Growth of matter perturbations in an interacting dark energy scenario emerging from metric-scalar-torsion couplings

TL;DR

This paper investigates how scalar-torsion couplings in modified gravity theories influence the growth of matter perturbations, providing a new fitting formula for the growth index that aligns with observational data.

Contribution

It introduces a novel scalar-torsion coupling model affecting matter growth and derives a practical fitting formula for the growth index compatible with observations.

Findings

The growth index can be accurately fitted using the derived formula.

The model's predictions are consistent with current RSD and Hubble data.

The formalism remains viable within cosmological constraints.

Abstract

We study the growth of linear matter density perturbations in a modified gravity approach of scalar field couplings with metric and torsion. In the equivalent scalar-tensor formulation, the matter fields in the Einstein frame interact as usual with an effective dark energy component, whose dynamics is presumably governed by a scalar field that sources a torsion mode. As a consequence, the matter density ceases to be self-conserved, thereby making an impact not only on the background cosmological evolution but also on the perturbative spectrum of the local inhomogeneities. In order to estimate the effect on the growth of the linear matter perturbations, with the least possible alteration of the standard parametric form of the growth factor, we resort to a suitable Taylor expansion of the corresponding exponent, known as the growth index, about the value of the cosmic scale factor at the present epoch. In particular, we obtain an appropriate fitting formula for the growth index in terms of the coupling function and the matter density parameter. While the overall parametric formulation of the growth factor is found to fit well with the latest redshift-space-distortion (RSD) and the observational Hubble (OH) data at low redshifts, the fitting formula enables us to constrain the growth index to well within the concordant cosmological limits, thus ensuring the viability of the formalism.