Here it is without fanfare. If you have any questions about any part of it, please comment in the comments:

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To be theoretically consistent and compatible with experiment, a theory of gravitation must:

(1) Predict correct cosmological dynamics

a. Big bang nucleosynthesis

(2) Produce the correct evolution of cosmological perturbations

a. Cosmic microwave background

b. Large scale structure

(3) Have the correct weak-field limits

a. Reproduces Newtonian Mechanics

b. Predicts post-Newtonian experiments in weak field

c. Produces stable solutions

i. Matter-side instabilities (Dolgov-Kawasaki)

1. Ground states should be highly symmetric

ii. Gravity-side instabilities

1. Stable de Sitter solutions

iii. Stability of the first loop in quantum gravity

iv. Stability in the face of inhomogeneous but isotropic perturbations

v. Black hole nucleation

(4) Not contain any ghost fields

(5) Admit a well-posed Cauchy problem

(6) Reasonable theory of gravity waves