Astronomy and Astrophysics – Astrophysics – Cosmology and Extragalactic Astrophysics
Scientific paper
2009-07-13
Phys.Rev.D82:043004,2010
Astronomy and Astrophysics
Astrophysics
Cosmology and Extragalactic Astrophysics
18 pages, 10 figures, 3 tables, To match the version accepted by Physical Review D
Scientific paper
10.1103/PhysRevD.82.043004
There have been the approximate analytic solution \cite{Silveria} and several approximate analytic forms \cite{0508156,Carroll,0303112} of the growth factor $D_{g}$ for the general dark energy models with the constant values of its equation of state $\omde$ after Heath found the exact integral form of the solution of $D_{g}$ for the Universe including the cosmological constant or the curvature term. Recently, we obtained the exact analytic solutions of the growth factor for both $\omde = -1$ or $-\fr{1}{3}$ \cite{SK1} and the general dark energy models with the constant equation of state $\omde$ \cite{SK3} independently. We compare the exact analytic solution of $D_{g}$ with the other well known approximate solutions. We also prove that the analytic solutions for $\omde = -1$ or $-\fr{1}{3}$ in Ref. \cite{SK1} are the specific solutions of the exact solutions of the growth factor for general $\omde$ models in Ref. \cite{SK3} even though they look quite different. We scrutinize the issue of using the well known parameterizations of the growth index and its parameter given in Ref. \cite{WS} to obtain the growth factor for general dark energy models. We also investigate the possible extensions of the exact solution of $D_{g}$ to the time-varying $\omde$ for the comparison with observations.
Lee Seokcheon
Ng Kin-Wang
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