Title: Constraining cosmological dynamics of scalar-tensor models of dark energy in teleparallel gravity Show Chinese title

Title: 在遥测引力中约束标量-张量暗能量模型的宇宙学动力学

Abstract: We consider a scalar-tensor theory in teleparallel gravity where a general function of the scalar field, f(phi), is non-minimally coupled to the torsion scalar T. First, we derive the field equations in this framework. Then, we study the cosmological evolution in a spatially flat, homogeneous, and isotropic universe described by the FRW metric, containing radiation and non-relativistic matter with energy densities rho_r and rho_m, respectively. We analyze the system as an autonomous dynamical model of dark energy. The cosmological behavior depends on the coupling function sigma = f'(phi)/sqrt(f(phi)) and the potential parameter lambda = [V'(phi) * f(phi)] / [V(phi) * f'(phi)]. A constant coupling sigma leads to a quadratic form f(phi) proportional to (phi + c)^2, while a constant lambda results in a power-law potential V(phi) proportional to f(phi)^lambda. These forms are supported by mathematical and physical considerations. We perform phase space analysis and show that lambda much greater than 1 is a necessary condition to obtain a radiation-dominated era with effective equation of state w_eff approximately 1/3 and a matter-dominated era with w_eff approximately 0. Moreover, small sigma^2 ensures radiation and matter dominance in the respective eras. Finally, we derive the necessary conditions for a viable cosmological trajectory in this setting. Show Chinese abstract

Abstract: 我们考虑一种在平行引力中的标量-张量理论，其中标量场的任意函数f(φ)，与扭曲标量T非最小耦合。首先，我们在该框架中推导场方程。 然后，我们研究由FRW度规描述的平坦、均匀和各向同性的宇宙中的宇宙学演化，其中包含辐射和非相对论物质，能量密度分别为ρ_r和ρ_m。 我们将该系统分析为暗能量的自治动力学模型。 宇宙学行为取决于耦合函数σ = f'(φ)/√(f(φ))和势参数λ = [V'(φ) * f(φ)] / [V(φ) * f'(φ)]。 常数耦合σ会导致f(φ)成比例于(φ + c)^2的二次形式，而常数λ则会导致V(φ)成比例于f(φ)^λ的幂律势。 这些形式得到了数学和物理考虑的支持。 我们进行了相空间分析，并表明λ远大于1是获得有效状态方程w_eff约为1/3的辐射主导时代和w_eff约为0的物质主导时代的必要条件。 此外，小的σ^2可确保在各自的时代中辐射和物质主导。 最后，我们推导了在此设定下可行宇宙学轨迹的必要条件。