  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.
