利用Pantheon+与DES-SN5YR Ia型超新星数据并结合前身星年龄偏差修正对光度-距离对数关系的约束
Progenitor age-bias-corrected Type Ia supernovae favor a logarithmic luminosity-distance relation
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中文总结 AI 辅助
本研究利用Pantheon+与DES-SN5YR Ia型超新星数据，结合前身星年龄偏差修正，验证了单参数对数光度-距离关系的合理性，发现其比ΛCDM模型更适配数据，且能解释高红移额外距离模数。
中文摘要 AI 辅助
Ia型超新星（SNe Ia）是探测晚期宇宙加速膨胀的主要观测工具之一。近期Son等人（《 MNRAS》544, 975, 2025）提出，SNe Ia的光度与前身星年龄之间的相关性可能会在推导得到的光度中引入系统偏差，进而修正Pantheon+和DES-SN5YR数据集中的距离模数。受这一可能性的驱动，本研究探究经年龄偏差修正后的SNe Ia哈勃图是否符合光度-距离关系 $d_L = c/H_0\bigl(1+z\bigr)\bigl(1+z\bigr)$。研究发现，这一单参数对数关系对两个数据集均提供了高质量的描述，其中哈勃常数 $H_0$ 是其唯一自由参数。对于Pantheon+和DES单独数据集，该关系给出的 $\boldsymbol{\tilde{\text{χ}}^2}$ 值分别比双参数平坦ΛCDM模型低 $\boldsymbol{\tilde{\text{Δχ}}^2=12.0}$ 和 $\boldsymbol{2.1}$；对两个数据集进行联合似然分析得到 $\boldsymbol{\tilde{\text{Δχ}}^2=17.1}$，对应的（$\boldsymbol{\tilde{\text{ΔAIC}},\tilde{\text{ΔBIC}}}$）为（19.1, 25.2），支持该对数关系。进一步研究发现，经年龄偏差修正后，两个数据集均无需对该关系进行高阶修正，而爱因斯坦-德西特宇宙学模型则被明确排除。这些结果表明，闭合形式的关系 $d_L = c/H_0\bigl(1+z\bigr)\bigl(1+z\bigr)$ 可作为经年龄偏差修正的SNe Ia哈勃图的可行单参数描述，其渐近行为 $d_L \boldsymbol{\tilde{\text{∝}}} z \boldsymbol{\tilde{\text{ln}}} z$ 自然解释了高红移处观测到的额外距离模数。若前身星年龄偏差修正得到证实，可利用 $1 \boldsymbol{\tilde{\text{≲}}} z \boldsymbol{\tilde{\text{≲}}} 2$ 范围内更大样本的SNe Ia对该对数关系进行进一步检验，此时它已与平坦ΛCDM模型存在显著偏离。
英文摘要
Type Ia supernovae provide one of the principal observational probes of late-time cosmic acceleration. Recently, Son et al. [MNRAS 544, 975 (2025)] proposed that correlations between SNe Ia luminosity and progenitor age could introduce a systematic bias in the inferred luminosities, leading to revised distance moduli in the Pantheon+ and DES-SN5YR compilations. Motivated by this possibility, we test whether the age-bias-corrected SNe Ia Hubble diagrams comply with the luminosity-distance relation $d_L=c/H_0\,(1+z)\ln(1+z)$. We find that this one-parameter logarithmic relation provides a high-quality description of both datasets, with the Hubble constant $H_0$ as its sole free parameter. For Pantheon+ and DES separately, the relation yields lower $χ^2$ values than the two-parameter flat $Λ$CDM, with $Δχ^2=12.0$ and $2.1$, respectively. A joint likelihood analysis of both datasets yields $Δχ^2=17.1$, corresponding to $(Δ\text{AIC},Δ\text{BIC})=(19.1,25.2)$ in favor of the logarithmic relation. We further find that, after the age-bias correction, neither dataset requires higher-order corrections to the relation, whereas the Einstein-de Sitter cosmology is firmly rejected. These results indicate that the closed-form relation $d_L=c/H_0\,(1+z)\ln(1+z)$ provides a viable one-parameter description of progenitor age-bias-corrected SNe Ia Hubble diagrams. Its asymptotic behavior $d_L\propto z\,\ln z$ naturally accounts for the excess distance moduli observed at high redshift. Should the progenitor age-bias correction be confirmed, the logarithmic relation can be stringently tested using larger samples of SNe Ia within $1\lesssim z\lesssim2$, where it already departs markedly from flat $Λ$CDM.
