MTMVMG is claimed to admit stable FLRW perturbations, with the mass-varying scalar as dark energy or inflaton, but stability inequalities are unverified and the phenomenology is fitted.
SO(3) massive gravity
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In this paper, we propose a massive gravity theory with 5 degrees of freedom. The mass term is constructed by 3 Stuckelberg scalar fields, which respects SO(3) symmetry in the fields' configuration. By the analysis on the linear cosmological perturbations, we found that such 5 d.o.f are free from ghost instability, gradiant instability, and tachyonic instability.
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Stable Cosmology from Minimal Theory of Mass-Varying Massive Gravity
MTMVMG is claimed to admit stable FLRW perturbations, with the mass-varying scalar as dark energy or inflaton, but stability inequalities are unverified and the phenomenology is fitted.