%0 Journal Article
%T When is the growth index constant?
%+ Laboratoire Charles Coulomb (L2C)
%A Polarski, David
%A Starobinsky, Alexei A.
%A Giacomini, Hector
%Z 16 pages, 5 figure; incorrect reference corrected; v3 matches published version in JCAP; v4: comment added and expanded references. Réf Journal: JCAP 1612, no 12, 037 (2016)
%< avec comité de lecture
%Z L2C:17-393
%@ 1475-7508
%J Journal of Cosmology and Astroparticle Physics
%I Institute of Physics (IOP)
%V no 12
%P 037
%8 2016
%D 2016
%Z 1610.00363
%R 10.1088/1475-7516/2016/12/037
%Z Physics [physics]/General Relativity and Quantum Cosmology [gr-qc]Journal articles
%X The growth index $\gamma$ is an interesting tool to assess the phenomenology of dark energy (DE) models, in particular of those beyond general relativity (GR). We investigate the possibility for DE models to allow for a constant $\gamma$ during the entire matter and DE dominated stages. It is shown that if DE is described by quintessence (a scalar field minimally coupled to gravity), this behaviour of $\gamma$ is excluded either because it would require a transition to a phantom behaviour at some finite moment of time, or, in the case of tracking DE at the matter dominated stage, because the relative matter density $\Omega_m$ appears to be too small. An infinite number of solutions, with $\Omega_m$ and $\gamma$ both constant, are found with $w_{DE}=0$ corresponding to Einstein-de Sitter universes. For all modified gravity DE models satisfying $G_{\rm eff}\ge G$, among them the $f(R)$ DE models suggested in the literature, the condition to have a constant $w_{DE}$ is strongly violated at the present epoch. In contrast, DE tracking dust-like matter deep in the matter era, but with $\Omega_m <1$, requires $G_{\rm eff} > G$ and an example is given using scalar-tensor gravity for a range of admissible values of $\gamma$. For constant $w_{DE}$ inside GR, departure from a quasi-constant value is limited until today. Even a large variation of $w_{DE}$ may not result in a clear signature in the change of $\gamma$. The change however is substantial in the future and the asymptotic value of $\gamma$ is found while its slope with respect to $\Omega_m$ (and with respect to $z$) diverges and tends to $-\infty$.
%G English
%L hal-02021381
%U https://hal.science/hal-02021381
%~ CNRS
%~ L2C
%~ MIPS
%~ UNIV-MONTPELLIER
%~ UM-2015-2021