标题： 新年龄黑暗能量驱动的\boldmath{$f(Q)$}引力重建及其宇宙学含义 显示英文标题

标题： New Agegraphic Dark Energy Driven Reconstruction of \boldmath{$f(Q)$} Gravity and its Cosmological Implications

摘要： 在本工作中，我们进行了受新年代暗能量（NADE）模型启发的\( f(Q) \)引力的重建，旨在不引入宇宙学常数的情况下解释宇宙的晚期加速膨胀。利用幂律尺度因子\( a(t) = a_0 t^h \)，我们基于与 NADE 的对应关系推导出\( f(Q) \)的解析形式，其中共形时间作为红外截断。该模型在极限情况下自然恢复广义相对论，并表现出几何驱动的暗能量组分。我们通过马尔可夫链蒙特卡洛（MCMC）分析，利用最近的 DESI DR2 BAO 和之前 BAO 观测的重子声学振荡（BAO）数据对模型参数进行约束。重建的哈勃参数\( H(z) \)与观测数据高度一致，实现了高\( R^2 \)值和低\(\chi^2_{\min}\)、AIC 和 BIC 分数，优于标准的\( \Lambda \)CDM 模型。 此外，我们使用减速参数\( q(z) \)、有效状态方程\( \omega_{\mathrm{eff}}(z) \)和 Om 诊断方法研究了宇宙学演化。 该模型表现出从减速到加速的明显转变，当前值为\( q(0) \in \left[-0.5879, -0.3333\right] \)，转变红移为$z_{\mathrm{tr}} \sim 0.5209-0.8126$，同时保持\( -1 < \omega_{\mathrm{eff}}(z) < -1/3 \)，表明类似量子能的特性。 Om 诊断方法一致显示负斜率，进一步证实了与\( \Lambda \)CDM 的偏差。 能量条件分析显示 WEC、DEC 和 NEC 得到满足，而 SEC 仅在低红移时被违反，这与宇宙加速膨胀一致。 总体而言，重构的\( f(Q) \)模型为标准暗能量情景提供了一个可行、观测一致且理论上有根据的替代方案。 显示英文摘要

摘要： In this work, we perform reconstruction of \( f(Q) \) gravity inspired by the New Agegraphic Dark Energy (NADE) model, aiming to account for the Universe's late time acceleration without invoking a cosmological constant. Utilizing a power law scale factor \( a(t) = a_0 t^h \), we derive an analytic form for \( f(Q) \) based on a correspondence with NADE, where the conformal time serves as the infrared cutoff. The resulting model naturally recovers General Relativity in the limit and exhibits a geometrically motivated dark energy component. We constrain the model parameters using recent Baryon Acoustic Oscillation (BAO) data from DESI DR2 BAO and previous BAO observations through the Markov Chain Monte Carlo (MCMC) analysis. The reconstructed Hubble parameter \( H(z) \) demonstrates excellent agreement with observational data, achieving high \( R^2 \) values and low \(\chi^2_{\min}\), AIC, and BIC scores, outperforming the standard \( \Lambda \)CDM model. Further, we investigate the cosmological evolution using the deceleration parameter \( q(z) \), effective equation of state \( \omega_{\mathrm{eff}}(z) \), and Om diagnostics. The model exhibits a clear transition from deceleration to acceleration with a present value \( q(0) \in \left[-0.5879, -0.3333\right] \) and transition redshift $z_{\mathrm{tr}} \sim 0.5209-0.8126$, while maintaining \( -1 < \omega_{\mathrm{eff}}(z) < -1/3 \), indicating quintessence like behavior. Om diagnostics consistently show a negative slope, further confirming deviation from \( \Lambda \)CDM. Energy condition analysis reveals that WEC, DEC, and NEC are satisfied, while SEC is violated only at low redshifts which is consistent with cosmic acceleration. Overall, the reconstructed \( f(Q) \) model provides a viable, observationally consistent, and theoretically motivated alternative to standard dark energy scenarios.