We study a modification of the Plebanski action for general relativity, which leads to a modified theory of gravity with 8 degrees of freedom. We show how the action can be recasted as a bimetric theory of gravity, and expanding around a biflat background we identify the 6 extra degrees of freedom with a second, massive graviton and a scalar mode.
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Simone Speziale (2010) studied this question.
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