We combine the ghost-free bimetric theory of gravity with the concept of local Weyl invariance, realized in the framework of Einstein-Cartan gravity. The gravitational sector, characterized by two independent metrics and two independent connections, is coupled to a scalar field that can in principle develop a nonvanishing expectation value through radiative corrections. The spectrum of the model, apart from the massless standard graviton and a pair of axionlike pseudoscalars, associated with the presence of the Holst invariants in the action, includes an additional spin-2 state of a nonvanishing Fierz-Pauli mass proportional to the scalar field vacuum expectation value. We analyze the phenomenology of the model and specify the conditions under which the massive spin-2 state could be a primary dark matter candidate.
Gialamas et al. (Fri,) studied this question.
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