标题： 相互作用的$F(R,T)$引力与修正的卡普里金气体 显示英文标题

标题： Interacting $F(R,T)$ gravity with modified Chaplygin gas

摘要： 本文研究了在Friedmann-Lemaître-Robertson-Walker（FLRW）背景下的$F(R,T)$引力作为曲率和挠率标量的任意函数。然后，我们考虑了$F(R,T)$引力与修正Chaplygin气体之间的相互作用模型。该模型的新颖之处在于宇宙包含了曲率和挠率两种情况，并且由Chaplygin气体主导。为了计算宇宙学解，我们得到了Friedmann方程以及暗能量的状态方程（EoS）参数。通过采用相互作用模型，我们将宇宙的总能量密度和总压力视为暗能量成分和Chaplygin气体成分的组合。随后，我们通过一个名为正则量子场的标量场模型重构了该模型，其中场势已根据$F(R,T)$引力和修正Chaplygin气体的自由参数计算得出。接下来，我们使用参数化方法，并以红移$z$表示宇宙学参数。最后，我们绘制了宇宙学参数相对于三个变量（宇宙时间、红移$z$和$e$-折叠数$N=ln(a)$）的图，结果显示宇宙加速膨胀。 此外，我们通过$e$折叠数描述了早期时间、晚期时间和未来时间的三种状态场景。最后，通过一个名为声速的有用函数研究了该场景的稳定性，声速与$e$折叠数的关系图显示晚期存在稳定性。 显示英文摘要

摘要： In this paper, we have studied $F(R,T)$ gravity as an arbitrary function of curvature and torsion scalars in Friedmann--Lema\^{\i}tre--Robertson--Walker (FLRW) background. Then, we have considered interacting model between $F(R,T)$ gravity and modified Chaplygin gas. The novelty of this model is that the Universe includes both cases curvature and torsion, and one dominated by a Chaplygin gas. In order to calculate cosmological solutions, we obtained Friedmann equations and also equation of state (EoS) parameter of dark energy. By employing interacting model we considered the total energy density and the total pressure of Universe as the combination of components of dark energy and Chaplygin gas. Subsequently, we reconstructed the model by an origin of a scalar field entitled quintessence model with a field potential. The field potential has been calculated in terms of free parameters of $F(R,T)$ gravity and modified Chaplygin gas. In what follows, we used a parametrization, and the cosmological parameters have been written in terms of redshift $z$. Next, we plotted cosmological parameters with respect to three variable of cosmic time, redshift $z$ and $e$-folding number $N=ln(a)$, and the figures showed us an accelerated expansion of Universe. Also, we have described the scenario in three status early time, late time and future time by $e$-folding number. Finally, the stability of scenario has been investigated by a useful function named sound speed, and the graph of sound speed versus $e$-folding number has been showed us that there is the stability in late time.