Non-uniqueness of massless transverse-traceless graviton

Abstract

We study a theory of minimally modified gravity called cuscuton/VCDM that propagates only two gravitational degrees of freedom. Despite being apparently different from general relativity (GR), it is in principle possible that this theory might be obtained via a field redefinition starting from the GR action. This would make the vacuum theory equivalent to GR and the theory would differ from GR only in the presence of matter. In this paper, studying the dispersion relation of gravitational waves and the dynamics of the Bianchi-I universe, we prove that such a field redefinition does not exist and that the theory differs from GR already in vacuum.

arXiv comment19 pages, 1 figure

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• Spatially covariant gravity with two degrees of freedom: perturbative analysis
• Bouncing Cosmology in VCDM
• Static, spherically symmetric objects in Type-II minimally modified gravity
• Distinguishing modified gravity with just two tensorial degrees of freedom from general relativity: Black holes, cosmology, and matter coupling
• Dynamical Dark Energy in Minimally Modified Gravity
• Gravitational collapse and formation of a black hole in a type II minimally modified gravity theory
• Cuscuton Bounce Beyond the Linear Regime: Bispectrum and Strong Coupling Constraints
• Self-tuning of the cosmological constant in brane-worlds with $P(X,\varphi )$
• How Much NEC Breaking Can the Universe Endure?
• Spatially covariant gravity with two degrees of freedom in the presence of an auxiliary scalar field: Hamiltonian analysis