Spatially covariant gravity with a dynamic lapse function

Abstract

In the framework of spatially covariant gravity, it is natural to extend a gravitational theory by putting the lapse function $N$ and the spatial metric $h_{ij}$ on an equal footing. We find two sufficient and necessary conditions for ensuring two physical degrees of freedom (DoF) for the theory with the lapse function being dynamical by Hamiltonian analysis. A class of quadratic actions with only two DoF is constructed. In the case that the coupling functions depend on $N$ only, we find that the spatial curvature term cannot enter the Lagrangian and thus this theory possesses no wave solution and cannot recover general relativity (GR). In the case that the coupling functions depend on the spatial derivatives of $N$, we perform a spatially conformal transformation on a class of quadratic actions with nondynamical lapse function to obtain a class of quadratic actions with $\dot{N}$. We confirm this theory has two DoF by checking the two sufficient and necessary conditions. Besides, we find that a class of quadratic actions with two DoF can be transformed from GR by disformal transformation.

References in corpus (60)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Modified Gravity and Cosmology
• Quantum Gravity at a Lifshitz Point
• k-Inflation
• The galileon as a local modification of gravity
• Generalized G-inflation: Inflation with the most general second-order field equations
• Perturbations in k-inflation
• The Effective Field Theory of Inflation
• From k-essence to generalised Galileons
• Covariant Galileon
• Ghost Condensation and a Consistent Infrared Modification of Gravity
• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability
• Transforming gravity: from derivative couplings to matter to second-order scalar-tensor theories beyond the Horndeski Lagrangian
• Starting the Universe: Stable Violation of the Null Energy Condition and Non-standard Cosmologies
• G-inflation: inflation driven by the Galileon field
• The Relation between Physical and Gravitational Geometry
• Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order
• Extended Scalar-Tensor Theories of Gravity
• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Mimetic Dark Matter
• Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations
• Lorentz symmetry breaking as a quantum field theory regulator
• Cuscuton: A Causal Field Theory with an Infinite Speed of Sound
• Mimetic gravity: a review of recent developments and applications to cosmology and astrophysics
• Disformal invariance of second order tensor-scalar theories: framing the Horndeski action
• Hamiltonian analysis of higher derivative scalar-tensor theories
• Unifying framework for scalar-tensor theories of gravity
• Effective Description of Higher-Order Scalar-Tensor Theories
• Healthy degenerate theories with higher derivatives
• Horndeski: beyond, or not beyond?
• Cuscuton Cosmology: Dark Energy meets Modified Gravity
• Primordial black holes and secondary gravitational waves from k/G inflation
• Hamiltonian analysis of spatially covariant gravity
• Derivative-dependent metric transformation and physical degrees of freedom
• Self-accelerating universe in scalar-tensor theories after GW170817
• Extended Cuscuton: Formulation
• Extended mimetic gravity: Hamiltonian analysis and gradient instabilities
• The two faces of mimetic Horndeski gravity: disformal transformations and Lagrange multiplier
• Exorcising the Ostrogradsky ghost in coupled systems
• A new formulation of non-relativistic diffeomorphism invariance
• General invertible transformation and physical degrees of freedom
• Primordial black holes and secondary gravitational waves from the Higgs field
• Hamiltonian analysis of the cuscuton
• Spatially covariant gravity theories with two tensorial degrees of freedom: the formalism
• Spatially covariant gravity with velocity of the lapse function: the Hamiltonian analysis
• Cosmological evolution in DHOST theories
• Minimally modified gravity with an auxiliary constraint: a Hamiltonian construction
• New approach to nonrelativistic diffeomorphism invariance and its applications
• Tracker and scaling solutions in DHOST theories
• Spatially covariant theories of gravity: disformal transformation, cosmological perturbations and the Einstein frame
• Spatially Covariant Theories of a Transverse, Traceless Graviton, Part I: Formalism
• Spatially covariant gravity: Perturbative analysis and field transformations
• Gauge invariances vis-{á}-vis Diffeomorphisms in second order metric gravity: A new Hamiltonian approach
• Higher derivative scalar-tensor theory and spatially covariant gravity: the correspondence
• Higher derivative scalar-tensor theory through a non-dynamical scalar field
• Higher derivative scalar-tensor theory from the spatially covariant gravity: a linear algebraic analysis
• The Hamiltonian Dynamics of Horava Gravity
• Taming galileons in curved spacetime

Cited by in corpus (7)

• Spatially covariant gravity with two degrees of freedom: perturbative analysis
• Cuscuton Inflation
• Covariant 3+1 correspondence of the spatially covariant gravity and the degeneracy conditions
• Dynamical Dark Energy in Minimally Modified Gravity
• Minimally modified gravity with auxiliary constraints formalism
• PPN meets EFT of dark energy: Post-Newtonian approximation in higher-order scalar-tensor theories
• Spatially covariant gravity with two degrees of freedom in the presence of an auxiliary scalar field: Hamiltonian analysis