On the Lorentz symmetry in conformally reduced quantum gravity

Abstract The functional renormalization group treatment of the conform reduced Einstein–Hilbert gravity is extended by following evolution time and space derivatives separately, in order to consider Lorentz symmetry during evolution. We found Reuter fixed point ultraviolet region. It shown that starting from Gaussian breaks down vicinity point. Similarly, broken phase it also infrared region close a critical singularity scale. By calculating anomalous dimension form kinetic term action, we new relevant coupling belonging curvature.