Weyl covariant theories of gravity in 3-dimensional Riemann–Cartan–Weyl space-times (original) (raw)
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Annalen der Physik, 2001
In this paper, two things are done. (i) Using cohomological techniques, we explore the consistent deformations of linearized conformal gravity in 4 dimensions. We show that the only possibility involving no more than 4 derivatives of the metric (i.e., terms of the form ∂ 4 g µν , ∂ 3 g µν ∂g αβ , ∂ 2 g µν ∂ 2 g αβ , ∂ 2 g µν ∂g αβ ∂g ρσ or ∂g µν ∂g αβ ∂g ρσ ∂g γδ with coefficients that involve undifferentiated metric components -or terms with less derivatives) is given by the Weyl action d 4 x √ −gW αβγδ W αβγδ , in much the same way as the Einstein-Hilbert action describes the only consistent manner to make a Pauli-Fierz massless spin-2 field self-interact with no more than 2 derivatives. No a priori requirement of invariance under diffeomorphisms is imposed: this follows automatically from consistency. (ii) We then turn to "multi-Weyl graviton" theories. We show the impossibility to introduce cross-interactions between the different types of Weyl gravitons if one requests that the action reduces, in the free limit, to a sum of linearized Weyl actions. However, if different free limits are authorized, cross-couplings become possible. An explicit example is given. We discuss also how the results extend to other spacetime dimensions.
On the cosmology of Weyl's gauge invariant gravity
2012
Recently the vector inflation has been proposed as the alternative to inflationary models based on scalar bosons and quintessence scalar fields. In the vector inflationary model, the vector field non-minimally couples to gravity. We should, however, inquire if there exists a relevant fundamental theory which supports the inflationary scenario. We investigate the possibility that Weyl's gauge gravity theory could be such a fundamental theory. That is the reason why the Weyl's gauge invariant vector and scalar fields are naturally introduced. After rescaling the Weyl's gauge invariant Lagrangian to the Einstein frame, we find that in four dimensions the Lagrangian is equivalent to Einstein-Proca theory and does not have the vector field non-minimally coupled to gravity, but has the scalar boson with a polynomial potential which leads to the spontaneously symmetry breakdown.
2011
A Weyl geometric scale covariant approach to gravity due to Omote, Dirac, and Utiyama (1971ff) is reconsidered. It can be extended to the electroweak sector of elementary particle fields, taking into account their basic scaling freedom. Already Cheng (1988) indicated that electroweak symmetry breaking, usually attributed to the Higgs field with a boson expected at 0.1 − 0.3 T eV , may be due to a coupling between Weyl geometric gravity and electroweak interactions. Weyl geometry seems to be well suited for treating questions of elementary particle physics, which relate to scale invariance and its "breaking". This setting suggests the existence of a scalar field boson at the surprisingly low energy of ∼ 1 eV. That may appear unlikely; but, as a payoff, the acquirement of mass arises as a result of coupling to gravity in agreement with the understanding of mass as the gravitational charge of fields.
Weyl-invariant scalar-tensor gravities from purely metric theories
arXiv (Cornell University), 2023
We describe a method to generate scalar-tensor theories with Weyl symmetry, starting from arbitrary purely metric higher derivative gravity theories. The method consists in the definition of a conformally-invariant metricĝ µν , that is a rank (0,2)-tensor constructed out of the metric tensor and the scalar field. This new object has zero conformal weight and is given by ϕ 2/∆ g µν , where (−∆) is the conformal dimension of the scalar. As g µν has conformal dimension of 2, the resulting tensor is trivially a conformal invariant. Then, the generated scalar-tensor theory, which we call the Weyl uplift of the original purely metric theory, is obtained by replacing the metric byĝ µν in the action that defines the original theory. This prescription allowed us to define the Weyl uplift of theories with terms of higher order in the Riemannian curvature. Furthermore, the prescription for scalar-tensor theories coming from terms that have explicit covariant derivatives in the Lagrangian is discussed. The same mechanism can also be used for the derivation of the equations of motion of the scalar-tensor theory from the original field equations in the Einstein frame. Applying this method of Weyl uplift allowed us to reproduce the known result for the conformal scalar coupling to Lovelock gravity and to derive that of Einsteinian cubic gravity. Finally, we show that the renormalization of the theory given by the conformal scalar coupling to Einstein-Anti-de Sitter gravity originates from the Weyl uplift of the original renormalized theory, which is relevant in the framework of conformal renormalization.
The Weyl–Cartan Gauss–Bonnet gravity
Classical and Quantum Gravity, 2015
In this paper, we consider the generalized Gauss-Bonnet action in 4-dimensional Weyl-Cartan space-time. In this space-time, the presence of torsion tensor and Weyl vector implies that the generalized Gauss-Bonnet action will not be a total derivative in four dimension space-time. It will be shown that the higher than two time derivatives can be removed from the action by choosing suitable set of parameters. In the special case where only the trace part of the torsion remains, the model reduces to GR plus two vector fields. One of which is massless and the other is massive. We will then obtain the healthy region of the 5-dimensional parameter space of the theory in some special cases.
Quadratic curvature theories formulated as covariant canonical gauge theories of gravity
Physical Review D
The covariant canonical gauge theory of gravity is generalized by including at the Lagrangian level all possible quadratic curvature invariants. In this approach, the covariant Hamiltonian principle and the canonical transformation framework are applied to derive a Palatini type gauge theory of gravity. The metric g μν , the affine connection γ λ μν and their respective conjugate momenta, k μνσ and q η αξβ tensors, are the independent field components describing the gravity. The metric is the basic dynamical field, and the connection is the gauge field. The torsion-free and metricity-compatible version of the spacetime Hamiltonian is built from all possible invariants of the q η αξβ tensor components up to second order.