the vierbein language as follows. The 4D version of Einstein field equations in 5D is read where is the vector normal to the 4D slice. Using the definition of massive extrinsic curvature it is straightforward to see that terms containing extrinsic curvatures take the functional form in the tetradic action. Therefore, up to the numerical coefficients, the full dRGT action in its tensorial form is where the functions take forms similar to that of the . Then, up to some numerical coefficients, the action takes the integral form where the first term is the Einstein-Hilbert part of the tetradic Palatini action and is the Levi-Civita symbol. As the decoupling limit guarantees that and by comparing to , it is legit to think of the tensor Comparing this with the definition of the 1-form one can define covariant components of frame field i.e. , to replace the such that the last three interaction terms in the vierbein action becomes This can be done because one is allowed to freely move the diffeomorphism transformations onto the reference vierbein through the Lorentz transformations . More importantly, the diffeomorphism transformations help manifesting the dynamics of the helicity-0 and helicity-1 modes, hence the easiness of gauging them away when the theory is compared with its version with the only gauge transformations while the Stueckelberg fields are turned off. One may wonder why the coefficients are dropped, and how to guarantee they are numerical with no explicit dependence of the fields. In fact this is allowed because the variation of the vierbein action with respect to the locally Lorentz transformed Stueckelberg fields yields this nice result. Moreover, we can solve explicitly for the Lorentz invariant Stueckelberg fields, and on substituting back into the vierbein action we can show full equivalence with the tensorial form of dRGT massive gravity. Cosmology If the graviton mass is comparable to the Hubble rate , then at cosmological distances the mass term can produce a repulsive gravitational effect that leads to cosmic acceleration. Because, roughly speaking, the enhanced diffeomorphism symmetry in the limit protects a small graviton mass from large quantum corrections, the choice is in fact technically natural. Massive gravity thus may provide a solution to the cosmological constant problem: why do quantum corrections not cause the Universe to accelerate at extremely early times? However, it turns out that flat and closed Friedmann–Lemaître–Robertson–Walker cosmological solutions do not exist in dRGT