TestingΛCDMwith the growth functionδ(a): Current constraints

Growth index of DGP model and current growth rate data

“…We confront the growth index of DGP model with currently available growth rate data and find that the DGP model is still consistent with it. On the other hand, it is shown that the ΛCDM model is also consistent with current growth rate data [31]. This implies that more and better growth rate data are required to distinguish between dark energy and modified gravity models.…”

“…In Einstein gravity, the growth function δ(z) at scales much smaller than the Hubble radius obeys the following differential equation [18,19,20,21,31,40] δ + 2Hδ = 4πGρ m δ.…”

“…The most useful currently available growth rate data involve the redshift distortion parameter β L [41] observed through the anisotropic pattern of galactic redshifts on cluster scales [42] (see also [31]). The parameter β L is related to the growth rate f as [31] Notice that Ref.…”

“…Recently, it is argued that the measurement of growth function δ(z) might be competent, see e.g. [18,19,20,21,22,23,24,25,26,27,28,29,30,31,38]. If two models, especially dark energy and modified gravity models, share a same cosmic expansion history, they might have different growth history.…”

“…This parameterized approach has been tested in some works recently, see e.g. [18,19,20,22,28,29,30,31,38]. The theoretical value of γ for ΛCDM model is 6/11 ≃ 0.545 [18,19] whereas γ ≃ 0.55 for other parameterized dark energy models [19].…”