Nonderivative Modified Gravity: a Classification

Abstract

We analyze the theories of gravity modified by a generic nonderivative potential built from the metric, under the minimal requirement of unbroken spatial rotations. Using the canonical analysis, we classify the potentials $V$ according to the number of degrees of freedom (DoF) that propagate at the nonperturbative level. We then compare the nonperturbative results with the perturbative DoF propagating around Minkowski and FRW backgrounds. A generic $V$ implies 6 propagating DoF at the non-perturbative level, with a ghost on Minkowski background. There exist potentials which propagate 5 DoF, as already studied in previous works. Here, no $V$ with unbroken rotational invariance admitting 4 DoF is found. Theories with 3 DoF turn out to be strongly coupled on Minkowski background. Finally, potentials with only the 2 DoF of a massive graviton exist. Their effect on cosmology is simply equivalent to a cosmological constant. Potentials with 2 or 5 DoF and explicit time dependence appear to be a further viable possibility.

No comment

References in corpus (53)

• Modified Gravity and Cosmology
• The Dynamics of General Relativity
• The galileon as a local modification of gravity
• Resummation of Massive Gravity
• Massive Gravity
• Resolving the Ghost Problem in non-Linear Massive Gravity
• Effective Field Theory for Massive Gravitons and Gravity in Theory Space
• Classical and Quantum Consistency of the DGP Model
• Ghost-free Massive Gravity with a General Reference Metric
• Massive Cosmologies
• Partial Masslessness of Higher Spins in (A)dS
• Infrared-modified gravities and massive gravitons
• Phases of massive gravity
• Improved constraints on non-Newtonian forces at 10 microns
• Open FRW universes and self-acceleration from nonlinear massive gravity
• Cosmological Solutions in Bimetric Gravity and their Observational Tests
• Cosmological solutions with massive gravitons in the bigravity theory
• Null Propagation of Partially Massless Higher Spins in (A)dS and Cosmological Constant Speculations
• FRW Cosmology in Ghost Free Massive Gravity
• Stability of Massive Cosmological Gravitons
• Perturbations in Massive Gravity Cosmology
• Effective Lagrangians and Universality Classes of Nonlinear Bigravity
• A dynamical inconsistency of Horava gravity
• Effective theory for the Vainshtein mechanism from the Horndeski action
• Acausality of Massive Gravity
• Nonlinear stability of cosmological solutions in massive gravity
• Spherically Symmetric Solutions in Ghost-Free Massive Gravity
• Evidence for and Obstructions to Non-Linear Partially Massless Gravity
• Spontaneous Lorentz Breaking and Massive Gravity
• Lorentz Breaking Massive Gravity in Curved Space
• Nonlinear Partially Massless from Massive Gravity?
• Degrees of Freedom in Massive Gravity
• Massive Gravity Acausality Redux
• FRW Cosmological Perturbations in Massive Bigravity
• Exact Spherically Symmetric Solutions in Massive Gravity
• Massive gravity: a General Analysis
• Lorentz-violating massive gauge and gravitational fields
• Mixed Galileons and Spherically Symmetric Solutions
• Stability of the Self-accelerating Universe in Massive Gravity
• Strong Coupling and Bounds on the Graviton Mass in Massive Gravity
• Quantum corrections in Galileon theories
• No consistent bimetric gravity?
• Weak Massive Gravity
• Cosmology in General Massive Gravity Theories
• Remarks on the consistency of minimal deviations from General Relativity
• Spatially Covariant Theories of a Transverse, Traceless Graviton, Part I: Formalism
• Bigravity in Kuchar's Hamiltonian formalism. 1. The general case
• On the Origin of Gravitational Lorentz Covariance
• Bigravity in Kuchar's Hamiltonian formalism. 2. The special case
• Cosmology in rotation-invariant massive gravity with non-trivial fiducial metric
• Suppression of Quantum Corrections by Classical Backgrounds
• Lorentz-Violating Massive Gravity in Curved Space
• Finite Energy of Black Holes in Massive Gravity

Cited by in corpus (17)

• Graviton Mass Bounds
• Living with ghosts in Horava-Lifshitz gravity
• Spatially covariant gravity with velocity of the lapse function: the Hamiltonian analysis
• CMB Scale Dependent Non-Gaussianity from Massive Gravity during Inflation
• Massive and modified gravity as self-gravitating media
• Minimally modified theories of gravity: a playground for testing the uniqueness of general relativity
• Fluids, Superfluids and Supersolids: Dynamics and Cosmology of Self Gravitating Media
• Resonant Primordial Gravitational Waves Amplification
• The ${\Lambda }_2$ limit of massive gravity
• Minimal theory of quasidilaton massive gravity
• Massive gravity and the suppression of anisotropies and gravitational waves in a matter-dominated contracting universe
• New Branches of Massive Gravity
• An effective field theory of holographic dark energy
• Self-gravitating $\Lambda$-media
• On the 6th Mode in Massive Gravity
• Extended minimal theories of massive gravity
• Dynamical diffeomorphisms