Field transformations and invariant quantities in scalar-teleparallel theories of gravity
arXiv:2312.17609 · doi:10.1103/PhysRevD.109.064003
Abstract
We study transformations of the dynamical fields - a metric, a flat affine connection and a scalar field - in scalar-teleparallel gravity theories. The theories we study belong either to the general teleparallel setting, where no further condition besides vanishing curvature is imposed on the affine connection, or the symmetric or metric teleparallel gravity, where one also imposes vanishing torsion or nonmetricity, respectively. For each of these three settings, we find a general class of scalar-teleparallel action functionals which retain their form under the aforementioned field transformations. This is achieved by generalizing the constraint of vanishing torsion or nonmetricity to non-vanishing, but algebraically constrained torsion or nonmetricity. We find a number of invariant quantities which characterize these theories independently of the choice of field variables, and relate these invariants to analogues of the conformal frames known from scalar-curvature gravity. Using these invariants, we are able to identify a number of physically relevant subclasses of scalar-teleparallel theories. We also generalize our results to multiple scalar fields, and speculate on further extended theories with non-vanishing, but algebraically constrained curvature.
arXiv comment27 pages, no figures, journal version
References in corpus (72)
- Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
- Modified Gravity and Cosmology
- Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
- Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
- In the Realm of the Hubble tension a Review of Solutions
- Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
- f(T) teleparallel gravity and cosmology
- Generalized G-inflation: Inflation with the most general second-order field equations
- Einstein's Other Gravity and the Acceleration of the Universe
- From k-essence to generalised Galileons
- Healthy theories beyond Horndeski
- The teleparallel equivalent of general relativity
- Horndeski theory and beyond: a review
- Transforming gravity: from derivative couplings to matter to second-order scalar-tensor theories beyond the Horndeski Lagrangian
- Teleparallel Gravity: From Theory to Cosmology
- Beyond CDM: Problems, solutions, and the road ahead
- The Relation between Physical and Gravitational Geometry
- A systematic approach to generalisations of General Relativity and their cosmological implications
- "Teleparallel" Dark Energy
- The conformal frame freedom in theories of gravitation
- Disformal invariance of second order tensor-scalar theories: framing the Horndeski action
- Modified Gravity and Cosmology: An Update by the CANTATA Network
- The (pseudo)issue of the conformal frame revisited
- Recent Advances on Inflation
- Nonmetricity formulation of general relativity and its scalar-tensor extension
- Linking Tests of Gravity On All Scales: from the Strong-Field Regime to Cosmology
- Equivalence of the Einstein and Jordan frames
- Comparing Equivalent Gravities: common features and differences
- Einstein and Jordan frames reconciled: a frame-invariant approach to scalar-tensor cosmology
- Can Horndeski Theory be recast using Teleparallel Gravity?
- Covariant formulation of scalar-torsion gravity
- Cosmological perturbations in modified teleparallel gravity models
- Physical non-equivalence of the Jordan and Einstein frames
- Conformal-Frame (In)dependence of Cosmological Observations in Scalar-Tensor Theory
- General Teleparallel Quadratic Gravity
- Invariant quantities in the scalar-tensor theories of gravitation
- Frame-dependence of higher-order inflationary observables in scalar-tensor theories
- A frame independent classification of single field inflationary models
- Local symmetries and physical degrees of freedom in gravity: a Dirac Hamiltonian constraint analysis
- Scale transformations in metric-affine geometry
- Family of scalar-nonmetricity theories of gravity
- Modified gravity: a unified approach
- Stellar and substellar objects in modified gravity
- Conformal equivalence in classical gravity: the example of "veiled" General Relativity
- Scalar-torsion theories of gravity III: analogue of scalar-tensor gravity and conformal invariants
- Perturbations in Non-Flat Cosmology for gravity
- Reviving Horndeski Theory using Teleparallel Gravity after GW170817
- Foundational issues in f(T) gravity theory
- Scalar-torsion theories of gravity I: general formalism and conformal transformations
- Scalar-torsion theories of gravity II: theory
- Minkowski space in gravity
- Post-Newtonian limit of Teleparallel Horndeski gravity
- Non-trivial Minkowski backgrounds in f(T) gravity
- Homogeneous and isotropic cosmology in general teleparallel gravity
- Transformation properties and general relativity regime in scalar-tensor theories
- Non-Linear Obstructions for Consistent New General Relativity
- Variational Principles in Teleparallel Gravity Theories
- Invariant slow-roll parameters in scalar-tensor theories
- Invariant quantities in the multiscalar-tensor theories of gravitation
- Symmetric Teleparallel Horndeski Gravity
- Field redefinitions in theories beyond Einstein gravity using the language of differential forms
- Distinguishing Jordan and Einstein frames in gravity through entanglement
- Post-Newtonian limit of generalized scalar-torsion theories of gravity
- Post-Newtonian limit of scalar-torsion theories of gravity as analogue to scalar-curvature theories
- Equivalence of cosmological observables in conformally related scalar tensor theories
- Teleparallel gravity
- Disformal Transformations in Scalar-Torsion Gravity
- Disformal transformations in modified teleparallel gravity
- Parametrized post-Newtonian limit of generalized scalar-nonmetricity theories of gravity
- Irregular universe in the Nieh-Yan modified teleparallel gravity
- Degrees of freedom and Hamiltonian formalism for gravity
- Fifth forces and frame invariance