Global properties of the growth index of matter inhomogeneities in the Universe

Physical Review D - Particles, Fields, Gravitation and Cosmology. 2019. Vol. 100. No. 8. P. 083503.

Calderon R., Felbacq D., Gannouji R., Polarski D., Starobinsky A.A.

We perform here a global analysis of the growth index γ 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 γ(Ω_m) is unique when the decaying mode of scalar perturbations is negligible. However, γ_∞, the value of γ in the asymptotic future, is unique even in the presence of a non-negligible decaying mode today. Moreover, γ becomes arbitrarily large deep in the matter era. Only in the limit of a vanishing decaying mode do we get a finite γ , from the past to the future in this case. We find further a condition for γ(Ω_m) to be monotonically decreasing (or increasing). This condition can be violated inside GR for varying w_{DE} though generically γ(Ω_m) will be monotonically decreasing (like ΛCDM ), except in the far future and past. A bump or a dip in Geff can also lead to a significant and rapid change in the slope dγ/dΩ_m . On a ΛCDM background, a γ substantially lower (higher) than 0.55 with a negative (positive) slope reflects the opposite evolution of G_{eff}. In Dvali-Gabadadze-Porrati (DGP) models, γ(Ω_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 γ_∞^{DGP} = γ_∞^{ΛCDM} = 2/3 . In contrast, despite G_eff^{DGP}→G in the past, γ does not tend to its value in GR because dG_{eff}^{DGP}/ dΩ_m |_{-∞} ≠ 0.

Keywords: cosmology, космология, matter inhomogeneity, growth index, неоднородности материи, индекс роста