Modified-gravity theories with nondynamical background fields

Abstract

We study the dynamics of a modified-gravity theory, which is supplemented by an extended Gibbons-Hawking-York boundary term and incorporates diffeomorphism violation through nondynamical background fields denoted as $u$ and $s^{\mu \nu }$ in the literature. An ADM decomposition allows us to project the modified Einstein equations into purely spacelike hypersurfaces, which implies the field equations for the induced dynamical three-metric. We also obtain the Hamilton-Jacobi equations of motion for the canonical variables of the theory based on its Hamiltonian, which was derived in a previous work. The computations show that the dynamical field equations obtained from the Lagrangian and Hamiltonian approaches are consistent with each other. Connections to Brans-Dicke theory and ghost-free massive gravity are established.

arXiv comment25 pages

References in corpus (84)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• The Confrontation between General Relativity and Experiment
• f(R) theories
• 4D Gravity on a Brane in 5D Minkowski Space
• Quantum Gravity at a Lifshitz Point
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• The Dynamics of General Relativity
• Is Cosmic Speed-Up Due to New Gravitational Physics?
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• Resummation of Massive Gravity
• Data Tables for Lorentz and CPT Violation
• Gravity, Lorentz Violation, and the Standard Model
• Massive Gravity
• From k-essence to generalised Galileons
• Modern tests of Lorentz invariance
• Gravity Probe B: Final Results of a Space Experiment to Test General Relativity
• Effective Field Theory for Massive Gravitons and Gravity in Theory Space
• Membranes at Quantum Criticality
• A healthy extension of Horava gravity
• Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability
• Nonperturbative Continuity in Graviton Mass versus Perturbative Discontinuity
• Gravity on a Brane in Infinite-Volume Extra Space
• Signals for Lorentz Violation in Post-Newtonian Gravity
• Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity
• Confirmation of the Secondary Constraint and Absence of Ghost in Massive Gravity and Bimetric Gravity
• Ghost-free Massive Gravity with a General Reference Metric
• On Non-Linear Actions for Massive Gravity
• Einstein-Aether Waves
• A systematic approach to generalisations of General Relativity and their cosmological implications
• Infrared-modified gravities and massive gravitons
• Interacting Spin-2 Fields
• Phases of massive gravity
• Ghost free Massive Gravity in the Stückelberg language
• An exact Schwarzschild-like solution in a bumblebee gravity model
• Spontaneous Lorentz and Diffeomorphism Violation, Massive Modes, and Gravity
• Testing local Lorentz invariance with gravitational waves
• A Nonsingular Cosmology with a Scale-Invariant Spectrum of Cosmological Perturbations from Lee-Wick Theory
• Lower Bound on the Propagation Speed of Gravity from Gravitational Cherenkov Radiation
• Extended Horava gravity and Einstein-aether theory
• Constraining the New Aether: Gravitational Cherenkov Radiation
• Hamiltonian analysis of higher derivative scalar-tensor theories
• Black holes with a cosmological constant in bumblebee gravity
• On couplings to matter in massive (bi-)gravity
• Proof of Consistency of Nonlinear Massive Gravity in the Stuckelberg Formulation
• Helicity Decomposition of Ghost-free Massive Gravity
• Constraints on Lorentz violation from gravitational Cherenkov radiation
• Gravity from spontaneous Lorentz violation
• Backgrounds in gravitational effective field theory
• The Lense--Thirring Effect and Mach's Principle
• Unimodular relativity and cosmological constant
• Modified Gravity via Spontaneous Symmetry Breaking
• Explicit versus Spontaneous Diffeomorphism Breaking in Gravity
• Signals for Lorentz violation in gravitational waves
• Einstein-Hilbert Graviton modes modified by the Lorentz-violating bumblebee Field
• How unimodular gravity theories differ from general relativity at quantum level
• Hidden Gravity in Open-String Field Theory
• Lorentz and Diffeomorphism Violations in Linearized Gravity
• Time-delay and Doppler tests of the Lorentz symmetry of gravity
• Lorentz violation in the gravity sector: The t puzzle
• Limits on violations of Lorentz Symmetry from Gravity Probe B
• Combined search for anisotropic birefringence in the gravitational-wave transient catalog GWTC-1
• Vector models of gravitational Lorentz symmetry breaking
• Nonlinear Dynamics of 3D Massive Gravity
• Light-bending tests of Lorentz invariance
• Gravity with explicit spacetime symmetry breaking and the Standard-Model Extension
• Comments About Hamiltonian Formulation of Non-Linear Massive Gravity with Stuckelberg Fields
• Spontaneous Lorentz symmetry breaking and one-loop effective action in the metric-affine bumblebee gravity
• Search for the birefringence of gravitational waves with the third observing run of Advanced LIGO-Virgo
• New limits on the Lorentz/CPT symmetry through fifty gravitational-wave events
• New proposal for non-linear ghost-free massive $F(R)$ gravity: cosmic acceleration and Hamiltonian analysis
• 3+1 Formulation of the Standard-Model Extension Gravity Sector
• Tests of CPT invariance in gravitational waves with LIGO-Virgo catalog GWTC-1
• Analysis of birefringence and dispersion effects from spacetime-symmetry breaking in gravitational waves
• Hamiltonian formulation of an effective modified gravity with nondynamical background fields
• Searches for beyond-Riemann gravity
• Explicit Lorentz violation in a static and spherically-symmetric spacetime
• On "New Massive" 4D Gravity
• Quantum gravitational states of ultracold neutrons as a tool for probing of beyond-Riemann gravity
• Spontaneous Lorentz violation and asymptotic flatness
• Singular Hamiltonians in models with spontaneous Lorentz symmetry breaking
• Lorentz-violating gravity and the bootstrap procedure

Cited by in corpus (4)

• Probing the Lorentz Symmetry Violation Using the First Image of Sagittarius A*: Constraints on Standard-Model Extension Coefficients
• Polarizations of Gravitational Waves in the Bumblebee Gravity Model
• Short-range forces due to Lorentz-symmetry violation
• Tree-level unitarity, causality and higher-order Lorentz and CPT violation