Renormalization group flow of quantum gravity in the Einstein-Hilbert truncation

Abstract

The exact renormalization group equation for pure quantum gravity is used to derive the nonperturbative \ensuremath{\beta}-functions for the dimensionless Newton constant and cosmological constant on the theory space spanned by the Einstein-Hilbert truncation. The resulting coupled differential equations are evaluated for a sharp cutoff function. The features of these flow equations are compared to those found when using a smooth cutoff. The system of equations with a sharp cutoff is then solved numerically, deriving the complete renormalization group flow of the Einstein-Hilbert truncation in $d=4.$ The resulting renormalization group trajectories are classified and their physical relevance is discussed. The nontrivial fixed point which, if present in the exact theory, might render quantum Einstein gravity nonperturbatively renormalizable is investigated for various spacetime dimensionalities.