Spatially Covariant Theories of a Transverse, Traceless Graviton, Part I: Formalism
arXiv:1108.1397 · doi:10.1103/PhysRevD.85.084002
Abstract
General relativity is a covariant theory of two transverse, traceless graviton degrees of freedom. According to a theorem of Hojman, Kuchar, and Teitelboim, modifications of general relativity must either introduce new degrees of freedom or violate the principle of general covariance. In this paper, we explore modifications of general relativity that retain the same number of gravitational degrees of freedom, and therefore explicitly break general covariance. Motivated by cosmology, the modifications of interest maintain spatial covariance. Demanding consistency of the theory forces the physical Hamiltonian density to obey an analogue of the renormalization group equation. In this context, the equation encodes the invariance of the theory under flow through the space of conformally equivalent spatial metrics. This paper is dedicated to setting up the formalism of our approach and applying it to a realistic class of theories. Forthcoming work will apply the formalism more generally.
55 pages, no figures
References in corpus (34)
- Quantum Gravity at a Lifshitz Point
- Resummation of Massive Gravity
- Timing Measurements of the Relativistic Binary Pulsar PSR B1913+16
- Ghost-free Massive Gravity with a General Reference Metric
- Massive Cosmologies
- On the Extra Mode and Inconsistency of Horava Gravity
- Galileon Cosmology
- Galileon inflation
- Degravitation of the Cosmological Constant and Graviton Width
- DBI and the Galileon reunited
- Cuscuton: A Causal Field Theory with an Infinite Speed of Sound
- Multi-field galileons and higher co-dimension branes
- On Black Holes in Massive Gravity
- Symmetries for Galileons and DBI scalars on curved space
- Cascading DGP
- Helicity Decomposition of Ghost-free Massive Gravity
- Einstein gravity as a 3D conformally invariant theory
- Cuscuton Cosmology: Dark Energy meets Modified Gravity
- Cuscuton and low energy limit of Horava-Lifshitz gravity
- N-Body Simulations of DGP and Degravitation Theories
- Stability and superluminality of spherical DBI galileon solutions
- Mimicking Lambda with a spin-two ghost condensate
- Unveiling Chameleons in Tests of Gravitational Inverse-Square Law
- Linear Growth of Structure in the Symmetron Model
- Stochastic Inflation Revisited: Non-Slow Roll Statistics and DBI Inflation
- Towards a UV Completion for Chameleon Scalar Theories
- Conformal Superspace: the configuration space of general relativity
- Instabilities of Spherical Solutions with Multiple Galileons and SO(N) Symmetry
- Galileons on Cosmological Backgrounds
- Hamiltonian Analysis of Non-Relativistic Covariant RFDiff Horava-Lifshitz Gravity
- Halo Scale Predictions of Symmetron Modified Gravity
- Exact Solution to the "Auxiliary Extra Dimension" Model of Massive Gravity
- Screening bulk curvature in the presence of large brane tension
- A first-principles derivation of York scaling and the Lichnerowicz-York equation
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- Beyond the Cosmological Standard Model
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- Confirmation of the Secondary Constraint and Absence of Ghost in Massive Gravity and Bimetric Gravity
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- Mass-Varying Massive Gravity
- Galileon inflation evades the no-go for PBH formation in the single-field framework
- New Kinetic Interactions for Massive Gravity?
- Primordial non-Gaussianity from ultra slow-roll Galileon inflation
- Scalar induced gravity waves from ultra slow-roll Galileon inflation
- Minimally modified theories of gravity: a playground for testing the uniqueness of general relativity
- Generalized massive gravity in arbitrary dimensions and its Hamiltonian formulation
- Large fluctuations and Primordial Black Holes
- New Kinetic Terms for Massive Gravity and Multi-gravity: A No-Go in Vielbein Form
- On the Origin of Gravitational Lorentz Covariance
- Nonderivative Modified Gravity: a Classification
- A cosmic glitch in gravity
- Inflationary model in minimally modified gravity theories
- Spatially covariant gravity with a dynamic lapse function
- Energy in ghost-free massive gravity theory
- On the scalar graviton in n-DBI gravity
- How General Relativity and Lorentz Covariance Arise from the Spatially Covariant Effective Field Theory of the Transverse, Traceless Graviton
- Observational Constraints and Preheating in Cuscuton Inflation
- Hamiltonian Analysis of the Conformal Decomposition of the Gravitational Field
- Spatially covariant gravity with two degrees of freedom in the presence of an auxiliary scalar field: Hamiltonian analysis
- Conformal Traceless Decomposition of Lagrange Multiplier Modified Horava-Lifshitz Gravity