ar X iv : 0 90 5 . 15 22 v 2 [ as tr o - ph . C O ] 1 8 M ay 2 00 9 Growth index in an accelerating universe

We find the exact analytic solution of the linear density perturbation δ for any given value of constant equation of state of dark energy ωde. We also obtain the exact analytic form of growth index (f = Ωm(a) ) at present epoch in a flat universe with including ωde from this solution of δ. For the cosmological constant (ωde = −1) we obtain γ = 0.5547 which is very close to the well known value 6/11. However, if ωde = −0.9, then γ gives rise to 0.6405. Ω 0 m dependence of γ is fairly small for the viable range of the current matter energy density 0.2 ≤ Ω0m ≤ 0.3. (0.6% and 3% changes in γ for ωde equal to −1 and −0.9, respectively.) The difference of peculiar velocity values from the different choices of γ is about 11% for Ω0m = 0.3. This simple but accurate formula which covers a large class of dark energy models will provide a practical tool for galaxy redshift survey to measure the matter density and the peculiar velocity. The background evolution equations in a flat Friedmann-RobertsonWalker universe (ρm + ρde = ρcr) are ( ȧ a )2 = 8πG 3 (ρm + ρde) = 8πG 3 ρcr , (1) 2 ä a + ( ȧ a )2 = −8πGωdeρde , (2) where ωde is the equation of state (eos) of dark energy, ρm and ρde are the energy densities of the matter and the dark energy, respectively. We