广义相对论（GR）告诉我们宇宙是如何从一个初始奇点演变出来的，自爱因斯坦提出广义相对论以来，其在宇宙学领域得到了广泛的应用。在太阳系的尺度上该理论已经成功地通过了观测数据的检验，在宇宙尺度上对其进行检验就成为研究引力物理方面的下个目标。在本文中，我们关心的是一种一致性关系，这个一致性关系检验了宇宙学中的常规理论框架：暗能量下的广义相对论模型。从观测上来说，我们可以通过观测数据来验证这种一致性。从理论上来说，通过不同表达式之间的比较也可得到我们所需要的一致性关系。通由距离——红移关系和密度扰动两种途径都可以得到宇宙的膨胀率H(z)。使它们相等便可从理论上得到一个一致关系表达式。在广义相对论是实际正确的引力理论和暗能量不可忽略的情况下这个关系一定成立。采用同样的方法，进一步检验宇宙常数 的一致性，即宇宙常数的零检验。在考虑广义相对论下的一致关系的同时，引入DGP模型，并建立起在该模型下的一致关系。最后将DGP模型和GR模型相比较。

General relativity tells us how the universe evolves from the initial single point, as it has been put forward by Einstein, it develops rapidly and has been applied widely in cosmology. This theory has passed the experimental tests on the scales of the solar system with flying colors. Probing general relativity on cosmological scales will be the next target for gravitational physics. In this paper, we focus on a consistency relation which tests the conventional theoretical framework in cosmology: general relativistic CDM model with (almost homogeneous) dark energy. With respect to observation, we can validate this consistency via observation datum. And with respect to theory, we can get the consistency relation that we want by comparing parameter expression in different form. We can gain the expansion rate by two ways: the distance-redshift relation and density perturbation. Equating them with each other gives the consistency relation in theory. The consistency relation should be satisfied if general relativity is the correct theory of gravity and dark energy clustering is negligible. In the same way, we can further test the consistency of cosmological constant , namely null test of the cosmological constant. As an extension, we also provide the DGP model, and establish the consistency relation in it. Finally we make a comparison between DGP and GR.