Contiguous redshift parameterizations of the growth index

The growth rate of matter perturbations can be used to distinguish between different gravity theories and to distinguish between dark energy and modified gravity at cosmological scales as an explanation to the observed cosmic acceleration. We suggest here parameterizations of the growth index as functions of the redshift. The first one is given by γ(a)=γ∼(a)(1)/(1+(a_ttc/a))+γ_early(1)/(1+(a/a_ttc)), which interpolates between a low/intermediate redshift parameterization γ∼(a)=γ_late(a)=γ₀+(1-a)γ_a and a high redshift γ_early constant value. For example, our interpolated form γ(a) can be used when including the cosmic microwave background to the rest of the data, while the form γ_late(a) can be used otherwise. It is found that the parameterizations proposed achieve a fit that is better than 0.004% for the growth rate in a ΛCDM model, better than 0.014% for quintessence-cold-dark-matter models, and better than 0.04% for the flat Dvali-Gabadadze-Porrati model (with Ω_m⁰=0.27) for the entire redshift range up to z_CMB. We find that the growth index parameters (γ₀,γ_a) take distinctive values for dark energy models and modified gravity models, e.g. (0.5655,-0.02718) for the ΛCDM model and (0.6418, 0.062 61) for the flat Dvali-Gabadadze-Porrati model. This provides a means for future observational data to distinguish between the models.