Equivalence of scalar-tensor theories and scale-dependent gravity
arXiv:2511.04467 · doi:10.1088/1361-6382/ae4203
Abstract
We present a novel equivalence between scale-dependent gravity and scalar-tensor theories that have only a single scalar field with a canonical kinetic term in the Einstein frame and a conformal coupling to the metric tensor. In particular, we show that the set of well-behaved scale-dependent gravity theories can be fully embedded into scalar-tensor theories in a unique way. Conversely, there are multiple ways to write a scalar-tensor theory as a scale-dependent theory. This equivalence is established both on the level of the actions and on the level of field equations. We find that, in the context of this equivalence, the scale-setting relation is naturally promoted to a dynamical field, which is made manifest by including a corresponding kinetic term in the scale-dependent action. In addition, we demonstrate that the new equivalence fits well into the framework of existing equivalences involving the aforementioned theories and -gravity. Finally, we apply the equivalence relations to explicit examples from both scale-dependent gravity and scalar-tensor theories.
43 pages, 2 figures, Minor changes to agree with published version
References in corpus (97)
- f(R) Theories Of Gravity
- Modified Gravity and Cosmology
- Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
- Chameleon Fields: Awaiting Surprises for Tests of Gravity in Space
- Chameleon Cosmology
- The String Dilaton and a Least Coupling Principle
- Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale
- Tests of the Gravitational Inverse-Square Law
- Healthy theories beyond Horndeski
- Symmetron Fields: Screening Long-Range Forces Through Local Symmetry Restoration
- Quintessence as a run-away dilaton
- Violations of the equivalence principle in a dilaton-runaway scenario
- Runaway dilaton and equivalence principle violations
- Environmental Dependence of Masses and Coupling Constants
- A Minimal Spontaneously Broken Hidden Sector and its Impact on Higgs Boson Physics at the Large Hadron Collider
- Tests of Chameleon Gravity
- Limit to General Relativity in f(R) theories of gravity
- Atom-interferometry constraints on dark energy
- Symmetron Cosmology
- The Dilaton and Modified Gravity
- Testing sub-gravitational forces on atoms from a miniature, in-vacuum source mass
- Renormalization group improved gravitational actions: a Brans-Dicke approach
- Gravity Resonance Spectroscopy Constrains Dark Energy and Dark Matter Scenarios
- Experiment to detect dark energy forces using atom interferometry
- Dark Energy Condensation
- Running Newton Constant, Improved Gravitational Actions, and Galaxy Rotation Curves
- Quantum Gravity at Astrophysical Distances?
- A Critique of the Asymptotic Safety Program
- Probing Dark Energy with Atom Interferometry
- Invariant quantities in the scalar-tensor theories of gravitation
- A Compendium of Chameleon Constraints
- Chameleon Dark Energy and Atom Interferometry
- Testing Screened Modified Gravity
- Nonlinear Structure Formation with the Environmentally Dependent Dilaton
- Neutron Interferometry constrains dark energy chameleon fields
- Acoustic Rabi oscillations between gravitational quantum states and impact on symmetron dark energy
- Direct detection of dark energy: the XENON1T excess and future prospects
- A frame independent classification of single field inflationary models
- Exact renormalization group with optimal scale and its application to cosmology
- Quantum equivalence of gravity and scalar-tensor theories
- Equivalence of inflationary models between the metric and Palatini formulation of scalar-tensor theories
- Radial acceleration relation from symmetron fifth forces
- Can scale-dependent cosmology alleviate the tension?
- Symmetron Scalar Fields: Modified Gravity, Dark Matter or Both?
- Scale Setting for Self-consistent Backgrounds
- Scale-dependent polytropic black hole
- Challenging theories of dark energy with levitated force sensor
- Constraining symmetron fields with atom interferometry
- Measuring gravity by holding atoms
- Transformation properties and general relativity regime in scalar-tensor theories
- Fifth forces, Higgs portals and broken scale invariance
- Open quantum dynamics induced by light scalar fields
- Using Atom Interferometry to Detect Dark Energy
- Renormalization group scale-setting from the action - a road to modified gravity theories
- Quantum Equivalence of Gravity and Scalar-tensor Theories in the Jordan and Einstein Frames
- Exact Solutions to Non-Linear Symmetron Theory: One and Two Mirror Systems
- Stellar kinematics from the symmetron fifth force in the Milky Way disk
- Screened Scalar Fields in the Laboratory and the Solar System
- Running Newton Coupling, Scale Identification and Black Hole Thermodynamics
- Lensing with generalized symmetrons
- Exact Solution for Chameleon Field, Self-Coupled Through the Ratra-Peebles Potential with n = 1 and Confined Between Two Parallel Plates
- Cosmological constant problem: deflation during inflation
- Dilaton Solutions for Laboratory Constraints and Lunar Laser Ranging
- Quantum Chameleons
- Detecting solar chameleons through radiation pressure
- Constraining the scalar-tensor gravity theories with and without screening mechanisms by combined observations
- Are there really conformal frames? Uniqueness of affine inflation
- Exact Solutions to Non-Linear Symmetron Theory II: One and Two Mirror Systems
- Dilaton-induced open quantum dynamics
- Strongly coupled chameleon fields: possible test with a neutron Lloyd's mirror interferometer
- Gravity Resonance Spectroscopy and Dark Energy Symmetron Fields
- SELCIE: A tool for investigating the chameleon field of arbitrary sources
- Quantum-enhanced screened dark energy detection
- Quantum simulation of dark energy candidates
- Search for environment-dependent dilatons
- Searching for Chameleon Dark Energy with Mechanical Systems
- Dynamics of the scalar field in 5-dimensional Kaluza-Klein theory
- Solar chameleons: Novel channels
- Search for dark energy with neutron interferometry
- Imprints of screened dark energy on nonlocal quantum correlations
- Chameleon Screening in Cosmic Voids
- The effects of running gravitational coupling on three dimensional black holes
- Global Portraits of Nonminimal Inflation: Metric and Palatini
- Potential of the neutron Lloyd's mirror interferometer for the search for new interactions
- The Nature of Dark Energy and Constraints on Its Hypothetical Constituents from Force Measurements
- A particle's perspective on screening mechanisms
- Frequency shifts induced by light scalar fields
- Scale-dependent cosmology from effective quantum gravity in the invariant framework
- Testing screened scalar-tensor theories of gravity with atomic clocks
- Screening Mechanisms on White Dwarfs: Symmetron & Dilaton
- Dynamical Casimir effect with screened scalar fields
- Quantum and thermal pressures from light scalar fields
- Chameleon Gravity as an Alternative to Dark Matter
- A Universe from a Lagrangian Fixed Point
- Structural Implications of the Chameleon Mechanism on White Dwarfs
- Scalar radiation zeros at the LHC
- Scale-dependent gravity and covariant scale-setting