For all degenerate f(R) models, the linearized spectrum on maximally symmetric backgrounds is empty: no graviton and no scalaron.
Massive gravitational waves from f(R) theories of gravity: Potential detection with LISA
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This letter is a generalization of previous results on gravitational waves (GWs) from f(R) theories of gravity. In some previous papers, particular f(R) theories have been linearized for the first time in the literature. Now, the process is further generalized, showing that every f(R) theory can be linearized producting a third massive mode of gravitational radiation. In this framework, previous results are particular cases of the more general problem that is discussed in this letter. The potential detectability of such massive GWs with LISA is also discussed with the auxilium of longitudinal response functions.
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Propagating degrees of freedom on maximally-symmetric backgrounds in $f(R)$ theories of gravity
For all degenerate f(R) models, the linearized spectrum on maximally symmetric backgrounds is empty: no graviton and no scalaron.