Asymptotically free mimetic gravity
Ali Chamseddine (Physics Department, American University of Beirut, Beirut, Lebanon, Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen, Heyendaalseweg 135, Nijmegen, 6525 AJ, The Netherlands); Viatcheslav Mukhanov (Theoretical Physics, Ludwig Maxmillians University, Theresienstr. 37, Munich, 80333, Germany, MPI for Physics, Foehringer Ring, 6, Munich, 80850, Germany, School of Physics, Korea Institute for Advanced Study, Seoul, 02455, Korea); Tobias Russ (Theoretical Physics, Ludwig Maxmillians University, Theresienstr. 37, Munich, 80333, Germany)
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.
