4G: Pure fourth-order gravity

Abstract

Einstein field equations are second-order differential equations. In this paper, we propose a new gravity theory with pure fourth-order field equations, which we call 4G for brevity. We discuss the applications of 4G in cosmology, gravitational waves, and local gravitational systems. 4G predicts the scale factor $a\propto t^{4/3}$ for the matter-dominated universe, and $a\propto t$ for the radiation-dominated universe. The former can explain the late-time acceleration without suffering from the coincidence and fine-tuning problems, while the latter can solve the horizon problem. 4G is a massless gravity, which means the speed of gravitational waves equals to the speed of light. Based on the discussions about exact vacuum solution and weak field approximation, we argue that Schwarzschild metric should be the real physical metric to describe solar system in 4G.