作为爱因斯坦广义相对论预言之一，引力波打开了探索宇宙的全新观测窗口。从1916 年爱因斯坦预言了引力波的存在，又经历了长达一个世纪的时间来探测引力波。直到Advanced LIGO 在2015年9月14日成功探测到第一个引力波信号GW150914，开启了引力波天文学的大门。LIGO-VIRGO-KAGAR合作组在第三次观测结束前已经观测到90例由致密双星双向并合产生的引力波事例。产生引力波的起源是丰富多样的，不同引力波源产生的引力波会处于不同的频率范围内。LIGO、VIRGO和KAGAR是地面的引力波探测器，主要用于高频引力波的探测。我们研究的是低频引力波源，采用空间的引力波探测。未来空间引力波天文台将在毫赫频段上以极高的精度测量来自于超大质量双黑洞并合、极端质量比旋进、双白矮星旋进等天体源发射的引力波信号。超大质量双黑洞并合产生的引力波事件作为空间引力波探测的主要科学目标，适用于精确宇宙学的研究。
本文中我们搭建了用于毫赫兹频段的引力波数据模拟和参数估计系统，主要包括大质量双黑洞并合产生的引力波波形的生成、仪器的高斯噪声的生成、高阶模、利用时间延迟干涉方法计算引力波的响应以及基于贝叶斯方法的参数估计。空间引力波探测相比较地面引力波探测，会有更高的信噪比，因此有希望探测到高阶模的存在。我们研究了引力波高阶模对引力波参数限制的重要作用。引力波是多个模式的叠加，（2，2）模是最主要的模式，其他高阶模会相对较弱。研究不同模式的振幅与倾角之间的关系，可以发现不同模式对倾角的依赖性不同。考虑含高阶模的波形，光度距离和倾角的简并有可能被打破。另外空间引力波探测器之间的激光臂长不可能维持相等。因此采用时间延迟干涉方法计算引力波在探测器上的响应。结果表明，模拟了一个典型的大质量双黑洞并合的引力波源，建立简易的激光等臂长的解析轨道，与只用$(\ell,|m|)=(2,2)$ 模的情况相比，包含高阶模的情况下光度距离的限制精度大约提高了50倍。这说明引力波高阶模有效地破除了光度距离和倾角的简并。而且我们研究了LISA空间引力波探测对检验广义相对论的能力。LISA超强的灵敏度和来自于大质量双黑洞并合的强烈引力波信号，使得我们能够以相当高的信噪比探测致密双星的铃宕阶段。从结果表明，LISA探测来自大质量双黑洞并合的引力波，可以同时限制高阶模振幅与广义相对论预言的振幅之间的偏差参数，在$95\%$置信度的限制结果为$c_{21}=0.54^{+0.82}_{-1.05}$, $c_{32}=-0.65^{+3.02}_{-1.42}$, $c_{33}=0.56^{+0.79}_{-0.96}$ 和$c_{44}=1.57^{+3.22}_{-2.19}$。与LIGO探测的引力波事件GW190412对比，LISA空间引力波探测可以显著提高检验广义相对论的能力。此外，细致地讨论激光不等臂的数值轨道对信号响应和噪声功率谱密度的影响，然后模拟相同的数据并作参数估计。研究发现，A和E渠道信号响应和噪声功率谱密度对激光是否等臂并不敏感，T渠道上的对激光臂长的变化比较敏感。基于不等臂的数值轨道，T渠道上的信号平均响应和噪声功率谱密度在低频部分有一定程度的提高。
 考虑数值轨道，参数估计结果没有明显的变化。

此外，致密双星并合产生的引力波提供了限制哈勃常数的全新手段。通过模拟大质量双黑洞双黑洞并合产生的引力波波形，假设没有观测到引力波电磁对应体，我们利用“暗汽笛”的方法研究了“LISA-Taiji”引力波联合探测网络对哈勃常数的限制能力。研究表明不同红移和质量的双黑洞并合事件在联网观测或Taiji单独观测对哈勃常数的限制能力是不同的，其中也发现“LISA-Taiji”引力波联网观测由于能够以很高的精度对引力波事件进行定位，从而可以大大提高对哈勃常数的限制结果。我们还预言了针对不同黑洞形成模型，双黑洞并合事件分别由联网观测或Taiji单独观测1 年、3年、5 年的平均事件率。从统计结果来看，在5年的“LISA-Taiji”联网观测时间内，有希望对哈勃常数的限制提高到1%的精度，这对解决“哈勃危机”具有重要意义。

Gravitational waves(GWs), one prediction of Einstein's General Relativity(GR), open a new observational window to explore the nature of the universe. In 1916, Einstein predicted the existence of GWs, and it took another century to detect them. It was not until advanced LIGO successfully detected the first GW signal, GW150914, on Septeber 14, 2015, which opened the door to GW astronomy. The LIGO-VIRGO-KAGRA collaboration has detected 90 GWs from compact binary coalescence events up to the end of third observing run(O3). The origins of GWs are rich and diverse, and the GWs generated by different GW sources will be in different frequency ranges. LIGO, VIRGO and KAGAR are ground-based GW detectors, which are mainly used for high-frequency GW detection. We study low-frequency GW sources and use space-based GW detection. The future space-borne gravitational wave observatory will be able to measure the GW events in the millihertz band with unprecedented accuracy, which contains massive black hole binary(MBHB) mergers, extreme mass-ratio inspiral(EMRI) and white dwarf binaries, etc. MBHB mergers are one of the main scientific goals of the space-borne gravitational wave observatory, which are suitable for the precise cosmology studies.
We present a data simulation and parameter inference system for the gravitational wave measured in the millihertz band. This system includes the following features: the GW waveform originated from MBHB, the stationary instrumental gaussian noise, the higher-order harmonic modes, the full response function from the time delay interferometry (TDI) and parameter estimation based on the bayesian method. Space GW detection will have a higher signal-to-noise ratio compared to ground-based GW detection, and thus holds promise for detecting the presence of higher-order modes. We investigate the important role of higher-order modes of GWs on the GW parameter estimation. GWs are the superposition of multiple harmonic modes. The $(\ell,|m|=(2,2))$ harmonics is the dominant harmonic. Other higher-order modes are relatively weak. Studying the relationship between the amplitude of different modes and inclination angle, it can be found that the dependence of different modes on the inclination angle is different.
Considering waveforms containing higher-order modes, the degeneracy between the luminosity distance and inclination angle can be broken. In addition, the laser arm lengths between space GW detectors cannot be kept equal. Therefore the response of GWs on the detectors is calculated using the time delay interferometry technique. The results show that we simulate a typical MBHB source, build simple resolved orbits with laser equal arm length and the luminosity distance estimation precision can be improved roughly by a factor of 50 including higher-order modes, compared with the case with only the leading order$(\ell,|m|)=(2,2)$mode. This indicates that the higher-order modes of GWs effectively break the degeneracy between the luminosity distance and inclination angle. Moreover, we investigate the capability of testing general relativity by LISA space GW detectors. The superb sensitivity of LISA and robust GW signals from MBHB allow us to detect the ringdown phase of the compact binary coalescence process with a fairly high signal-to-noise ratio. Our results show that the GW from MBHB detected by LISA can simultaneously constrain the deviation parameters between the amplitude of the higher-order modes and the amplitude predicted by GR with a $95\%$ confidence level of$c_{32}=-0.65^{+3.02}_{-1.42}$, $c_{33}=0.56^{+0.79}_{-0.96}$ and $c_{44}=1.57^{+3.22}_{-2.19}$. In contrast to GW190412 detected by LIGO, the LISA space GW detection can significantly improve the ability to test GR. In addition, we meticulously discuss the effect of the numerical orbit with the laser unequal arm length on the signal response and noise power spectral density, and then simulate the same data and make parameter estimation. It was found that the signal response and noise power spectral density in A and E channels are not sensitive to whether the laser arm lengths are equal, and those on the T channel are more sensitive to changes in the laser arm length. Based on the numerical orbit with unequal arm lengths, the average signal response and noise power spectral density on the T channel are increased to some extent in the low-frequency part. Considering the numerical orbit, there is no significant change in the parameter estimation results.
Moreover, GWs from compact binary coalescence events provide a novel means of limiting the Hubble parameter. By simulating the GWs generated by the merger of MBHB, we investigated the ability of the LISA-Taiji network to estimate the Hubble parameter using the dark sirens, assuming that no electromagnetic counterpart is observed. The result shows that the Hubble parameter is constrained differently for the MBHB mergers at different redshifts and masses by the LISA-Taiji network and Taiji alone. It is found that the LISA-Taiji network can significantly improve the constraint on the Hubble parameter because it will be able to localise the GW events with unprecedented accuracy. We also predict the averaged event numbers of massive black hole binary mergers in 1-year, 3-year and 5-year observation times of network observations and Taiji observations alone, respectively for different black hole formation models. By including several statistical and instrumental noises, we show that within 5 years operation time, the LISA-Taiji network is able to constrain the Hubble parameter within $1\%$ accuracy, which is important for solving the Hubble tension.