AI 中文总结
该研究提出暗能量最优红移的概念，推导其解析表达式并建立与相关红移的关系，经多数据集验证其能更显著检验暗能量与宇宙学常数的偏离，相关原理可扩展至其他暗能量研究框架。
AI 中文摘要
我们引入暗能量最优红移的概念，这是一个具有统计意义的红移，在该红移处可最有效地检验暗能量状态方程（EOS）与宇宙学常数取值的偏离。在广义CPL参数化框架内，我们通过最大化EOS与$w=-1$的差值相对于对应不确定度的比值，推导出最优红移的解析表达式，并建立了最优红移与 phantom 穿越红移、枢轴红移的关系。作为示例，我们将该形式化方法应用于DESI DR2 BAO测量、DES第6年独立BAO测量及重新校准的DES-Dovekie超新星样本的组合数据集。采用原假设$\boldsymbol{\textit{H}}_0:w(a_{\rm opt})=-1$，我们发现最优红移处与$\boldsymbol{\rm \u039CDM}$模型的宇宙学常数预测存在约$2.8\boldsymbol{\u03c3}$的张力，而枢轴红移处的张力约为$2.6\boldsymbol{\u03c3}$，尽管后者的EOS不确定度更小。该特性反映了最优红移的特定设计目标：最大化EOS与$\boldsymbol{\rm \u039CDM}$模型中-1值偏离的统计显著性。我们进一步对最优红移提供了统计和几何解释：在CPL参数空间中，枢轴对应于最小化EOS方差的投影，而最优红移则最大化其与宇宙学常数值的平方距离除以方差的比值。尽管最优红移依赖于数据集和参数化方式，但其背后的优化原理和最优红移的定义可扩展至CPL框架之外。未来将其应用于DESI、Rubin LSST、Euclid、Roman空间望远镜及其他第四阶段暗能量巡天项目，前景尤为广阔。
英文摘要
We introduce the concept of the optimal redshift for dark energy, a statistically motivated redshift at which departures of the dark-energy equation of state (EOS) from the cosmological-constant value are tested most effectively. Within a generalized CPL parameterization, we derive an analytic expression for the optimal redshift by maximizing the separation of the EOS from $w=-1$ relative to the corresponding uncertainty. We establish the optimal redshift relationship to the phantom-crossing and pivot redshifts. As an illustration, we apply the formalism to the dataset combination of DESI DR2 BAO measurements, the DES Year-6 independent BAO measurement, and the recalibrated DES-Dovekie supernova sample. Adopting the null hypothesis $\mathcal{H}_0:w(a_{\rm opt})=-1$, we find a tension of ~$2.8σ$ with the cosmological-constant prediction at the optimal redshift, compared with ~$2.6σ$ at the pivot redshift, despite the latter having a smaller EOS uncertainty. This behavior reflects the specific design of the optimal redshift to maximize the statistical significance of a departure of the EOS from the -1 value of the $Λ$CDM model. We further provide statistical and geometrical interpretations of the optimum. In the CPL parameter space, the pivot corresponds to the projection that minimizes the variance of the equation of state, whereas the optimum maximizes its squared-distance from the cosmological-constant value over its variance. While the optimum is dataset and parameterization dependent, the underlying optimization principle and definition of the optimal redshift can be extended beyond the CPL framework. Future applications to DESI, Rubin LSST, Euclid, Roman Space Telescope, and other Stage-IV dark-energy surveys appear particularly promising.
Comments13 pages, 2 figures
