  An effective theory of gravity in the infrared is proposed, which involves
the determinant of the metric relative to the determinant of a prior metric
taken to be that of Minkowski spacetime. This effective theory can be
interpreted as a generalization of unimodular gravity. In a cosmological
context with ultrarelativistic or cold matter, the resulting field equations
have only one solution, empty Minkowski spacetime (selected by the prior metric
of the theory). The introduction of energy exchange between vacuum and matter
gives rise to nonstatic cosmic solutions. It is found that Minkowski spacetime
(from the prior metric) appears as an attractor of the dynamic equations. A
further result is that energy-momentum conservation of any localized material
system is violated in a nonconstant gravitational background. The impact for
experiment appears, however, negligible if the vacuum-energy mass scale is of
order meV.
