Contiguous redshift parameterizations of the growth index

Abstract

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 $\gamma(a)=\tilde\gamma(a) \frac{1}{1+(a_{_{ttc}}/a)}+\gamma_{_{early}} \frac{1}{1+(a/a_{_{ttc}})}$ that interpolates between a low/intermediate redshift parameterization $\tilde\gamma(a)=\gamma_{_{late}}(a)= \gamma_0 + (1-a) \gamma_a$ and a high redshift $\gamma_{_{early}}$ constant value. For example, our interpolated form $\gamma(a)$ can be used when including the CMB to the rest of the data while the form $\gamma_{_{late}}(a)$ 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 $\Lambda$CDM model, better than 0.014% for Quintessence-Cold-Dark-Matter (QCDM) models, and better than 0.04% for the flat Dvali-Gabadadze-Porrati (DGP) model (with $\Omega_m^0=0.27$) for the entire redshift range up to $z_{_{CMB}}$. We find that the growth index parameters $(\gamma_0,\gamma_a)$ take distinctive values for dark energy models and modified gravity models, e.g. $(0.5655,-0.02718)$ for the $\Lambda$CDM model and $(0.6418,0.06261)$ for the flat DGP model. This provides a means for future observational data to distinguish between the models.Comment: 7 pages, 6 figures, matches PRD accepted versio

Linear growth in power lawf(T)gravity

“…(46) As expected, for the Λ cosmology (b = 0) the above formula reduces to its standard expression [45][46][47][48][49]. Lastly, inserting γ 0 = γ ∞ − γ 1 into Eq.…”

“…(31) and (38). In this work we consider the most popular γ(a) parametrization that has appeared in the literature (see [45][46][47][48][49]), which is a Taylor expansion around a(z) = 1…”

Observational constraints on modified Chaplygin gas from cosmic growth

“…One such parametrisation is γ(z) [52,53]. It has been shown recently [54] that the parametrization smoothly interpolates a low and intermediate redshift range to a high redshift range up to the cosmic microwave background scale. The above parametrization is also taken up in different contexts [55].…”

Constraints on scalar-tensor theories of gravity from observations

“…Although γ is time dependent by its definition even for the simple dark energy models [14,15,16], the constant value of it can be well matched with some dark energy and modified gravity models [17,18,19,20,21,22]. However, it can be generalized as a time dependent γ(a) [23,24,25,27,28,29].…”