Key points are not available for this paper at this time.
We perform here a global analysis of the growth index 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 (₌) is unique when the decaying mode of scalar perturbations is negligible. However, _, the value of in the asymptotic future, is unique even in the presence of a non-negligible decaying mode today. Moreover, becomes arbitrarily large deep in the matter era. Only in the limit of a vanishing decaying mode do we get a finite, from the past to the future in this case. We find further a condition for (₌) to be monotonically decreasing (or increasing). This condition can be violated inside GR for varying w₃₄ though generically (₌) will be monotonically decreasing (like), except in the far future and past. A bump or a dip in G₄₅₅ can also lead to a significant and rapid change in the slope dd{₌}. On a background, a substantially lower (higher) than 0. 55 with a negative (positive) slope reflects the opposite evolution of G₄₅₅. In Dvali-Gabadadze-Porrati (DGP) models, (₌) 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 _^DGP=_^=23. In contrast, despite G₄₅₅^DGP in the past, does not tend to its value in GR because dG₄₅₅^{DGP}d{₌}|-0.
Calderón et al. (Wed,) studied this question.