In a spatially flat Friedmann–Lemaître–Robertson–Walker background space, we consider a scalar-torsion gravitational model which has similar properties to the dilaton theory. This teleparallel model is invariant under a discrete transformation similar to the Gasperini–Veneziano duality transformation. Moreover, in the gravitational action integral, we introduce the Lagrangian function of a pressureless fluid source which is coupled to the teleparallel dilaton field. This specific gravitational theory with interaction in the dark sector of the universe was investigated by using methods of the dynamical system analysis. We calculate that the theory provides various areas of special interest for the evolution of the cosmological history. Inflationary scaling solutions and the de Sitter universe are recovered. Furthermore, we calculate that there exist an attractor which provides a stable solution where the two fluid components, the scalar field and the pressureless matter, contribute in the cosmological fluid. This solution is of special interest because it can describe the present epoch. Finally, the qualitative evolution of the cosmographic parameters is discussed.

中文翻译：

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相互作用标量扭转宇宙学中的动力学

在空间平坦的 Friedmann-Lemaître-Robertson-Walker 背景空间中，我们考虑了一个与膨胀理论具有相似性质的标量扭转引力模型。这种远平行模型在类似于 Gasperini-Veneziano 对偶变换的离散变换下是不变的。此外，在引力作用积分中，我们引入了与远平行膨胀场耦合的无压流体源的拉格朗日函数。使用动力学系统分析的方法研究了这种与宇宙暗区相互作用的特定引力理论。我们计算出该理论为宇宙学历史的演化提供了各种特别感兴趣的领域。通货膨胀缩放解决方案和德西特宇宙得以​​恢复。此外，我们计算出存在一个提供稳定解的吸引子，其中标量场和无压物质这两个流体成分对宇宙流体有贡献。这个解决方案特别有趣，因为它可以描述当前的时代。最后，讨论了宇宙学参数的定性演变。