非最小挠率-物质耦合理论中物质超密度的增长
Growth of matter overdensities in non-minimal torsion-matter coupling theories
摘要：
在非最小挠率-物质耦合扩展的$f(T)$引力理论框架下，研究了均匀各向同性背景下宇宙学扰动的演化。我们关注的是非最小耦合项对物质超密度增长的影响。在准静态近似下，我们导出了控制物质密度扰动演化的方程，并证明了由于非最小的物质-扭转耦合项，有效引力耦合“常数”获得了额外的贡献。这样，这个结果推广了以前在最小$f(T)$引力情况下对物质超密度增长所得到的结果。为了得到我们的结果的感觉，我们将它们应用到幂律耦合函数的重要情况下，我们假设这是负责后期的加速膨胀的暗能量制度。从而，在暗物质占主导地位的制度和暗能量时代的物质密度微扰方程的解析解，以及该方程的一个完整的数值积分。特别是，我们表明，该模型预测的增长指数大于$Λ$ CDM模型获得的，因此表明一个较小的增长率。同时，我们表明，该模型在手是潜在的能够缓解现有的$σ_{8}$ -紧张局势，因为它可以为我们提供一个$fσ_{8}$预测是$\sim 4-5$百分比低于各自的一致性模型的预测。
英文摘要：
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 $Λ$CDM model, indicating therefore a smaller growth rate. Concomitantly, we show that the model at hand is potentially capable in alleviating the existing $σ_{8}$-tension, being that it can provide us a $fσ_{8}$ prediction which is $\sim 4-5$ per cent below the respective prediction of concordance model.
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