Conformal transformations in modified teleparallel theories of gravity revisited

Abstract

It is well known that one cannot apply a conformal transformation to $f(T)$ gravity to obtain a minimally coupled scalar field model, and thus no Einstein frame exists for $f(T)$ gravity. Furthermore nonminimally coupled "teleparallel dark energy models" are not conformally equivalent to $f(T)$ gravity. However, it can be shown that $f(T)$ gravity is conformally equivalent to a teleparallel phantom scalar field model with a nonminimal coupling to a boundary term only. In this work, we extend this analysis by considering a recently studied extended class of models, known as $f(T,B)$ gravity, where $B$ is a boundary term related to the divergence of a contraction of the torsion tensor. We find that nonminimally coupled "teleparallel dark energy models" are conformally equivalent to either an $f(T,B)$ or $f(B)$ gravity model. Finally conditions on the functional form of $f(T,B)$ gravity are derived to allow it to be transformed to particular nonminimally coupled scalar field models.

13 pages, 1 figure

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Cited by in corpus (57)

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• Gravitational Waves in Modified Teleparallel Theories
• Cosmological bouncing solutions in f(T,B) gravity
• Hamiltonian formalism for f(T) gravity
• Cosmological viable models in $f(T,B)$ gravity as solutions to the $H_0$ tension
• Conformal Gravity and Transformations in the Symmetric Teleparallel Framework
• Scale transformations in metric-affine geometry
• Black Holes in $f(T,B)$ Gravity: Exact and Perturbed Solutions
• Scalar-torsion theories of gravity III: analogue of scalar-tensor gravity and conformal invariants
• Foundational issues in f(T) gravity theory
• Constraining Teleparallel Gravity through Gaussian Processes
• Quest for the extra degree of freedom in f(T) gravity
• Scalar-torsion theories of gravity II: $L(T,X,Y,\varphi )$ theory
• Effective gravitational coupling in modified teleparallel theories
• Reconstructing teleparallel gravity with cosmic structure growth and expansion rate data
• Cosmological applications of Myrzakulov gravity
• Higgs inflation and teleparallel gravity
• Thick brane in f(T,B) gravity
• Spherical and cylindrical solutions in f (T) gravity by Noether Symmetry Approach
• Cosmological perturbations in modified teleparallel gravity models: Boundary term extension
• Reflections on the covariance of modified teleparallel theories of gravity
• Impact of $H_0$ priors on $f(T)$ late time cosmology
• Modified teleparallel gravity with higher-derivative torsion terms
• McVittie solution in f(T) gravity
• Testing the violation of the equivalence principle in the electromagnetic sector and its consequences in $f(T)$ gravity
• Slow-roll inflation in generalized scalar-torsion gravity
• Pseudoinvariance and the extra degree of freedom in f(T) gravity
• Dynamical complexity of the Teleparallel gravity cosmology
• Classification of Teleparallel Horndeski Cosmology via Noether Symmetries
• Fermion localization in braneworld teleparallel f(T,B) gravity
• Symmetron and de Sitter attractor in a teleparallel model of cosmology
• Qualitative Stability Analysis of Cosmological Parameters in $f(T,B)$ Gravity
• Disformal Transformations in Scalar-Torsion Gravity
• Disformal transformations in modified teleparallel gravity
• Ghost and Laplacian Instabilities in the Teleparallel Horndeski Gravity
• Inflation with F(T) Teleparallel Gravity
• Scattering of Fermions by Gravitons
• Localization of abelian gauge fields with Stueckelberg-like geometrical coupling on $f(T,B)$-thick brane
• $f(T,B)$ Gravity in the late Universe in the context of local measurements
• Geodesic Congruences and a Collapsing Stellar Distribution in f (T ) Theories
• Scale-invariant cosmology in de Sitter gauge theory
• Coupled dark energy model inspired from general conformal transformation
• Generalised Proca Theories in Teleparallel Gravity
• Conformal Transformations and Cosmological Perturbations in New General Relativity
• Cosmological Dark sector from a Mimetic-Metric-Torsion perspective
• Propagating Gravitational Waves in Teleparallel Gauss-Bonnet Gravity
• String-like brane splitting in the context of $f(T,B)$ gravity
• The first non-static inhomogeneous exact solution in $f(T,B)$ gravity
• Global portraits of nonminimal teleparallel inflation
• From Special Relativity to embedded generators in Cartan subalgebras of rank-4 spin algebras
• Kalb-Ramond field induced cosmological bounce in generalized teleparallel gravity
• $O(d,d)$ symmetry in teleparallel dark energy
• $f(T,B)$ cosmography for high redshifts