Consistency relation in cosmology

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. As an extension, we also provide the DGP counterpart of the relation.

Figure 1

The ratio of RHS to LHS of Eq. (8). We assume true cosmology to be a flat DGP model and reconstruct $H(z)$ using general relativity Eq. (7). The solid (dashed) curve is for ${\Omega }_{M0}=0.3(0.2)$. The dotted line is the result of the case when $H(z)$ is reconstructed using DGP Eq. (21).