Asymptotic Freedom in Curvature-Satured Gravity

Abstract

For a spatially flat Friedmann model with line element $ds^2=a^2 [ da^2/B(a)-dx^2-dy^2-dz^2 ] $, the 00-component of the Einstein field equation reads $8\pi G T_{00}=3/a^2$ containing no derivative. For a nonlinear Lagrangian ${\cal L}(R)$, we obtain a second--order differential equation for $B$ instead of the expected fourth-order equation. We discuss this equation for the curvature-saturated model proposed by Kleinert and Schmidt. Finally, we argue that asymptotic freedom $G_{{\rm eff}}^{-1}\to 0$ is fulfilled in curvature-saturated gravity.