AI 中文总结
研究引力波宇宙学的$H_0$约束问题，提出CosmoPyro代码用高斯过程建模质量分布，基于GWTC-5得到$h$的结果，其$H_0$测量与LVK结果一致且稳健。
AI 中文摘要
对恒星质量致密并合的引力波（GW）观测可直接测量光源的光度距离，结合光源红移后，这些测量能约束宇宙当前的膨胀率——哈勃常数$H_0$，或其归一化形式$h=H_0/[100\rm{\thinspace km\thinspace s^{-1}\thinspace Mpc^{-1}}]$。对于多数引力波信号，预计无法获得电磁红移测量，但引力波信号本身依赖于红移后的探测器框架质量。假设存在光源框架质量分布，即可对每个光源进行红移估计；将红移估计与距离测量结合，能为单个光源提供对$H_0$的弱约束，且该约束会随目录中光源数量的增加而收紧。然而，光源框架质量分布的形状事先未知，过往研究依赖参数化模型（带高斯分量的分段幂律）和一维高斯过程。本文提出CosmoPyro，一种完全可微的分层贝叶斯推断代码，使用一维或二维高斯过程对质量分布建模。利用最新引力波瞬变目录（GWTC-5），我们得到一维情形下$h=0.66^{+0.17}_{-0.20}$、二维情形下$h=0.57^{+0.20}_{-0.15}$（中位数及1σ不确定度）。尽管推断出的质量分布存在明显差异，两种模型给出的$H_0$值均与最新LVK测量结果在1σ范围内一致。虽然我们的主要结果对高斯过程功率谱超参数进行了边缘化处理，但当固定这些超参数的范围与测量不确定度相当，测量结果仍具有稳健性。
英文摘要
Gravitational-wave (GW) observations of stellar-mass compact binary coalescences directly measure the source luminosity distance. Combined with the source redshift, these measurements constrain the current expansion rate of the Universe, the Hubble constant, $H_0$, or $h=H_0 / [100 \,{\rm km \,s^{-1} \, Mpc^{-1}}]$. For most GW signals no electromagnetic redshift measurement is expected, but the GW signal itself depends on the redshifted (detector-frame) masses. Assuming a source-frame mass distribution therefore enables a redshift estimate for each source. Combining the redshift estimates with the distance measurements provides a weak constraint on $H_0$ for each individual source that tightens with the number of sources in the catalog. However, the shape of the source-frame mass distribution is not known a priori, and previous work has relied on parametric models (piecewise power-laws with Gaussian components), and one-dimensional Gaussian processes. Here, we introduce CosmoPyro, a fully differentiable hierarchical Bayesian inference code that models the mass distribution using either one- or two-dimensional Gaussian processes. With the latest GW transient catalog (GWTC-5) we find $h = 0.66^{+0.17}_{-0.20}$ and $h = 0.57^{+0.20}_{-0.15}$ (median with $1σ$ uncertainty), for the one- and two-dimensional case, respectively. Despite the noticeably different inferred mass distributions, both models yield $H_0$ values consistent with the latest LVK measurements within $1 σ$. While our main results marginalize over the Gaussian-process power-spectrum hyperparameters, the measurement is also robust against fixing these hyperparameters over a range comparable to their measured uncertainty.
Comments18 + 23 pages, 7 + 7 figures
