  One of the deepest and most long-standing mysteries in physics has been the
huge discrepancy between the observed vacuum density and our expectations from
theories of high energy physics, which has been dubbed the Old Cosmological
Constant problem. One proposal to address this puzzle at the semi-classical
level is to decouple quantum vacuum from space-time geometry via a modification
of gravity that includes an incompressible fluid, known as Gravitational
Aether. In this paper, we discuss classical predictions of this theory along
with its compatibility with cosmological and experimental tests of gravity. We
argue that deviations from General Relativity (GR) in this theory are sourced
by pressure or vorticity. In particular, the theory predicts that the
gravitational constant for radiation is 33% larger than that of
non-relativistic matter, which is preferred by (most) cosmic microwave
background (CMB), Lyman-Alpha forest, and Lithium-7 primordial abundance
observations, while being consistent with other cosmological tests at ~2-sigma
level. It is further shown that all Parametrized Post-Newtonian (PPN)
parameters have the standard GR values aside from the anomalous coupling to
pressure, which has not been directly measured. A more subtle prediction of
this model (assuming irrotational aether) is that the (intrinsic)
gravitomagnetic effect is 33% larger than GR prediction. This is consistent
with current limits from LAGEOS and Gravity Probe B at ~2-sigma level.
