哈勃参量H(z)是近10年来，在宇宙学参量限制上日益得到广泛应用的另一重要观测量，它表征了宇宙在任意时刻t(或红移z处)的膨胀率，它是所有宇宙学观测量中唯一能够直接度量宇宙膨胀历史的物理量。哈勃参量H(z)最大优势是无需通过积分就可以直接与宇宙学模型建立联系，而超新星光度距离通过关于H(z)的积分，建立了与宇宙学参量的依赖关系。在本论文中，我们发挥哈勃参量的优势，把现有的43个哈勃参量观测数据(OHD)用于宇宙中微子特性和Rh = ct 宇宙模型限制中。
       第一，为了探索宇宙中微子的性质，即中微子质量(∑mν)之和以及中微子有效代数(Ne?)，在ΛCDM模式下，考虑到观测哈勃参量数据(OHD)在约束宇宙学参量方面的能力, 我们利用OHD来约束宇宙中微子的性质，并且把∑mν 和Ne?的效应考虑在精确的H(z)函数中。首先，我们在现有的43个OHD之外模拟新的OHD。根据哈勃常数H0(即今天的H(z)值)、重子声学振荡(BAO)、 Sandage-Leob (SL)检验和宇宙微波背景辐射(CMB)的测量结果，我们假设OHD的观测精度可达2% ，红移值 0 < z . 5。其次，利用从基准模型得到的模拟的H(z) 数据，我们对∑mν 和Ne?这两个参数进行了约束。当所有其他参数设置为自由时，我们得到∑mν < 0.196 eV (95%)和Ne? = 2.984 ± 0.826 (68%)；当将 Ne?固定为标准基线3.046 时，结果得到∑mν < .240 eV (95%)。这些使用模拟数据的约束结果，比现有的OHD得到的结果要严格得多，这使得OHD在约束宇宙学参数方面的应用前景随着其精度和数量的增加而更加广阔和有希望。
       第二，我们使用三种不同的数据集，特别是来自宇宙时钟的H(z)测量值，HII星系哈勃图和重构的类星体核角大小测量值，对三个平坦宇宙模型，即Rh = ct,ΛCDM, 和wCDM宇宙进行了联合分析。对于Rh = ct宇宙，哈勃常数H0的1σ最佳拟合值为H0=62.336 ± 1.464 km/s/Mpc，该值与之前基于单个数据集的最佳拟合测量值～ 63km/s/Mpc相匹配。对于ΛCDM，我们拟合推断出的哈勃常数值H0 = 67.013 ± 2.578 k-m/s/Mpc，该值与使用Cepheid 变星的本地测量值相比，与Planck优化结果更为一致，并且物质密度?m = 0.347 ± 0.049同样与其Planck值在1σ内一致。对于wCDM宇宙，优化拟合得到的参数H0 = 64.718 ± 3.088 km/s/Mpc, ?m = 0.247 ± 0.108 和w = ?0.693 ± 0.276，也与Planck一致。使用贝叶斯信息准则对这三种模型进行直接比较表明，相比于另外两个宇宙模型，联合分析结果以～ 97% 比. 3%可能性，更加支持Rh = ct宇宙。

The Hubble parameter H(z) is another important observational measurement which has been widely used in cosmological parameter constraint in recent 10 years. It represents the expansion rate of the universe at any time of t (or redshift Z), which is the only physical quantity that can directly measure the expansion history of the universe. The biggest advantage of the Hubble parameter H(z)is that it can be directly linked to the cosmological model without integration, while the supernova luminosity distance is dependent on the cosmological parameters through an integral about H(z)。 In this paper, we take advantage of the Hubble parameter, and use the current 43 observational Hubble parameter data (OHD) to study the properties of cosmic neutrinos and the constraints on the Rh=ct universe model.

Firstly, in order to explore the properties of the cosmic neutrinos, i.e. the sum of the neutrino mass (∑mν) and the effective number of neutrino species (Neff), taking effect on the Hubble expansion rate H(z) and the power of observational Hubble parameter data (OHD) in constraining the cosmological parameters under the ΛCDM model, we utilize OHD in constraining the properties of the cosmic neutrinos and applying the accurate H(z) function with ∑mν and Neff. First, we simulate new OHD beyond existing 43 OHD. According to the predictions of measurements of H0 (the current H(z) value), baryonic acoustic peak (BAO), Sandage-Leob (SL) test and cosmic microwave background (CMB), we assume observational accuracy up to 2% and redshift 0 < z ≤5. With the simulated H(z) data obtained from the fiducial model, we constrain the parameters including ∑mν and Neff. When all parameters are set free, ∑mν < 0.196eV(95%) and Neff=2.984±0.826 (68%) are obtained, and when fixing Neff as the standard baseline 3.046, we attain ∑mν < 0.240 eV(95%). These constraining results are much tighter than the ones obtained by the current OHD, which makes the prospect of OHD in constraining cosmological parameters more promising as its accuracy and quantity grows.

Secondly, we use three different data sets, specifically H(z) measurements from cosmic chronometers, the HII-galaxy Hubble diagram, and reconstructed quasar-core angular-size measurements, to perform a joint analysis of three flat cosmological models: the Rh=ct Universe, ΛCDM, and wCDM. For Rh=ct, the 1σ best-fit value of the Hubble constant H0 is 62.336±1.464 km/s/Mpc, which matches previous measurements (~63km/s/Mpc) based on best fits to individual data sets. For ΛCDM, our inferred value of the Hubble constant, H0=67.013±2.578km/s/Mpc, is more consistent with the Planck optimization than the locally measured value using Cepheid variables, and the matter density ?m  =0.347±0.049 similarly coincides with its Planck value to within 1σ. For wCDM, the optimized parameters are H0=64.718±3.088km/s/Mpc, ?m =0.247±0.108 and w=-0.693±0.276, also consistent with Planck. A direct comparison of these three models using the Bayesian Information Criterion shows that the Rh=ct universe is favored by the joint analysis with a likelihood of ~ 97%  versus ≤3% for the other two cosmologies.