Growth Index with the Cosmological Constant

Seokcheon Lee ； Kin-Wang Ng

《Chinese Journal of Physics》 50卷3期 (2012/06) Pp. 367-374

並列摘要

We obtain the exact analytical form of the growth index at the present epoch (α = 1) in a flat universe with a cosmological constant (i.e., dark energy with the equation of state ω(subscript de) = −1). For the cosmological constant, we obtain the exact value of the current growth index parameter γ = 0.5547, which is very close to the well known value 6/11. We also obtain the exact analytic solution of the growth factor for ω(subscript de) = −1/3 or −1. We investigate the growth index and its parameter at any epoch with this exact solution. In addition to this, we are able to find the exact Ω(superscript 0 subscript m) dependence of those observable quantities. The growth index is quite sensitive to Ω(superscript 0 subscript m) at z = 0.15, where we are able to use the 2 degree field (2dF) observations. If we adopt the 2dF value of the growth index, then we obtain the constraint 0.11 ≤Ω(superscript 0 subscript m) ≤ 0.37 for the cosmological constant model. Especially, the growth index is quite sensitive to Ω(superscript 0 subscript m) around z ≤ 1. We might be able to obtain interesting observations around this epoch. Thus, the analytic solution for this growth factor provides a very useful tool for future observations to constrain the exact values of observational quantities at any epoch related to the growth factor for ω(subscript de) = −1 or −1/3.