横向重子声学振荡（BAO）校准中的一个盲区
A blind spot in transverse BAO calibration
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中文总结 AI 辅助
该研究发现横向BAO校准存在与$r_{\rm d} h$简并的盲区，提出通过斜率为$\varepsilon$的一致性检验诊断横向BAO测量链的不一致，应用于SDSS两汇编发现其一与1偏差达3.8σ，两汇编差异达3.9σ。
中文摘要 AI 辅助
横向重子声学振荡（BAO）测量越来越多地用于宇宙学推断，其存在一种任何此类推断都无法约束的校准：横向BAO尺度的恒定误差与组合量$r_{\rm d} h$完全简并，它不会改变拟合优度且能使恢复的参数看似合理，因此仅使用这些测量的任何分析都无法察觉该误差。径向BAO部分通过积分提供$D_{\rm M}/r_{\rm d}$，无需参考$H_0$或任何膨胀率模型，从而消除了这种简并。在平坦的弗里德曼-勒梅特-罗伯逊-沃尔克（FLRW）几何中，两个部分的关系是恒等式，因此声视界和暗能量状态方程也会抵消。该恒等式的积分形式将一致性检验简化为一条直线，其斜率测量相对横向校准$\varepsilon$。$\varepsilon = 1$的偏差既不能由任何暗能量模型产生，也不能由空间曲率产生，它表明的是测量链而非宇宙学的不一致。我们将该检验应用于两个主要的SDSS横向BAO汇编，得到$\varepsilon$分别为$1.073 \pm 0.021$和$1.021 \pm 0.029$：前者使用已发表的独立误差与1的差异达到$3.8\sigma$，后者与1一致；两个汇编本身的差异为$(5.4 \pm 1.4)\\%$，即$3.9\sigma$，且偏移在红移中恒定。该检验为当前及未来的角BAO测量提供了直接诊断工具。
英文摘要
Transverse baryon acoustic oscillation (BAO) measurements are increasingly used for cosmological inference, and carry a calibration that no such inference can constrain. A constant error in the transverse BAO scale is exactly degenerate with the combination $r_{\rm d} h$: it leaves the goodness of fit unchanged and the recovered parameters plausible, and is therefore invisible to any analysis that uses these measurements alone. The radial BAO sector removes this degeneracy, supplying $D_{\rm M}/r_{\rm d}$ by integration without reference to $H_0$ or to any model for the expansion rate. In flat Friedmann--Lemaître--Robertson--Walker (FLRW) geometry the relation between the two sectors is an identity, so the sound horizon and the dark-energy equation of state cancel as well. An integrated form of this identity reduces the consistency test to a straight line, whose slope measures a relative transverse calibration $\varepsilon$. A departure from $\varepsilon = 1$ cannot be produced by any dark-energy model, nor by spatial curvature: it indicates an inconsistency in the measurement chain rather than in the cosmology. We apply the test to the two main SDSS transverse BAO compilations, which give $\varepsilon = 1.073 \pm 0.021$ and $1.021 \pm 0.029$. The first differs from unity at $3.8σ$ using the published independent errors, while the second is consistent with unity. The two compilations themselves differ by $(5.4 \pm 1.4)\%$, or $3.9σ$, and the offset is constant in redshift. The test provides a direct diagnostic for current and future angular BAO measurements.
