标题： 反弹宇宙的相空间分析与弦效应 显示英文标题

标题： Phase space analysis of the bouncing universe with stringy effects

摘要： 我们使用从弦论T对偶效应中得到的最近修改的弗里德曼方程来研究反弹早期宇宙的相空间分析，这些方程编码了零点长度（Phys. Lett. B 836 (2023), 137621）。这种弦论效应的一个重要含义是，它们可以缓解初始奇点，因为雷乔杜里方程被修改了。我们研究宇宙是否可以在状态方程参数的特定领域经历加速膨胀阶段。弦论效应被编码在参数$\Gamma$中，该参数不仅取决于零点长度，还取决于状态参数$\omega$。我们构建了两个动力系统，这取决于$-1 < \omega \leq -1/3$和$\omega \geq -1/3$的情况，并对每个系统的平衡点进行分类。讨论了精确解和宇宙学意义。 显示英文摘要

摘要： We use the recently modified Friedmann equations obtained from string T-duality effects that encode the zero-point length (Phys. Lett. B 836 (2023), 137621) to study the phase space analyses of a bouncing early universe. An important implication of such stringy effects is that they can alleviate the initial singularity since the Raychaudhuri equation is modified. We investigate if the Universe can undergo an accelerated expansion phase for a specific domain of the equation of state parameter. The stringy effects are encoded in the parameter $\Gamma$, which depends not only on the zero-point length but also on the state parameter $\omega$. We construct two dynamical systems depending on whether $-1 < \omega \leq -1/3$ and $\omega \geq -1/3$, and we classify the equilibrium points of each system. Exact solutions and cosmological implications are discussed.