Correlation of structure growth index with current cosmic acceleration: Constraints on dark energy models

Abstract

We study dynamical dark energy (DE) models within Einstein’s theory by means of matter perturbations and the growth index [Formula: see text]. Within four-dimensional General Relativity, we assume that DE does not cluster, and we adopt a linear ansatz for the growth index to investigate its impact on the deceleration parameter, [Formula: see text], and on the DE equation-of-state parameter, [Formula: see text]. Following this approach, we identify a relationship between [Formula: see text] (today’s value of [Formula: see text]) and [Formula: see text], which to the best of our knowledge is new. For [Formula: see text], we find that in most of the cases considered it crosses the [Formula: see text] line (quintom) ending at a present day value [Formula: see text]. Furthermore, we show that an analytic expression for [Formula: see text] may be obtained in the form of order (4,4) (or higher) Padé parametrizations.