DOE OSTI2016
The growth index γ 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 γ 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 γ 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 Ω {sub m} appears to be too small. An infinite number of solutions, with Ω {sub m} and γ both constant, are found with w {sub DE} = 0 corresponding to Einstein-de Sitter universes. For all modified gravity DE models satisfying G {sub eff} ≥ G , among them the f ( R ) DE models suggested in the literature, the condition to have a constant w {sub DE} is strongly violated at the present epoch. In contrast, DE tracking dust-like matter deep in the matter era, but with Ω {sub m} <1, requires G {sub eff} > G and an example is given using scalar-tensor gravity for a range of admissible values of γ. For constant w {sub DE} inside GR, departure from a quasi-constant value is limited until today. Even a large variation of w {sub DE} may not result in a clear signature in the change of γ. The change however is substantial in the future and the asymptotic value of γ is found while its slope with respect to Ω {sub m} (and with respect to z ) diverges and tends to −∞.
79 ASTRONOMY AND ASTROPHYSICS↗