基于广义相对论下的宇宙学，即标准宇宙学，是建立在爱因斯坦引力理论基础上的。在太阳系的尺度上，广义相对论已经通过了观测上的检验。接下来的工作就是在更大的尺度上，即宇宙学尺度上，对广义相对论进行检验。在本文中我们建立了一种不依赖于暗能量状态方程的一致性关系。如果广义相对论是正确的，并且忽略暗能量的成团效应，那么这种一致性关系就应该成立。在理论上，我们根据不同方法下对于宇宙膨胀率的定义，来进行一致性关系的检验，并在不同的广义相对论模型下进行了探讨。在观测上，我们对一致性关系的检验方法进行了推导，最终得出了两个可行的方法:利用超新星的观测数据建立光度距离与红移之间的关系;利用哈勃参量以及膨胀率f(z)、线性增长因子 g(z)的观测数据得到一致性关系。

General relativity cosmological, which is also known as Standard cosmological, is based on Einstein's theories of gravity. It has passed the experimental tests on the scales of the solar system. Probing general relativity on larger scales will be the next target. We provide a consistency relation between cosmological observables in general relativity without relying on the equation of state of dark energy.The consistency relation should be satisfied if general relativity is the correct theory of gravity and dark energy clustering is negligible. We reconstructed the expansion rate of the universe in different ways to show the consistency relation and discuss it in different general relativity models in theory. While in observation, we made some derivation to test the consistency relation and found two ways. Using the observations of type I a supernovae can provide a relationship between luminosity distance and redshift. Using the observations of Hubble parameter, growth rate f(z) and the linear growth factor g(z), we can also inspect the consistency relation.