English

Improved parametrization of the growth index for dark energy and DGP models

General Relativity and Quantum Cosmology 2010-04-30 v3

Abstract

We propose two improved parameterized form for the growth index of the linear matter perturbations: (I) γ(z)=γ0+(γγ0)zz+1\gamma(z)=\gamma_0+(\gamma_{\infty}-\gamma_0){z\over z+1} and (II) γ(z)=γ0+γ1zz+1+(γγ1γ0)(zz+1)α\gamma(z)=\gamma_0+\gamma_1 \frac{z}{z+1}+(\gamma_{\infty}-\gamma_1-\gamma_0)(\frac{z}{z+1})^{\alpha}. With these forms of γ(z)\gamma(z), we analyze the accuracy of the approximation the growth factor ff by Ωmγ(z)\Omega^{\gamma(z)}_m for both the ω\omegaCDM model and the DGP model. For the first improved parameterized form, we find that the approximation accuracy is enhanced at the high redshifts for both kinds of models, but it is not at the low redshifts. For the second improved parameterized form, it is found that Ωmγ(z)\Omega^{\gamma(z)}_m approximates the growth factor ff very well for all redshifts. For chosen α\alpha, the relative error is below 0.003% for the Λ\LambdaCDM model and 0.028% for the DGP model when Ωm=0.27\Omega_{m}=0.27. Thus, the second improved parameterized form of γ(z)\gamma(z) should be useful for the high precision constraint on the growth index of different models with the observational data. Moreover, we also show that α\alpha depends on the equation of state ω\omega and the fractional energy density of matter Ωm0\Omega_{m0}, which may help us learn more information about dark energy and DGP models.

Keywords

Cite

@article{arxiv.0908.4379,
  title  = {Improved parametrization of the growth index for dark energy and DGP models},
  author = {Jiliang Jing and Songbai Chen},
  journal= {arXiv preprint arXiv:0908.4379},
  year   = {2010}
}

Comments

11 pages, 10 figures, references add; the correct version accepted for publication in PLB