Conformal gravity does not predict flat galaxy rotation curves

Hobson, M.; Lasenby, A.

doi:10.1103/physrevd.104.064014

Cited by 14 publications

(26 citation statements)

References 73 publications

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“…Eight dimensions. As mentioned above, there are 7 quadratic Lorentz scalar with ∆ = leading to the ansatz, (2,2) | C [2](2,2) + c 2 C [5] (3,2) | C [3](3,2) + c 3 C [5](2,1) | C [3](2,1) + c 4 C [4] (4,2) | C [4](4,2) + c 5 C [4] (3,1) | C [4] (3,1) + c 6 C [4](2,2) | C [4](2,2) + c 7 C [4](2,0) | C [4](2,0) + O(C 3 ) .…”

Section: Quadratic Weyl Invariantsmentioning

confidence: 96%

“…(2.46) 5 The maximal compact subalgebra of so(2, d) is not so(1, 1) ⊕ so(1, d − 1) but so(2) ⊕ so(d). However, the two subalgebras are intimately related as we shall comment later in section 4.1.…”

Section: Unfolding Conformal Geometrymentioning

confidence: 99%

“…(C [5] ) ∂C [5] = 0 , (5.15) and it determines E (C [2] , C [2] , C [2] ) . With these, E [5],a (C) is completely determined as it is at most cubic in C.…”

Section: Jhep12(2021)092mentioning

confidence: 99%

“…Since its introduction by Weyl and Bach, many studies were devoted to it (see e.g. [3][4][5] and references therein). As a four-derivative gravitational theory in four dimensions, it is power-counting renormalizable 1 as opposed to Einstein gravity and has many interesting features which might be relevant in phenomenological models of gravity: notably, it has the conformal symmetry which the early universe seems to exhibit, and hence conformal gravity or its variant may replace Einstein gravity in the very early time of the universe (see e.g.…”

Section: Jhep12(2021)092 1 Introductionmentioning

confidence: 99%

“…As a four-derivative gravitational theory in four dimensions, it is power-counting renormalizable 1 as opposed to Einstein gravity and has many interesting features which might be relevant in phenomenological models of gravity: notably, it has the conformal symmetry which the early universe seems to exhibit, and hence conformal gravity or its variant may replace Einstein gravity in the very early time of the universe (see e.g. recent works [5,8] and references therein). More generally, when we consider various modifications of gravity, conformal geometry also plays a distinguished role since the diffeomorphism plus Weyl rescaling is the maximum gauge symmetry that a theory of symmetric rank-two tensor field can afford.…”

Section: Jhep12(2021)092 1 Introductionmentioning

confidence: 99%

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Unfolding conformal geometry

Joung

Kim

2021

J. High Energ. Phys.

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Conformal geometry is studied using the unfolded formulation à la Vasiliev. Analyzing the first-order consistency of the unfolded equations, we identify the content of zero-forms as the spin-two off-shell Fradkin-Tseytlin module of $$ \mathfrak{so}\left(2,d\right) $$ so 2 d . We sketch the nonlinear structure of the equations and explain how Weyl invariant densities, which Type-B Weyl anomaly consist of, could be systematically computed within the unfolded formulation. The unfolded equation for conformal geometry is also shown to be reduced to various on-shell gravitational systems by requiring additional algebraic constraints.

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Section: Quadratic Weyl Invariantsmentioning

confidence: 96%

Section: Unfolding Conformal Geometrymentioning

confidence: 99%

“…(C [5] ) ∂C [5] = 0 , (5.15) and it determines E (C [2] , C [2] , C [2] ) . With these, E [5],a (C) is completely determined as it is at most cubic in C.…”

Section: Jhep12(2021)092mentioning

confidence: 99%

Section: Jhep12(2021)092 1 Introductionmentioning

confidence: 99%

Section: Jhep12(2021)092 1 Introductionmentioning

confidence: 99%

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Unfolding conformal geometry

Joung

Kim

2021

J. High Energ. Phys.

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On the ghost problem of conformal gravity

Hell,

Lüst,

Zoupanos

2023

J. High Energ. Phys.

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We study the metric perturbations around the de Sitter and Minkowski backgrounds in Conformal Gravity. We confirm the presence of ghosts in both cases. In the de Sitter case, by applying the Maldacena boundary conditions — the Neumann boundary condition and the positive-frequency mode condition — to the metric, we show that one cannot recover a general solution for the perturbations. In turn, alongside the Neumann boundary condition, we derive an additional condition with which the perturbations of conformal gravity and dS perturbations of Einstein gravity with cosmological constant coincide. We further show that the Neumann boundary condition does not lead to a general solution in Minkowski space. Conversely, we derive the alternative boundary conditions, with which we attain an agreement between the perturbations of conformal and Einstein gravity in full generality, thus removing the ghost of conformal gravity.

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The $\kappa $-model, a minimal model alternative to dark matter: application to the galactic rotation problem

Pascoli

2022

Astrophys Space Sci

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Conformal gravity does not predict flat galaxy rotation curves

Cited by 14 publications

References 73 publications

Unfolding conformal geometry

Unfolding conformal geometry

On the ghost problem of conformal gravity

The $\kappa $-model, a minimal model alternative to dark matter: application to the galactic rotation problem

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