标题： 线性扰动与稳定性分析在$f(T)$膜宇宙情景中 显示英文标题

标题： Linear Perturbations and Stability Analysis in $f(T)$ Braneworld Scenario

摘要： 我们对在$f(T)$引力理论中的膜世界场景下的全线性扰动进行了详细分析。 通过将理论的扰动分解为标量、横矢量、反对称赝张量和对称横截张量模式，我们推导了每种模式的二次作用量。 结果表明，总共有1个标量、1个无质量矢量和1个张量传播自由度。 因此，在线性化理论中，与广义相对论相比，在平坦膜世界背景下没有出现额外的自由度。 对于具有$f(T)=T+ \alpha T^2$的厚膜模型，我们发现它在面对线性扰动时表现出稳定性。 显示英文摘要

摘要： We conduct a detailed analysis of the full linear perturbations in the braneworld scenario within $f(T)$ gravity. By decomposing the perturbations of the theory into the scalar, transverse vector, antisymmetric pseudotensor, and symmetric transverse-traceless tensor modes, we derive the quadratic action for each mode. The results indicate that there is a total of one scalar, one massless vector, and one tensor propagating degrees of freedom. Consequently, in comparison to general relativity, no additional degrees of freedom appear under the flat braneworld background in the linearized theory. For a thick brane model with $f(T)=T+ \alpha T^2$, we find that it exhibits stability against linear perturbations.