Minimal theory of quasidilaton massive gravity

Abstract

We introduce a quasidilaton scalar field to the minimal theory of massive gravity with the Minkowski fiducial metric, in such a way that the quasidilaton global symmetry is maintained and that the theory admits a stable self-accelerating de Sitter solution. We start with a precursor theory that contains three propagating gravitational degrees of freedom without a quasidilaton scalar and introduce Stückelberg fields to covariantize its action. This makes it possible for us to formulate the quasidilaton global symmetry that mixes the Stückelberg fields and the quasidilaton scalar field. By the Hamiltonian analysis we confirm that the precursor theory with the quasidilaton scalar contains four degrees of freedom, three from the precursor massive gravity and one from the quasidilaton scalar. We further remove one propagating degree of freedom to construct the minimal quasidilaton theory with three propagating degrees of freedom, corresponding to two polarizations of gravitational waves from the minimal theory of massive gravity and one scalar from the quasidilaton field, by carefully introducing two additional constraints to the system in the Hamiltonian language. Switching to the Lagrangian language, we find self-accelerating de Sitter solutions in the minimal quasidilaton theory and analyze their stability. It is found that the self-accelerating de Sitter solution is stable in a wide range of parameters.

19 pages, 4 figures; title changed to adapt to published version, references added, minor typos corrected (equations (60) and (84)), minor changes to text

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• Horndeski extension of the minimal theory of quasidilaton massive gravity
• Bounds from ISW-galaxy cross-correlations on generalized covariant Galileon models
• Non-linear dynamics of the minimal theory of massive gravity
• Stable cosmology in ghost-free quasidilaton theory
• Cosmological Instabilities and the Role of Matter Interactions in Dynamical Dark Energy Models
• Phenomenology of minimal theory of quasidilaton massive gravity
• Gravitational collapse and formation of a black hole in a type II minimally modified gravity theory
• Extended minimal theories of massive gravity
• Cosmological model due to dimensional reduction of higher-dimensional massive gravity theory
• Gravitational ringdown in the Minimal Theory of Massive Gravity
• Higher-Dimensional Minimal Theory of Mass-Varying Massive Gravity And Its Cosmological Consequences