标题： 在f(Q,C)引力中约束模型参数：观测分析与几何诊断 显示英文标题

标题： Constraining model parameters in f(Q,C) gravity: Observational analysis and geometric diagnostics

摘要： 我们研究了带有$f(Q,C)$的$f(Q,C)=\alpha Q+\beta C$引力的宇宙学意义，其中$Q$是非度规标量，$C$包含宇宙膨胀项。测试了三种暗能量状态方程的参数化形式，$\omega=\omega_{0}+\omega_{1}z$、$\omega=\omega_{0}+\frac{\omega_{1}z(1+z)}{1+z^{2}}$和$\omega=\omega_{0}+\frac{\omega_{1}z^{2}}{1+z^{2}}$，使用哈勃、哈勃加BAO、哈勃加BAO加Pantheon数据集来限制模型参数。得到的哈勃参数和减速参数显示从减速到加速的转变，支持当前宇宙加速观测。能量密度和压力的分析确认了暗能量的正能量密度和负压，可能驱动晚期加速。我们检查了能量条件，显示符合NEC、WEC和DEC，而SEC保持负值，支持加速膨胀。 状态因子诊断表明，两个方程状态参数化导致类似量子能的行为，具有随时间变化的暗能量成分，而第三个参数化则接近$\Lambda$冷暗物质，表现出与最新观测结果一致的微小偏差。声速分析证明了所有参数化的物理稳定性。 显示英文摘要

摘要： We investigate the cosmological implications of $f(Q,C)$ gravity with $f(Q,C)=\alpha Q+\beta C$, where $Q$ is the non-metricity scalar and $C$ encapsulates cosmological expansion terms. Three parameterizations of the EoS for dark energy, $\omega=\omega_{0}+\omega_{1}z$, $\omega=\omega_{0}+\frac{\omega_{1}z(1+z)}{1+z^{2}}$ and $\omega=\omega_{0}+\frac{\omega_{1}z^{2}}{1+z^{2}}$ are tested using the Hubble, Hubble plus BAO, and Hubble plus BAO plus Pantheon datasets to constrain model parameters. The resulting Hubble and deceleration parameters reveal a transition from deceleration to acceleration, supporting current cosmic acceleration observations. Analysis of the energy density and pressure confirms positive energy density and a negative pressure for dark energy, potentially driving the late-time acceleration. We examine energy conditions, showing compliance with NEC, WEC and DEC, while SEC remains negative, supporting an accelerated expansion. Statefinder diagnostics suggest that two of the EoS parameterizations lead to Quintessence-like behavior with a time-varying dark energy component, while the third closely approaches $\Lambda$CDM showing slight deviations consistent with recent observations. Sound speed analysis demonstrates the physical stability of all parameterizations.