Arnowitt-Deser-Misner形式中的修正引力
Modified gravity in Arnowitt-Deser-Misner formalism
摘要：
受Horava-Lifshitz引力理论的启发，我们在Arnowitt-Deser-Misner（ADM）形式下提出并研究了两类修正引力理论：f（R）类和K-本质类. f（R）类包括一个紫外（UV）项和一个红外（IR）项以及爱因斯坦-希尔伯特作用量。我们发现，这两项自然地提出了紫外和红外修正的弗里德曼方程。紫外和红外修正分别避免了过去的Big-Bang奇异和未来的Big-Rip奇异。此外，IR修正自然可以解释宇宙当前的加速。K-本质类修正引力的拉格朗日量由三维Ricci标量和任意外曲率项函数构成。我们发现宇宙加速也可以自然地解释，而不需要调用任何类型的暗能量。两个理论的静态、球对称和真空解都是Schwarzschild或Schwarzschild-de Sitter解。因此，这些修正的引力理论对于太阳系的测试是可行的。
英文摘要：
Motivated by Horava-Lifshitz gravity theory, we propose and investigate two kinds of modified gravity theories, the f(R) kind and the K-essence kind, in the Arnowitt-Deser-Misner (ADM) formalism. The f(R) kind includes one ultraviolet (UV) term and one infrared (IR) term together with the Einstein-Hilbert action. We find that these two terms naturally present the ultraviolet and infrared modifications to the Friedmann equation. The UV and IR modifications can avoid the past Big-Bang singularity and the future Big-Rip singularity, respectively. Furthermore, the IR modification can naturally account for the current acceleration of the Universe. The Lagrangian of K-essence kind modified gravity is made up of the three dimensional Ricci scalar and an arbitrary function of the extrinsic curvature term. We find the cosmic acceleration can also be naturally interpreted without invoking any kind of dark energy. The static, spherically symmetry and vacuum solutions of both theories are Schwarzschild or Schwarzschild-de Sitter solution. Thus these modified gravity theories are viable for solar system tests.
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