Abstract
We study the evolution of cosmological perturbations around a homogeneous and isotropic background in the framework of the non-minimal torsion-matter coupling extension of f(T) gravity. We are concerned with the effects of the non-minimal coupling term on the growth of matter overdensities. Under the quasi-static approximation, we derive the equation which governs the evolution of matter density perturbations, and it is shown that the effective gravitational coupling ‘constant’ acquires an additional contribution due to the non-minimal matter-torsion coupling term. In this way, this result generalizes those previously obtained for the growth of matter overdensities in the case of minimal f(T) gravity. In order to get a feeling of our results we apply them to the important case of a power-law coupling function, which we assume to be the responsible for the late-time accelerated expansion in the dark energy regime. Thereby, analytic solutions for the matter density perturbation equation in the regime of dark matter dominance and the dark energy epoch are obtained, along with a complete numerical integration of this equation. In particular, we show that this model predicts a growth index larger than those obtained for varLambda CDM model, indicating therefore a smaller growth rate. Concomitantly, we show that the model at hand is potentially capable in alleviating the existing sigma _{8}-tension, being that it can provide us a fsigma _{8} prediction which is sim 4–5% below the respective prediction of concordance model.
Highlights
It is well known that gravity can be described in terms of curvature, as is usually done in General Relativity (GR) and f (R) gravity theories, or through torsion, in which case we have the so-called teleparallel equivalent of GR or Teleparallel Gravity (TG) [33,34,35,36,37,38,39,40]
In studying the dark energy problem of cosmology a very interesting class of modified gravity models are the so-called f (T ) gravity theories [45,46,47], that generalize the teleparallel equivalent of GR [33,34,35,36,37,38,39,40], in which gravity is described through torsion and not curvature [41,42,43,44]
It is fundamental a study of cosmological perturbations in order to compare all the predictions and results obtained from the model with the observational data of cosmic microwave background (CMB) and large-scale structure (LSS) [10]
Summary
It is well known that gravity can be described in terms of curvature, as is usually done in GR and f (R) gravity theories, or through torsion, in which case we have the so-called teleparallel equivalent of GR or Teleparallel Gravity (TG) [33,34,35,36,37,38,39,40]. A very important generalization of f (T ) gravity is obtained by allowing a non-minimal coupling between torsion and matter [78,79,80,81]. For the Friedmann-Robertson-Walker (FRW) background geometry, they have shown that this novel theory allows us to obtain an effective dark energy sector whose equation-of-state (EOS) parameter can be quintessence- or phantom-like, or exhibit the phantom-divide crossing, being that for a large range of the model parameters the Universe undergoes a de Sitter, dark-energy-dominated, accelerating phase. It can provide an early-time inflationary solution too, and it is possible an unified description of the history of cosmological expansion.
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