Asymptotic Freedom in Curvature-Satured Gravity

TL;DR

This paper investigates a curvature-saturated gravity model, deriving a second-order differential equation for the metric component and demonstrating that the model exhibits asymptotic freedom, where the effective gravitational constant vanishes at high energies.

Contribution

It derives a second-order differential equation for the metric in a curvature-saturated gravity model and shows that asymptotic freedom occurs in this framework.

Findings

The differential equation for the metric component is second-order, not fourth-order.

Asymptotic freedom is realized in the curvature-saturated gravity model.

The model aligns with the behavior of the effective gravitational constant approaching zero at high energies.

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.