Modified gravity changes the gravitational dynamics described by general relativity, for example through additional gravitational fields or curvature terms beyond the Einstein-Hilbert action. A proposed theory must specify both its equations and how matter couples to the geometry before trajectories, light propagation or cosmological evolution can be predicted.
The regime of a test matters. Linearized f(R) gravity about Minkowski spacetime can coincide with the Linearized Einstein equations for suitable derivatives of its defining function, while nonlinear terms still differ. Agreement in one weak-field calculation therefore need not identify the full theory. Comparisons involving orbital motion, gravitational lensing and gravitational waves constrain different combinations of dynamics, matter assumptions and observational geometry.
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