, i.e., when only the Levi-Civita part of the connection is present. We expand the action in terms of Riemannian quantities and obtain vector-tensor theories. We find that all the free parameters only appear in the kinetic term of the vector field, so two branches are possible: one with a propagating vector field and another one where the vector field does not propagate. We focus on the propagating case. We find that in four dimensions, the theory is equivalent to Einstein's gravity plus a Proca field. This field is naturally decoupled from matter, so it represents a natural dark matter candidate. Also for d = 4, we discuss a non-trivial cubic term in the curvature that can be constructed without spoiling the second-order nature of the field equations, because it leads to the vector-tensor Horndeski interaction. In arbitrary dimensions, the theory becomes more involved. We show that, even though the vector field presents kinetic interactions which do not have U(1) symmetry, there are no additional propagating degrees of freedom with respect to the usual massive case. We show that, interestingly, this relies on the fact that the corresponding Stuckelberg field belongs to a specific class within the general Horndeski theories. Finally, since Weyl geometries provide the natural ground on which to build scale invariant theories, we apply the usual Weyl gauging in order to make the Horndeski action locally scale invariant, and discuss new terms that can be added.
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| 7. |
- Jimenez, Jose Beltran, et al.
(författare)
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Modified Gravity with Vector Distortion and Cosmological Applications
- 2017
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Ingår i: Universe. - : MDPI AG. - 2218-1997. ; 3:2
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Tidskriftsartikel (refereegranskat)abstract
- We briefly review the basics of Weyl geometry and its natural extension by a general linear "distortion" of the metric connection by a vector field. A special class of the connections has torsion but retains the Weyl's semi-metricity condition. We present ghost-free gravitational theories in this geometrical setup and highlight their possible cosmological applications, such as new self-tuning solutions and new bouncing solutions found in the quadratic-curvature theories. The vector distortion can mimic the cosmological effects of dark matter.
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| 8. |
- Jimenez, Jose Beltran, et al.
(författare)
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Spacetimes with vector distortion : Inflation from generalised Weyl geometry
- 2016
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Ingår i: Physics Letters B. - : Elsevier. - 0370-2693 .- 1873-2445. ; 756, s. 400-404
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Tidskriftsartikel (refereegranskat)abstract
- Spacetime with general linear vector distortion is introduced. Thus, the torsion and the nonmetricity of the affine connection are assumed to be proportional to a vector field (and not its derivatives). The resulting two-parameter family of non-Riemannian geometries generalises the conformal Weyl geometry and some other interesting special cases. Taking into account the leading nonlinear correction to the Einstein-Hilbert action results uniquely in the one-parameter extension of the Starobinsky inflation known as the alpha-attractor. The most general quadratic curvature action introduces, in addition to the canonical vector kinetic term, novel ghost-free vector-tensor interactions.
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