Asymptotically free mimetic gravity

The idea of asymptotically free gravity is implemented using a constrained mimetic scalar field. The effective gravitational constant is assumed to vanish at some limiting curvature. As a result singularities in spatially flat Friedmann and Kasner universes are avoided. Instead, the solutions in both cases approach a de Sitter metric with limiting curvature. We show that quantum metric fluctuations vanish when this limiting curvature is approached.