Frame-invariant approach to higher-dimensional scalar-tensor gravity

Abstract

The recent interest in modified theories of gravity, involving some type of non-minimal coupling to the Ricci scalar, and the calculation of cosmological observables in the Einstein or the Jordan frame, motivate the formulation of these theories in terms of quantities that are invariant under frame transformations. Furthermore, in view of the description of gravity and its geometry motivated by string theory, such a formulation could be extended to include theories of extra spatial dimensions. In the present article, we generalize the construction of frame-invariant quantities, concerning a general, $D$-dimensional scalar-tensor theory. Then, we limit our scope to the 5D braneworld scenario, where we study thick brane solutions that are localized on the 3-brane and extend the invariant formulation to the case of multiple scalar fields (non-)minimally coupled to gravity.

arXiv commentPRD accepted version, 16 pp, no figures

References in corpus (87)

• A Large Mass Hierarchy from a Small Extra Dimension
• An Alternative to Compactification
• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• New Dimensions at a Millimeter to a Fermi and Superstrings at a TeV
• f(R) theories
• Extended Theories of Gravity
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Phenomenology, Astrophysics and Cosmology of Theories with Sub-Millimeter Dimensions and TeV Scale Quantum Gravity
• Modeling the fifth dimension with scalars and gravity
• Reconstruction of a scalar-tensor theory of gravity in an accelerating universe
• Scalar-tensor gravity in an accelerating universe
• Gauge bosons in a five-dimensional theory with localized gravity
• Localization of Matter and Cosmological Constant on a Brane in Anti de Sitter Space
• The conformal frame freedom in theories of gravitation
• Localized Gravitons, Gauge Bosons and Chiral Fermions in Smooth Spaces Generated by a Bounce
• Thick brane solutions
• Localization of Matters on a String-like Defect
• Question of quantum equivalence between Jordan frame and Einstein frame
• Thick domain walls and singular spaces
• Equivalence of the Einstein and Jordan frames
• Fermion localization on thick branes
• Physical non-equivalence of the Jordan and Einstein frames
• Quantum dilatonic gravity in d = 2,4 and 5 dimensions
• Some aspects of the cosmological conformal equivalence between ``Jordan Frame'' and ``Einstein Frame''
• Conformal-Frame (In)dependence of Cosmological Observations in Scalar-Tensor Theory
• Scalar kinks and fermion localisation in warped spacetimes
• Invariant quantities in the scalar-tensor theories of gravitation
• Fermions on Thick Branes in the Background of Sine-Gordon Kinks
• Frame-dependence of higher-order inflationary observables in scalar-tensor theories
• Correspondence of $F(R)$ Gravity Singularities in Jordan and Einstein Frames
• Braneworld models with a non-minimally coupled phantom bulk field: a simple way to obtain the -1-crossing at late times
• Localization of Matters on Pure Geometrical Thick Branes
• A frame independent classification of single field inflationary models
• Domain wall brane in squared curvature gravity
• Deceleration versus Acceleration Universe in Different Frames of $F(R)$ Gravity
• Fermion Resonances on Multi-field Thick Branes
• Solving higher curvature gravity theories
• Braneworld solutions for F(R) models with non-constant curvature
• Massive vector trapping as a gauge boson on a brane
• Conformal Frame Dependence of Inflation
• Quantum equivalence of $f(R)$ gravity and scalar-tensor theories
• The conformal transformation's controversy: what are we missing?
• Scalar-torsion theories of gravity III: analogue of scalar-tensor gravity and conformal invariants
• Localization of bulk matter fields, the hierarchy problem and corrections to Coulomb's law on a pure de Sitter thick braneworld
• Solutions to the problem of ELKO spinor localization in brane models
• Localization of abelian gauge fields on thick branes
• Thick brane models in generalized theories of gravity
• Self-gravitating domain walls and the thin-wall limit
• Gauge field localization on brane worlds
• Brane Models with a Ricci-Coupled Scalar Field
• Gravity localization and mass hierarchy in scalar-tensor branes
• Localization of Matters on Anti-de Sitter Thick Branes
• Pure geometric thick $f(R)$-branes: stability and localization of gravity
• Fresh look at the scalar-tensor theory of gravity in Jordan and Einstein frames from undiscussed standpoints
• Brans-Dicke theory: Jordan vs Einstein Frame
• Transformation properties and general relativity regime in scalar-tensor theories
• Invariant slow-roll parameters in scalar-tensor theories
• Quantum Equivalence of $f(R)$ Gravity and Scalar-tensor Theories in the Jordan and Einstein Frames
• Brane modeling in warped extra-dimension
• Graviton localization and Newton's law for brane models with a non-minimally coupled bulk scalar field
• Invariant quantities in the multiscalar-tensor theories of gravitation
• Resonances of Kalb-Ramond field on symmetric and asymmetric thick branes
• Gravitational Localization of All Local Fields on the Brane
• Anomalies, equivalence and renormalization of cosmological frames
• Non-minimal Coupling Branes
• Vector and fermion fields on a bouncing brane with a decreasing warp factor in a string-like defect
• Are there really conformal frames? Uniqueness of affine inflation
• Gravitational wave astronomy: the definitive test for the "Einstein frame versus Jordan frame" controversy
• Brane Cosmology with a Non-Minimally Coupled Bulk-Scalar Field
• Comparison of Frames: Jordan vs Einstein Frame for a Non-minimal Dark Energy Model
• Noether and Abbott-Deser-Tekin conserved quantities in scalar-tensor theory of gravity both in Jordan and Einstein frames
• Localization of Gravitino Field on $f(R)$ Thick Branes
• Braneworld solutions for modified theories of gravity with non-constant curvature
• Post-Newtonian parameters $\gamma$ and $\beta$ of scalar-tensor gravity for a homogeneous gravitating sphere
• Einstein frame or Jordan frame ?
• Matter localization on brane-worlds generated by deformed defects
• Note on the Gauss-Bonnet braneworld scenario
• Attractor Cosmology from non-minimally Coupled Gravity
• Thick braneworlds generated by a non-minimally coupled scalar field and a Gauss-Bonnet term: conditions for localization of gravity
• Equivalence of Einstein and Jordan frames in quantized cosmological models
• Stability of braneworlds with non-minimally coupled multi-scalar fields
• Scalar field localization on a brane with cosmological constant
• Warped Brane worlds in Critical Gravity
• A Revision to the Issue of Frames by Non-minimal Large Field Inflation
• Periodic thick-brane configurations and their stability
• Conformal Frame dependence on Cosmological Observations in Scalar-Tensor Theories of Gravity

Cited by in corpus (35)

• Inflation driven by Einstein-Gauss-Bonnet gravity
• Equivalence of inflationary models between the metric and Palatini formulation of scalar-tensor theories
• Thermodynamical correspondence of $f(R)$ gravity in Jordan and Einstein frames
• Nonminimal Coleman--Weinberg Inflation with an $R^2$ term
• Palatini frames in scalar-tensor theories of gravity
• Frame Covariance in Quantum Gravity
• Frame (In)equivalence in Quantum Field Theory and Cosmology
• A minimal model of inflation and dark radiation
• Non-minimal (self-)running inflation: metric vs. Palatini formulation
• Braneworld in $f(T)$ Gravity Theory with Noncanonical Scalar Matter Field
• New class of hybrid metric-Palatini scalar-tensor theories of gravity
• Beyond the Poles in Attractor Models of Inflation
• On the number of $e$-folds in the Jordan and Einstein frames
• Multiple point criticality principle and Coleman-Weinberg inflation
• Gravitational resonances on $f(T)$-branes
• Metric-affine gravity effects on terrestrial (exo-)planets profiles
• Gravitational resonances in mimetic thick branes
• Dynamical equivalence of $f(R)$ gravity in Jordan and Einstein frames
• Radion induced inflation on non-flat brane and modulus stabilization
• Extended phase space thermodynamics of black holes: A study in Einstein's gravity and beyond
• On the Trans-Planckian Censorship Conjecture and the Generalized Non-Minimal Coupling
• Thermodynamic structure of a generic null surface and the zeroth law in scalar-tensor theory
• Fluid-gravity correspondence in the scalar-tensor theory of gravity: (in)equivalence of Einstein and Jordan frames
• Invariant quantities of Scalar-Tensor Theories for stellar structure
• Revisiting black holes and wormholes under Weyl transformations
• Evolution of scalar field resonances in a braneworld
• Exploring the inflation of $F(R)$ gravity
• A critical analysis of modulus stabilization in a higher dimensional F(R) gravity
• Scalar-tensor gravity from thermodynamic and fluid-gravity perspective
• Gravitational Echoes from Braneworlds
• Evolution of Fermion Resonance in Thick Brane
• Scalar-tensor theories of gravity from a thermodynamic viewpoint
• Fifth forces and frame invariance
• Boundary terms and Brown-York quasi-local parameters for scalar-tensor theory: a study on both timelike and null hypersurfaces
• The Scalar Mach-Sciama Theory of Gravitation