Conformal Gravity and Transformations in the Symmetric Teleparallel Framework

Abstract

Conformal symmetries appear in many parts of physics and play a unique role in exploring the Universe. In this work, we consider the possibility of constructing conformal theories of gravity in the Symmetric Teleparallel Gravity framework, where gravitation is expressed through non-metricity rather than curvature or torsion. We demonstrate that it is possible to formulate a family of conformal theories with second-order field equations and have the metric tensor as the fundamental variable. Moreover, we consider the addition of a scalar field to the theory, and compare the results to the Teleparallel Gravity setting. Finally, we present the scalar-tensor representation of modified symmetric teleparallel theories, and amongst others, we show that there is an interesting sub-case that has the possibility of playing the role of dark energy.

arXiv comment14 pages

References in corpus (56)

• Extended Theories of Gravity
• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• f(T) teleparallel gravity and cosmology
• Dark torsion as the cosmic speed-up
• Modified teleparallel gravity: inflation without inflaton
• Einstein's Other Gravity and the Acceleration of the Universe
• Coincident General Relativity
• On Born-Infeld Gravity in Weitzenbock spacetime
• Alternatives to Dark Matter and Dark Energy
• Cosmological perturbations in f(T) gravity
• The covariant formulation of f(T) gravity
• Modified teleparallel theories of gravity
• Coupling matter in modified $Q$-gravity
• Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach
• "Teleparallel" Dark Energy
• $f(T,\mathcal{T})$ gravity and cosmology
• Making the Case for Conformal Gravity
• Teleparallel equivalent of Gauss-Bonnet gravity and its modifications
• Good and bad tetrads in f(T) gravity
• Teleparallel Palatini theories
• Degrees of freedom of $f(T)$ gravity
• Phase-Space analysis of Teleparallel Dark Energy
• Nonmetricity formulation of general relativity and its scalar-tensor extension
• On the covariance of teleparallel gravity theories
• Conformal symmetry and accelerating cosmology in teleparallel gravity
• Symmetric teleparallel general relativity
• Lagrange formulation of the symmetric teleparallel gravity
• Covariant formulation of scalar-torsion gravity
• Cosmological applications of $F(T,T_G)$ gravity
• No further gravitational wave modes in $F(T)$ gravity
• $f(T)$ gravity after GW170817 and GRB170817A
• New classes of modified teleparallel gravity models
• Field equations in teleparallel spacetime: Einstein's Fernparallelismus approach towards unified field theory
• Modified teleparallel theories of gravity in symmetric spacetimes
• Solution to the ghost problem in fourth order derivative theories
• Gravitational Waves in Modified Teleparallel Theories
• The spectrum of symmetric teleparallel gravity
• Hamiltonian formalism for f(T) gravity
• Cosmological dynamics of tachyonic teleparallel dark energy
• New observational constraints on $f(T)$ gravity through gravitational-wave astronomy
• From conformal to Einstein Gravity
• Conformal transformations in modified teleparallel theories of gravity revisited
• Fitting dwarf galaxy rotation curves with conformal gravity
• Spin Connection and Renormalization of Teleparallel Action
• Scale transformations in metric-affine geometry
• Modified teleparallel theories of gravity -- Gauss-Bonnet and trace extensions
• Teleparallel theories of gravity as analogue of non-linear electrodynamics
• Propagation of gravitational waves in teleparallel gravity theories
• Conformally invariant teleparallel theories of gravity
• Quest for the extra degree of freedom in f(T) gravity
• Holographic Renormalization in Teleparallel Gravity
• On an integrable geometrical foundation of gravity
• Physical content of Quadratic Gravity
• Probing the small distance structure of canonical quantum gravity using the conformal group
• Premetric equivalent of general relativity: Teleparallelism
• Teleparallel origin of the Fierz picture for spin-2 particle

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• Comparing Equivalent Gravities: common features and differences
• Exploring physical properties of minimally deformed strange star model and constraints on maximum mass limit in $f(\mathcal{Q})$ gravity
• A class of static spherically symmetric solutions in $f(Q)$-gravity
• Cosmological bouncing scenarios in symmetric teleparallel gravity
• ADM formulation and Hamiltonian analysis of $f(Q)$ gravity
• Cosmological applications of Myrzakulov gravity
• The $3+1$ Formalism in the Geometric Trinity of Gravity
• Neural Network Reconstruction of $H^{\prime }(z)$ and its application in Teleparallel Gravity
• Nonmetricity theories and aspects of gauge symmetry
• Neutron Star in Covariant $f(Q)$ gravity
• The origin of Weyl gauging in metric-affine theories
• Conserved quantities in STEGR and applications
• Geometrical Trinity of Unimodular Gravity
• Testing scale-invariant inflation against cosmological data
• Tensor Perturbations from Bounce Inflation Scenario in f(Q) Gravity
• Chameleon Mechanism in Scalar Nonmetricity Cosmology
• Phenomenological signatures of gauge invariant theories of gravity with vectorial nonmetricity
• Myrzakulov Gravity in Vielbein Formalism: A Study in Weitzenböck Spacetime
• Weyl transverse diffeomorphism invariant theory of symmetric teleparallel gravity
• Symmetric Teleparallel Gauss-Bonnet Gravity and its Extensions
• Einstein-Gauss-Bonnet-Myrzakulov Gravity from $R+F(T,G)$: Numerical Insights and Torsion-Gauss-Bonnet Dynamics in Weitzenböck Spacetime
• Mimetic-$f(Q)$ gravity: cosmic reconstruction and energy conditions
• Polytropic Stars in $f(Q)=Q+\xi Q^2$ covariant formulation
• Lost in translation: the Abelian affine connection (in the coincident gauge)