  Here we show that, Eddington's pure affine gravity, when extended with
Riemann curvature, leads to gravitational field equations that incorporate
matter. This Riemanned Eddington gravity outfits a setup in which matter
gravitates normally with Newton's constant but vacuum gravitates differently
with an independent gravitational constant. This novel setup enables
degravitation of the vacuum to observed level not by any fine-tuning but by a
large hierarchy between its gravitational constant and its energy density.
Remarkably, degravitation of the cosmological constant is local, causal and
natural yet only empirical because the requisite degravitation condition is not
predicted by the theory.
