宇宙加速膨胀是过去二十多年最伟大的现代宇宙学发现之一，刷新了对宇宙演化的基本认识，并挑战了基础物理学关于能量存在形式的基本认识。虽然暗能量模型是宇宙加速膨胀机制最具共识的理论解释，但暗能量的本质依然是物理学面临的最大难题之一。以宇宙学常数-冷暗物质模型（ΛCDM)为基准的宇宙学模型，以及动力学暗能量模型、相互作用暗能量模型、修改引力理论等都在解释宇宙加速膨胀机制上不懈努力，然而这些模型间的区别却并不明显。

宇宙学的发展与观测方法的进步密不可分，以Ia型超新星和宇宙微波背景辐射为代表的观测标志着我们已经进入精确宇宙学的时代。随着观测精度的不断提升，现代宇宙学正面临着重大危机。早期宇宙观测所获得的新数据表明，当前宇宙的膨胀速度比宇宙学标准模型所预测的要快得多，与晚期宇宙探针的测量结果之间存在巨大的不一致。这使得宇宙学面临着理论和观测方面的巨大挑战，无论是蕴含着“新物理”的潜在可能性，还是在迫切需要发展出更多的精确宇宙探针方面。

为了揭开宇宙加速膨胀机制和探究哈勃常数危机，发展宇宙学模型无关的高精度晚期宇宙探针是最为重要的研究方向之一。宇宙学红移漂移和观测哈勃参量是宇宙膨胀加速度最为直接的两个测量探针。本文主要研究它们的观测方法及其对于哈勃常数测量和宇宙学模型区分的应用。

宇宙学红移漂移是一个极微小的物理量，成功测量这种信号面临诸多挑战。窄带的中性氢HI吸收线系统是一类十分理想的观测目标，我们可以通过地基射电望远镜在较宽的红移范围内测得大量样本，这对于提高红移漂移测量精度及其对宇宙学模型区分的意义重大。得益于500米球面射电望远镜FAST的超大巡天面积和超高灵敏度，我们面向其多科学目标共生扫描巡天（CRAFTS)做出预测，认为FAST望远镜可以作为盲巡HI吸收线系统的科学重器。针对\dot{z} ~ 10^-10 decade^-1量级的宇宙红移漂移率测量精度要求，我们提出了盲搜索和目标观测相结合的观测模式。随后，我们开展了首次目标观测，验证了我们的高精度谱线红移测量数据处理流程，为后续观测目标选择标准、优化观测参数设定、提升测量精度等探明了方向。

观测哈勃参量的测量主要有星系微分年龄法和径向重子声波震荡大小两个方法，我们重点研究宇宙学模型独立的前者。我们对350个从大型早型星系普查（LEGA-C）的第二次光谱巡天数据发布中挑选出来的大质量和被动星系进行了全谱拟合，并得出它们的恒星年龄、金属度和恒星形成历史。我们广泛地测试了我们的结果对尘埃的可能贡献的依赖性、噪声和信号的校准、以及结合光谱信息和测光数据；我们还确定了结果正确收敛的指标，包括后验分布的形状、特定光谱特征的分析、以及对观测光谱的正确重构。我们得到了明显与标准宇宙学模型中的老化相适应的年龄-红移演化趋势，显示出明显的星系形成缩减图景，相对于较低质量的星系(z_f~2.5)，较大质量的星系是在较高的红移下形成的(z_f~2)。从这些数据中，我们测量了这群宇宙计时器的不同老化程度，得出了哈勃参数的新测量值  H(z=0.8)=113.1 +- 15.1(stat. )_-11.3^+29.1( syst.  ) km s^-1 Mpc^-1。我们首次比较了用两种完全不同的方法，即全谱拟合（这项研究）和Lick线指数分析，在同一样本上测量的宇宙计时器的不同年龄，众所周知后者与星族的年龄和金属丰度相关。尽管所考虑的数据、假设和模型非常不同，在绝对年龄上存在一个可以理解的偏移，但事实证明这两种方法测量H(z)是极其兼容的，证明了该方法的稳健性。

充分应用上述两种探针模型独立的特点，我们提出了直接测量哈勃常数的新方法。基于哈勃常数与红移漂移量及哈勃参量的理论关系，通过红移对齐的统计方法，哈勃常数将成为一个可以直接计算的量，该方法是应用哈勃定律的本地距离阶梯法、宇宙学模型依赖的早期宇宙测量方法、以及模型无关的哈勃参量重构方法的有力补充。此外，联合以上两种探针还可以充分降低统计误差，进而最终实现高精度的H₀直接测量。基于同样的考量，哈勃参量作为距离指示体用于定标哈勃图的研究也日益成为新的研究热点，我们对该方法也做出进步一改进，放开了平坦宇宙假设，并考虑了重构协方差对于模型参数限制的影响，充分提高了相关结果的可靠性。
 

The accelerated expansion of the Universe is one of the most significant discoveries made in the past two decades in modern cosmology, which has refreshed our fundamental understanding of the evolution of the Universe and challenged fundamental physics about the existence of forms of energy. The dark energy model is the most widely accepted theoretical explanation of the mechanism of the accelerating expansion of the Universe. Yet, the question of the nature of dark energy remains one of the greatest puzzles in physics. Cosmological models based on the cosmological constant-cold dark matter model (ΛCDM), as well as dynamic dark energy models, interacting dark energy models, and modified gravity theories, have been strenuously studied to explain the mechanism of the accelerated expansion of the Universe, while the degeneracies between models remain.

The advancement of cosmology cannot be separated from the progress of observation methods. The observations represented by the type Ia supernova and cosmic microwave background radiation mark that we have entered the era of precision cosmology. At the same time, modern cosmology is going through a major crisis as observations are becoming more precise. New observations about the early Universe show that the present-day Universe is expanding faster than predicted by the standard model of cosmology and that there is a huge inconsistency between the measurements of the late-time cosmic probes. Theoretical and observational challenges to cosmology are enormous, both in terms of the potential for "new physics" and the urgent need to develop more accurate cosmological probes.

Developing cosmological model-independent high-precision late-time cosmological probes is one of the most important research directions to unravel the mechanism of the Universe's accelerated expansion and investigate the Hubble constant crisis. The cosmological redshift drift and the observation of the Hubble parametric are the two most direct probes for measuring the acceleration of the expansion of the Universe. This paper focuses on their observational methods and applications in Hubble constant measurements and cosmological model discrimination.

Cosmic redshift drift is a minuscule quantity, and succeeding in measuring this signal faces many challenges. The narrow-band neutral hydrogen HI absorption line system is a highly desirable type of observational target, and we can measure a large sample over a wide redshift range with ground-based radio telescopes, which is significant for improving the accuracy of redshift drift measurements and their implications for cosmological model discrimination. Thanks to the broad sky coverage and high sensitivity of the 500-m spherical radio telescope FAST, we predict that the FAST telescope can serve as a scientific heavyweight for the blind survey of the HI absorption line system, based on the Commensal Radio Astronomy FAST Survey (CRAFTS). Aiming to measure the cosmic redshift drift rate at the precision of \dot{z} ~ 10^-10 decade^-1, we propose combined observation mode with blind-searching and targeted observation. We then conduct the first target observation to validate our high-precision redshift measurement data processing pipeline, and to explore the optimization direction for subsequent target selection criteria, observation parameter settings, and improvement of measurement accuracy.

The galaxy differential age technique and the radial BAO magnitude are the two basic approaches for measuring the Hubble parameters, and we focus on the former for cosmological model independence consideration. We perform a full-spectrum fitting of 350 massive and passive galaxies selected as cosmic chronometers from the LEGA-C ESO public survey to derive their stellar ages, metallicities, and star-formation histories. We extensively test our results by assessing their dependence on the possible contribution of dust, calibration of noise and signal, and the use of photometric data in addition to spectral information; we as well identify indicators of the correct convergence of the results, including the shape of the posterior distributions, the analysis of specific spectral features, and the accurate reproduction of the observed spectrum. We derive a clear age-redshift trend compatible with the aging in a standard cosmological model, showing a clear downsizing pattern, with more massive galaxies being formed at higher redshift (z_f~2.5) with respect to lower massive ones (z_f~2). From these data, we measure the differential aging of this population of cosmic chronometers to derive a new measurement of the Hubble parameter, obtaining   H(z=0.8)=113.1 +- 15.1(stat. )_-11.3^+29.1( syst.  ) km s^-1 Mpc^-1. This analysis allows us, for the first time to compare the differential ages of cosmic chronometers measured on the same sample with two completely different methods, the full-spectrum fit (this work) and the analysis of Lick indices, known to correlate with the age and metallicity of the stellar populations. Albeit an understood offset in the absolute ages, the differential ages have proven to be extremely compatible between the two methods, despite the very different data, assumptions, and models considered, demonstrating the method's robustness.

Fully applying the model-independent characteristic of the above two probes, we propose a new method to measure the Hubble constant directly. Based on the theoretical relationship between the Hubble constant and the redshift drift and the Hubble parameter, the Hubble constant will become a directly calculable quantity through a statistical method of redshift alignment, which is different from the local distance ladder applying Hubble's law, the cosmological model-dependent early Universe measurement methods, and the model-independent reconstruction of Hubble parameter. In addition, combining the two measurements can sufficiently reduce the statistical error and thus eventually achieve a high precision direct H₀ measurement. Based on the same consideration, the study of the Hubble parameter as a distance indicator for calibrating Hubble diagrams is also known as a new research hotspot, and we improve the method by setting free of the flat Universe assumption, as well as considering the influence of the reconstruction covariance on the model parameter constraints, which fully improves the reliability of the related results.