There is a saying that the nonlinear completion of free massless spin-2 action in Minkovski spacetime (that is Fierz-Pauli action) must be Einstein-Hilbert action up to Lovelock invariants.
I find a reference tackling this problem
Wald R M. Spin-two fields and general covariance[J]. Physical Review D, 1986, 33(12): 3613.
However in this paper it only proves that the nonlinear completion of free massless spin-2 action must be general covariant. So how to prove it must be the Einstein-Hilbert action.