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Conformal Transformations in Metric-Affine Gravity and Ghosts
General Relativity and Quantum Cosmology · Submitted 28 Apr 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Therefore, metric-affine gravity provides an arena in which ghosts arising from conformal factor are avoided thanks to the independence of connection from the metric.
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The abstract, sentence by sentence
Conformal transformations play a widespread role in gravity theories in regard to their cosmological and other implications. In the pure metric theory of gravity, conformal transformations change the frame to a new one wherein one obtains a conformal-invariant scalar-tensor theory such that the scalar field, deriving from the conformal factor, is a ghost. In this work, conformal transformations and ghosts will be analyzed in the framework of the metric-affine theory of gravity. Within this framework, metric and connection are independent variables, and hence, transform independently under conformal transformations. It will be shown that, if affine connection is invariant under conformal transformations then the scalar field under concern is a non-ghost, non-dynamical field. It is an auxiliary field at the classical level, and might develop a kinetic term at the quantum level. Alternatively, if connection transforms additively with a structure similar to yet more general than that of the Levi-Civita connection, the resulting action describes the gravitational dynamics correctly, and more importantly, the scalar field becomes a dynamical non-ghost field. The equations of motion, for generic geometrical and matter-sector variables, do not reduce connection to the Levi-Civita connection, and hence, independence of connection from metric is maintained. Therefore, metric-affine gravity provides an arena in which ghosts arising from conformal factor are avoided thanks to the independence of connection from the metric.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Conformal transformations play a widespread role in gravity theories in regard to their cosmological and other implications. | background 1.00 | 0.03 | 0.02 | asserted 1.00 |
| s1 | In the pure metric theory of gravity, conformal transformations change the frame to a new one wherein one obtains a conformal-invariant scalar-tensor theory such that the scalar field, deriving from the conformal factor, is a ghost. | background 1.00 | 0.06 | 0.04 | asserted 1.00 |
| s2 | In this work, conformal transformations and ghosts will be analyzed in the framework of the metric-affine theory of gravity. | contribution 1.00 | 0.55 | 0.04 | asserted 0.80 |
| s3 | Within this framework, metric and connection are independent variables, and hence, transform independently under conformal transformations. | background 0.59 | 0.14 | 0.03 | asserted 1.00 |
| s4 | It will be shown that, if affine connection is invariant under conformal transformations then the scalar field under concern is a non-ghost, non-dynamical field. | result 1.00 | 0.77 | 0.25 | asserted 1.00 |
| s5 | It is an auxiliary field at the classical level, and might develop a kinetic term at the quantum level. | result 0.56 | 0.41 | 0.05 | speculative 0.57 |
| s6 | Alternatively, if connection transforms additively with a structure similar to yet more general than that of the Levi-Civita connection, the resulting action describes the gravitational dynamics correctly, and more importantly, the scalar field becomes a dynamical non-ghost field. | result 1.00 | 0.83 | 0.33 | asserted 0.99 |
| s7 | The equations of motion, for generic geometrical and matter-sector variables, do not reduce connection to the Levi-Civita connection, and hence, independence of connection from metric is maintained. | result 0.98 | 0.81 | 0.10 | asserted 1.00 |
| s8 | Therefore, metric-affine gravity provides an arena in which ghosts arising from conformal factor are avoided thanks to the independence of connection from the metric. | interpretation 0.78 | 0.75 | 0.87 | asserted 1.00 |
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Original abstract
Conformal transformations play a widespread role in gravity theories in regard to their cosmological and other implications. In the pure metric theory of gravity, conformal transformations change the frame to a new one wherein one obtains a conformal-invariant scalar-tensor theory such that the scalar field, deriving from the conformal factor, is a ghost. In this work, conformal transformations and ghosts will be analyzed in the framework of the metric-affine theory of gravity. Within this framework, metric and connection are independent variables, and hence, transform independently under conformal transformations. It will be shown that, if affine connection is invariant under conformal transformations then the scalar field under concern is a non-ghost, non-dynamical field. It is an auxiliary field at the classical level, and might develop a kinetic term at the quantum level. Alternatively, if connection transforms additively with a structure similar to yet more general than that of the Levi-Civita connection, the resulting action describes the gravitational dynamics correctly, and more importantly, the scalar field becomes a dynamical non-ghost field. The equations of motion, for generic geometrical and matter-sector variables, do not reduce connection to the Levi-Civita connection, and hence, independence of connection from metric is maintained. Therefore, metric-affine gravity provides an arena in which ghosts arising from conformal factor are avoided thanks to the independence of connection from the metric.
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References
How the literature uses it
7 arXiv papers cite this in 12 sentences
Papers citing it · 9 sentences without a confident label
Cites it as background 3 papers
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The total affine Ricci curvature gives the affine scalar curvature $R(g,Γ)≡g^μνℝ_μν(Γ)$ [ref] .
Primordial Gravitational Waves in Generalized Palatini Gravity · Generalized Palatini Gravity · 0.83
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Then, the conformal transformation accumulated in different studies in different context [ref] .
Gravitational Frames and Scalar Field Dynamics · Introduction · 0.98
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(Conformal transformations in Weyl gravity have been discussed in [ref] .)
Probing Geometric Proca in Metric-Palatini Gravity with Black Hole Shadow and Photon Motion · Einstein-Geometric Proca Model in AdS background · 0.96
What it cites · 25 sentences without a confident label
Cites as background 4 papers
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The metric-affine gravity (similar to the Palatini formalism [ref] in philosophy), which considers an independence of metric tensor and connection [ref] , encodes a more general approach to gravitation by breaking up the a priori relation ([ref]).
On white dwarfs and neutron stars in Palatini f(R) gravity · Introduction · 0.83
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The metric-affine gravity (similar to the Palatini formalism [ref] in philosophy), which considers an independence of metric tensor and connection [ref] , encodes a more general approach to gravitation by breaking up the a priori relation ([ref]).
Cosmological constraints on f(R) gravity theories within the Palatini approach · Introduction · 0.83
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The metric-affine gravity (similar to the Palatini formalism [ref] in philosophy), which considers an independence of metric tensor and connection [ref] , encodes a more general approach to gravitation by breaking up the a priori relation ([ref]).
Actions for Gravity, with Generalizations: A Review · Introduction · 0.83
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