  Energy conservation has the status of a fundamental physical principle.
However, measurements in quantum mechanics do not comply with energy
conservation. Therefore, it is expected that a more fundamental theory of
gravity -- one that is less incompatible with quantum mechanics -- should admit
energy nonconservations. This paper begins by identifying the conditions for a
theory to have an energy-momentum tensor that is not conserved. Then, the
trajectory equation for pointlike particles that lose energy is derived,
showing that energy nonconservation produces a particular acceleration. As an
example, the unimodular theory of gravity is studied. Interestingly, in
spherical symmetry, given that there is a generalized Birkhoff theorem and that
the energy-momentum tensor divergence is a closed form, the trajectories of
test particles that lose energy can be found using well known methods. Finally,
limits on the energy nonconservation parameters are set using Solar system
observations.

General Relativity and Quantum Cosmology