Asymptotic Freedom in Curvature-Satured Gravity

Abstract

For a spatially flat Friedmann model with line element $d{s}^2=a^2[d{a}^2/B(a)-d{x}^2-d{y}^2-d{z}^2]$, the 00-component of the Einstein field equation reads $8\pi G{T}_{00}=3/a^2$ containing no derivative. For a nonlinear Lagrangian $\mathcal{L}(R)$, 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 $G_{\mathrm{eff}}^{-1}\to 0$ is fulfilled in curvature-saturated gravity.

arXiv comment9 pages, World Scientific LATEX, to appear in "Fluctuating Paths and Fields", WSPC Singapore 2001, Eds: W. Janke, A. Pelster, H.-J. Schmidt, M. Bachmann