As described in the previous section, the FRGE lends itself to a systematic construction of nonperturbative approximations to the gravitational beta-functions by projecting the exact RG flow onto subspaces spanned by a suitable ansatz for Γ Γ k . In its simplest form, such an ansatz is given by the Einstein–Hilbert action where Newton's constant G k and the cosmological constant Λ Λ k depend on the RG scale k . Let g μ μ ν ν and g ¯ ¯ μ μ ν ν denote the dynamical and the background metric, respectively. Then Γ Γ k reads, for arbitrary spacetime dimension d ,