What question did this study set out to answer?

This research aims to explore the growth of matter perturbations in various dark energy models and determine their relationships with background parameters.

January 31, 2008Open Access

On the growth of linear perturbations

Key Points

This research aims to explore the growth of matter perturbations in various dark energy models and determine their relationships with background parameters.
Analyzed dark energy models and their impact on matter perturbations.
Investigated constraints on growth parameters at redshift z=0.
Assessed variations in the equation of state within General Relativity.
For ΛCDM, γ0′ lies within the interval −0.0195 to −0.0157 for matter density parameters 0.2≤Ωm,0≤0.35.
Constant equation of state models maintain γ0′ near −0.02, indicating limited variation in growth parameters.
Measurements of γ(z) at low redshifts could differentiate dark energy models, particularly those beyond General Relativity.

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.

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