ADM formulation and Hamiltonian analysis of $f(Q)$ gravity

Abstract

$f(Q)$ gravity is an extension of the symmetric teleparallel equivalent to general relativity. We demonstrate the Hamiltonian analysis of $f(Q)$ gravity with fixing the coincident gauge condition. Using the standard Dirac-Bergmann algorithm, we show that $f(Q)$ gravity has 8 physical degrees of freedom. This result reflects that the diffeomorphism symmetry of $f(Q)$ gravity is completely broken due to the gauge fixing. Moreover, in terms of the perturbations, we discuss the possible mode decomposition of these degrees of freedom.

19 pages

References in corpus (15)

• The teleparallel equivalent of general relativity
• Degrees of freedom of $f(T)$ gravity
• Covariant formulation of f(Q) theory
• Accelerated Expansion of the Universe in Non-minimally Coupled Gravity
• Black holes in $f(\mathbb{Q})$ Gravity
• Cosmography in $f(Q)$ gravity
• Model-independent reconstruction of $f(Q)$ non-metric gravity
• Spherically symmetric configuration in $f(Q)$ gravity
• Cosmological Perturbation Theory in $f(Q,T)$ Gravity
• A designer approach to $f(Q)$ gravity and cosmological implications
• Hamiltonian formulation of teleparallel gravity
• Hamiltonian formulation of unimodular gravity in the teleparallel geometry
• ADM formulation and Hamiltonian analysis of Coincident General Relativity
• 3+1 decomposition in modified gravities within the Palatini formalism and some applications
• Quantum Cosmology in $f(Q)$ theory

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• Exploring the stability of $f(Q)$ cosmology near general relativity limit with different connections
• Gravitational tensor and scalar modes in $f(Q,B)$ non-metric gravity
• Stability of symmetric teleparallel scalar-tensor cosmologies with alternative connections
• Tensor Perturbations from Bounce Inflation Scenario in f(Q) Gravity
• Influence of pressure anisotropy and non-metricity parameter on mass-radius relation and stability of millisecond pulsar in $f(Q)$ gravity
• Dynamical reconstruction of the $\Lambda$CDM model in the scalar-tensor representation of $f\left(Q,T\right)$ gravity
• Maxwell-$f(Q)$ theory
• Modeling and Analyzing Stability of Hybrid Stars within $f(Q)$ Gravity
• Viscous fluid cosmology in symmetric teleparallel gravity
• Constraining Exponential f(Q) Gravity with Cosmic Chronometers and Supernovae: A Data-Driven Analysis
• A unified-description of curvature, torsion, and non-metricity of the metric-affine geometry with the Möbius representation
• The Hamiltonian constraint in the symmetric teleparallel equivalent of general relativity
• Hamiltonian analysis of metric-affine-$R^2$ theory
• Phase space structure of symmetric teleparallel theory of gravity
• Vulnerability of f(Q) gravity theory and a possible resolution
• Degrees of Freedom of New General Relativity I: Type 2, Type 3, Type 5, and Type 8
• Scalar perturbation and density contrast evolution in $f(Q,C)$ gravity
• Issue of Branched Hamiltonian, Inflation and indispensability of scalar field in generalized Teleparallel theories
• Degrees of freedom of a quadratic scalar-nonmetricity theory