Hamiltonian analysis of nonprojectable Hořava-Lifshitz gravity with $U(1)$ symmetry

Abstract

We study the nature of constraints and count the number of degrees of freedom in the nonprojectable version of the $U(1)$ extension of Hořava-Lifshitz gravity, using the standard method of Hamiltonian analysis in the classical field theory. This makes it possible for us to investigate the condition under which the scalar graviton is absent at a fully nonlinear level. We show that the scalar graviton does not exist at the classical level if and only if two specific coupling constants are exactly zero. The operators corresponding to these two coupling constants are marginal for any values of the dynamical critical exponent of the Lifshitz scaling and thus should be generated by quantum corrections even if they are eliminated from the bare action. We thus conclude that the theory in general contains the scalar graviton.

arXiv comment15 pages, no figures

References in corpus (15)

• Quantum Gravity at a Lifshitz Point
• An introduction to the Vainshtein mechanism
• Horava-Lifshitz Cosmology: A Review
• General Covariance in Quantum Gravity at a Lifshitz Point
• Dark matter as integration constant in Horava-Lifshitz gravity
• Comment on `Strong coupling in extended Horava-Lifshitz gravity'
• Strong coupling in extended Horava-Lifshitz gravity
• An Alternative Approach for General Covariant Horava-Lifshitz Gravity and Matter Coupling
• General covariant Horava-Lifshitz gravity without projectability condition and its applications to cosmology
• U(1) symmetry and elimination of spin-0 gravitons in Horava-Lifshitz gravity without the projectability condition
• Scale hierarchy in Horava-Lifshitz gravity: a strong constraint from synchrotron radiation in the Crab nebula
• Post-Newtonian approximations in the Hořava-Lifshitz gravity with extra U(1) symmetry
• General relativity limit of Horava-Lifshitz gravity with a scalar field in gradient expansion
• Nonlinear superhorizon perturbations in Horava-Lifshitz gravity
• Hamiltonian Analysis of Non-Relativistic Covariant RFDiff Horava-Lifshitz Gravity

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• Minimally modified gravity with an auxiliary constraint: a Hamiltonian construction
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• Non-Projectable Horava-Lifshitz Gravity without Unwanted Scalar Graviton
• Revisiting Lorentz violation in Horava gravity
• Minimally modified gravity with auxiliary constraints formalism
• Effective action of the Horava theory: Cancellation of divergences
• Restricted f(R) Gravity and Its Cosmological Implications
• Constraints on Hořava-Lifshitz gravity from GRB 170817A
• Cosmological Perturbations in Restricted f(R)-Gravity
• Two Dimensional F(R) Horava-Lifshitz Gravity