Abstract
We consider the linear growth of matter perturbations in various dark energy (DE) models. We show the existence of a constraint valid at z=0 between the background and dark energy parameters and the matter perturbations growth parameters. For ΛCDM γ0′≡dγdz|0 lies in a very narrow interval −0.0195⩽γ0′⩽−0.0157 for 0.2⩽Ωm,0⩽0.35. Models with a constant equation of state inside General Relativity (GR) are characterized by a quasi-constant γ0′, for Ωm,0=0.3 for example we have γ0′≈−0.02 while γ0 can have a nonnegligible variation. A smoothly varying equation of state inside GR does not produce either |γ0′|>0.02. A measurement of γ(z) on small redshifts could help discriminate between various DE models even if their γ0 is close, a possibility interesting for DE models outside GR for which a significant γ0′ can be obtained.
Highlights
There is growing observational evidence for the late-time accelerated expansion of our universe [2]
While the usual Friedmann equations in the presence of a cosmological constant term Λ seem to be in good agreement with the data, it is clear that other models with a variable equation of state are allowed as well [2]
The background expansion going back to high redshifts is enough to rule out some models [7], but typically this is not the case: models of a very different kind will be able to have a viable background expansion where the low redfshift expansion is in accordance with SNIa data
Summary
There is growing observational evidence for the late-time accelerated expansion of our universe [2] This radical departure from conventional decelerated expansion is certainly a major challenge to cosmology. While a cosmological constant universe is appealing because of its simplicity it poses the problem of the magnitude of the cosmological constant Λ This is the basic incentive to look for other models where DE has a variable equation of state. Two DE models based on different gravitation theories can give the same late-time accelerated expansion and still differ in the matter perturbations they produce [10]. This fact could provide an additional important way to discriminate between various models This fact could provide an additional important way to discriminate between various models (see e.g. [11]) and it is important to characterize as accurately as possible the growth of matter perturbations which is the aim of the present work
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