标题： 宇宙学模型在$f(T,φ)$引力中的稳定性分析 显示英文标题

标题： Stability Analysis of Cosmological models in $f(T,φ)$ Gravity

摘要： 我们研究了在$f(T,\phi)$引力理论中考虑两种模型的稳定性条件，使用了动力系统。 我们假设$G(T)$的形式为$(i)$ $G(T)$ =$\alpha T+\frac{\beta}{T}$，$(ii)$ $G(T)$ =$\zeta T$ln$(\psi T)$，其中$\alpha$，$\beta$，$\zeta$和$\psi$是自由参数。 我们评估了这些模型的平衡点并检查了稳定性行为。 我们发现模型I有五个稳定的临界点，模型II有三个稳定的临界点。 检查并讨论了这些系统的相图的物理解释。 我们在每个固定点上展示了所有宇宙学参数，如$\Omega_{m}$, $\Omega_{\phi}$, $q$和$\omega_{Tot}$，并将这些参数与观测值进行比较。 此外，我们假设了混合尺度因子，红移和时间的方程是$t(z)=\frac{\delta}{\sigma}W\bigg[\frac{\sigma}{\delta}\bigg(\frac{1}{a_{1}(1+z)}\bigg)^{\frac{1}{\delta}}\bigg]$。 我们使用这个方程将所有参数转换为红移，并检查这些参数的行为。 我们的模型代表了宇宙的加速阶段。 在红移方面检查了能量条件，该模型不满足 SEC。 我们还找到了状态寻找参数$\{r,s\}$以z为基准，并讨论了$r-s$和$r-q$平面的性质。 对于两对$\{r,s\}$和$\{r,q\}$，我们的模型代表了$\Lambda$CDM 模型。 因此，我们确定我们的$f(T,\phi)$模型是稳定的，并且满足所有的观测值。 显示英文摘要

摘要： We investigated the stability condition in $f(T,\phi)$ gravity theory for considering two models by using dynamical system. We assume the forms of $G(T)$ are $(i)$ $G(T)$ = $\alpha T+\frac{\beta}{T}$, $(ii)$ $G(T)$ = $\zeta T$ ln$(\psi T)$, where $\alpha$, $\beta$, $\zeta$ and $\psi$ be the free parameters. We evaluated the equilibrium points for these models and examine the stability behavior. We found five stable critical points for Model I and three stable critical points for Model II. The phase plots for these systems are examined and discussed the physical interpretation. We illustrate all the cosmological parameters such as $\Omega_{m}$, $\Omega_{\phi}$, $q$ and $\omega_{Tot}$ at each fixed points and compare the parameters with observational values. Further, we assume hybrid scale factor and the equation of redshift and time is $t(z)=\frac{\delta}{\sigma}W\bigg[\frac{\sigma}{\delta}\bigg(\frac{1}{a_{1}(1+z)}\bigg)^{\frac{1}{\delta}}\bigg]$. We transform all the parameters in redshift by using this equation and examine the behavior of these parameters. Our models represent the accelerating stage of the Universe. The energy conditions are examined in terms of redshift and SEC is not satisfied for the model. We also find the statefinder parameters $\{r,s\}$ in terms of z and discuss the nature of $r-s$ and $r-q$ plane. For both pairs $\{r,s\}$ and $\{r,q\}$ our models represent the $\Lambda$CDM model. Hence, we determine that our $f(T,\phi)$ models are stable and it satisfies all the observational values.