How to prove that the nonlinear completion of free massless spin-2 action must be Einstein-Hilbert action?

Question

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.
http://journals.aps.org/prd/abstract/10.1103/PhysRevD.33.3613

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.

Comments

It must be the Einstein-Hilbert action only in the limit of low energy. In general, it can contain terms of higher dimensions. The Einstein-Hilbert action is dominant at low energy because it is the only generally covariant possibility with at most two derivatives in the metric.

Answer 1

The paper you are looking for is 

S. Weinberg, Photons and gravitons in perturbation theory: Derivation of Maxwell's and Einstein's equations, Physical Review B 138 (1965), B988-B1002.

Comments

Weinberg actually states in the paper that Feynman was the one to show the uniqueness ("the only that works") of the Einstein equations - with reference only to a conversation. Is there perhaps a later paper by Feynman where he describes his analysis?

---

@Void: Unfortunately, I don't know, but I think it is unlikely, since a long time ago I had systematically searched related literature. 

Answer 2

Videos by Nima Arkani-Hamed, on the IAS website:

https://video.ias.edu/pitp-2011-arkani-hamed1

https://video.ias.edu/pitp-2011-arkani-hamed2