Abstract
In this work we study the partially constrained vielbein formulation of the new quasidilaton theory of massive gravity, where the quasidilaton field couples to both physical and fiducial metrics simultaneously via a composite effective metric and Lorentz violation is introduced by a constraint on the vielbein. This formalism improves the new quasidilaton model since the Boulware-Deser ghost is removed fully non-linearly at all scales. This also yields crucial implications in the cosmological applications. We derive the governing cosmological background evolution and study the stability of the attractor solution.
Highlights
In this work we study the partially constrained vielbein formulation of the new quasidilaton theory of massive gravity, where the quasidilaton field couples to both physical and fiducial metrics simultaneously via a composite effective metric and Lorentz violation is introduced by a constraint on the vielbein
One way to realize this was initially thought to come from redefining the theory in the unconstrained vielbein formulation, in which the theory is formulated in the vielbein language and the dynamics of the vielbein is determined by its own equations of motion but not by the symmetric vielbein conditions [42]
In this work we studied the new quasidilaton theory in the partially-constrained vielbein formulation
Summary
We would like to introduce the new quasidilaton theory in the partially constrained vielbein formulation. We shall adapt the vielbein formulation of massive gravity. For this purpose, we express the two metrics by the following vielbeins as gμν = ηABeAμeBν and fμν = ηABEAμEBν ,. Since in quasi-dilaton theories, the fiducial metric only appears with the conformal factor e−2 σ/MPl, it is useful to further define an orthonormal basis for this combination as e−2 σ/MPl fμν = ηABEAμEBν , E. In this formulation, the mass term corresponds to the interactions between the two vielbeins eAμ and EAμ, constructed out of their wedge products [43]
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