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 are 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.
Highlights
The effect of the evolving dark energy (DE) on the rate of the large-scale structure (LSS) formation has been a prime area of investigation in modern cosmology, from the point of view of asserting the characteristics of the respective DE component [1–5]
In the formalism, we have briefly demonstrated that a non-minimal coupling of metric and torsion with a scalar field can give rise to a scalar-tensor action of DE in the Jordan frame which upon conformal transformation to the Einstein frame naturally makes a scalar field non-minimally coupled with the matter sector
In the perturbed FRW space-time, the scalar field and matter coupling enhances the growth of matter density perturbations in the sub-horizon regime, allowing it to cross the upper barrier of unity at large redshifts
Summary
The effect of the evolving dark energy (DE) on the rate of the large-scale structure (LSS) formation has been a prime area of investigation in modern cosmology, from the point of view of asserting the characteristics of the respective DE component [1–5]. Torsion’s axial (or, pseudo-trace) mode Aμ can lead to an effective potential, for, e.g., a mass term m2φ2 (with m = constant) in that scalar-tensor equivalent action, upon implementing a norm-fixing constraint (AμAμ = constant) as in the Einstein-aether theories [151–153], or incorporating a φ-coupled higher order term (AμAμ)2 [73] Such a mass term is shown to play a crucial role in giving rise to a viable cosmological scenario marked by an φ-induced DE component with a weak enough dynamical evolution amounting to cosmological parametric estimations well within the corresponding observational error limits for ΛCDM.
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