  A theory of gravitation is proposed, modeled after the notion of a Ricci
flow. In addition to the metric an independent volume enters as a fundamental
geometric structure. Einstein gravity is included as a limiting case. Despite
being a scalar-tensor theory the coupling to matter is different from
Jordan-Brans-Dicke gravity. In particular there is no adjustable coupling
constant. For the solar system the effects of Ricci flow gravity cannot be
distinguished from Einstein gravity and therefore it passes all classical
tests. However for cosmology significant deviations from standard Einstein
cosmology will appear.
