Astronomy and Astrophysics – Astrophysics – Cosmology and Extragalactic Astrophysics
Scientific paper
2009-03-30
Phys.Rev.D80:023514,2009
Astronomy and Astrophysics
Astrophysics
Cosmology and Extragalactic Astrophysics
Revised and extended version. No changes in results. 7 pages, 4 figures. The mathematica files used for the production of the
Scientific paper
10.1103/PhysRevD.80.023514
We demonstrate the scale dependence of the growth function of cosmological perturbations in dark energy models based on General Relativity. This scale dependence is more prominent on cosmological scales of $100h^{-1}Mpc$ or larger. We derive a new scale dependent parametrization which generalizes the well known Newtonian approximation result $f_0(a)\equiv \frac{d\ln \delta_0}{d\ln a}=\om(a)^\gamma$ ($\gamma ={6/11}$ for \lcdm) which is a good approximation on scales less than $50h^{-1}Mpc$. Our generalized parametrization is of the form $f(a)=\frac{f_0(a)}{1+\xi(a,k)}$ where $\xi(a,k)=\frac{3 H_{0}^{2} \omm}{a k^2}$. We demonstrate that this parametrization fits the exact result of a full general relativistic evaluation of the growth function up to horizon scales for both \lcdm and dynamical dark energy. In contrast, the scale independent parametrization does not provide a good fit on scales beyond 5% of the horizon scale ($k\simeq 0.01 h^{-1}Mpc$).
Dent James B.
Dutta Sourish
Perivolaropoulos Leandros
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