F(R) Gravity - Tensorial Generalization

Tensorial Generalization

f(R) gravity as presented in the previous sections is a scalar modification of general relativity. More generally, we can have a

coupling involving invariants of the Ricci tensor and the Weyl tensor. Special cases are f(R) gravity, conformal gravity, Gauss-Bonnet gravity and Lovelock gravity. It is suggested to consider dependency to the covariant derivative of the Riemann tensor in order to resolve more problems. Notice that with any nontrivial tensorial dependence, we typically have additional massive spin-2 degrees of freedom, in addition to the massless graviton and a massive scalar. An exception is Gauss-Bonnet gravity where the fourth order terms for the spin-2 components cancel out.