Abstract

We perform here a global analysis of the growth index gamma behavior from deep in the matter era till the far future. For a given cosmological model in general relativity (GR) or in modified gravity, the value of gamma(Omega(m)) is unique when the decaying mode of scalar perturbations is negligible. However, gamma(infinity), the value of gamma in the asymptotic future, is unique even in the presence of a non-negligible decaying mode today. Moreover, gamma becomes arbitrarily large deep in the matter era. Only in the limit of a vanishing decaying mode do we get a finite gamma, from the past to the future in this case. We find further a condition for gamma(Omega(m)) to be monotonically decreasing (or increasing). This condition can be violated inside GR for varying w(DE) though generically gamma(Omega(m)) will be monotonically decreasing (like Lambda CDM), except in the far future and past. A bump or a dip in G(eff) can also lead to a significant and rapid change in the slope d gamma/d Omega(m). On a ACDM background, a gamma substantially lower (higher) than 0.55 with a negative (positive) slope reflects the opposite evolution of G(eff). In Dvali-Gabadadze-Pmati (DGP) models, gamma(Omega(m)) is monotonically increasing except in the far future. While DGP gravity becomes weaker than GR in the future and w(DGP) -> -1, we still get gamma(DGP)(infinity) = gamma(Lambda CDM)(infinity) = 2/3 . In contrast, despite G(eff)(DGP) -> G in the past, gamma does not tend to its value in GR because dG(eff)(DGP)/d Omega(m) vertical bar(-infinity) not equal 0.