School of Physics and Astronomy, University of Nottingham, Nottingham NG8 2RD, UK.
Philos Trans A Math Phys Eng Sci. 2011 Dec 28;369(1957):4962-75. doi: 10.1098/rsta.2011.0291.
General relativity (GR) is a phenomenologically successful theory that rests on firm foundations, but has not been tested on cosmological scales. The deep mystery of dark energy (and possibly even the requirement of cold dark matter (CDM)) has increased the need for testing modifications to GR, as the inference of such otherwise undetected fluids depends crucially on the theory of gravity. Here, I discuss a general scheme for constructing consistent and covariant modifications to the Einstein equations. This framework is such that there is a clear connection between the modification and the underlying field content that produces it. I argue that this is mandatory for distinguishing modifications of gravity from conventional fluids. I give a non-trivial example, a simple metric-based modification of the fluctuation equations for which the background is exact ΛCDM, but differs from it in the perturbations. I show how this can be generalized and solved in terms of two arbitrary functions. Finally, I discuss future prospects and directions of research.
广义相对论（GR）是一种在坚实基础上取得了成功的经验理论，但尚未在宇宙学尺度上进行检验。暗能量的深刻奥秘（甚至可能需要冷暗物质（CDM））增加了对广义相对论修正的检验需求，因为这些否则未被检测到的流体的推断在很大程度上取决于引力理论。在这里，我讨论了一种构建对爱因斯坦方程进行一致和协变修正的一般方案。这个框架使得修正与产生它的基础场内容之间有明确的联系。我认为，这对于区分引力修正和传统流体是强制性的。我给出了一个非平凡的例子，一个简单的基于度量的波动方程修正，其背景是精确的ΛCDM，但在扰动方面与它不同。我展示了如何将其推广并根据两个任意函数求解。最后，我讨论了未来的前景和研究方向。
