AI 中文总结
研究$\boldsymbol{\textit{F}}(Q)$引力下的非奇异宇宙反弹，采用重构与动力系统分析，揭示几何耦合参数$\boldsymbol{\textit{\u03c8}}$的作用及临界能量密度等结果，为非奇异反弹宇宙提供自洽几何图景。
AI 中文摘要
本研究的核心聚焦于$\boldsymbol{\textit{F}}(Q)$引力框架下的非奇异宇宙反弹分析，其中$Q$代表非度量标量。我们考虑引力拉格朗日量$\boldsymbol{\textit{F}}(Q)=Q+\boldsymbol{\textit{\u03c8}}Q^n$，研究对象为具有平坦Friedmann-Robertson-Walker时空与理想物质分布的、含修正Chaplygin型物质源的宇宙模型。为推进研究，我们采用两种方法：利用标度因子假设的重构方法，以及二维自治动力系统分析。研究结果表明，几何耦合参数$\boldsymbol{\textit{\u03c8}}$发挥着重要作用，它会因违反零能量条件而产生几何排斥作用。对$(\boldsymbol{\rho}_0,\boldsymbol{\textit{\u03c8}})$参数空间的数值扫描显示，存在一个临界能量密度，低于该密度时宇宙会演化至标准奇异宇宙学解；此外，有效状态方程会缓慢演化至德西特值（$\boldsymbol{\u03c9}_{\text{eff}}\rightarrow -1$），且声速平方满足稳定性与因果性条件（$0\leq C_s^2\leq1$）。研究发现，$\boldsymbol{\textit{F}}(Q)$引力为符合宇宙加速膨胀的非奇异反弹宇宙提供了自洽的几何图景。
英文摘要
The key focus of this research work is the analysis of a non-singular cosmic bounce in the context of $\mathcal{F}(Q)$ gravity, with $Q$ representing the non-metricity scalar. We consider the gravitational Lagrangian $\mathcal{F}(Q)=Q+ψQ^n$ in the presence of a modified Chaplygin-type matter source with a flat Friedmann-Robertson-Walker spacetime and a perfect matter distribution. In order to proceed, we adopt two approaches: a reconstruction approach using scale-factor ansatz and analysis of a two-dimensional autonomous dynamical system. Our results imply that the geometry coupling parameter $ψ$ plays an important role and causes geometrical repulsion for violating the null energy condition. A numerical scan of the $(ρ_0,ψ)$ parameter space suggests that there is a critical energy density for the bounce to take place, below which the universe evolves towards the standard singular cosmological solution. Moreover, the effective equation of state slowly evolves towards the de Sitter value ($ω_{eff}\rightarrow -1$) and the squared sound speed is bounded by the stability and causality condition ($0\leq C_s^2\leq1$). It is found that $\mathcal{F}(Q)$ gravity provides a coherent geometric picture of the non-singular bouncing universe in accordance with the cosmic accelerated expansion.
Comments31 pages, 10 figures
