利用爱因斯坦望远镜引力波模拟数据估算宇宙学参数
Estimating cosmological parameters by the simulated data of gravitational waves from the Einstein Telescope
摘要：
利用第三代引力波探测器--爱因斯坦望远镜，研究了引力波（GW）作为标准警报器对宇宙学参数的约束能力。我们模拟了从100到1000 GW事件的光度距离和红移测量。我们使用两种不同的算法来约束宇宙学参数。对于哈勃常数$H_0$和暗物质密度参数$Ω_m$，我们采用马尔可夫链蒙特卡罗方法。我们发现，约500-600 GW的事件，我们可以约束哈勃常数的准确性与\textit{Planck}温度数据和\textit{Planck}透镜相结合的结果，而对于暗物质密度，GWs单独似乎不能提供的约束，作为好的哈勃常数; 1000 GW的事件的灵敏度是略低于\textit{Planck}数据。它应该需要超过1000个事件才能匹配\textit{Planck}灵敏度。然而，为了分析暗能量更复杂的动力学性质，即，在状态方程$w$的基础上，我们采用了一种新的非参数方法：高斯过程。我们可以直接从观测到的每一次红移的光度距离重建$w$。在低红移区，我们发现，约700 GW的事件可以给出的$w(z)$的约束相媲美的一个常数$w$的\textit{Planck}数据与Ia型超新星的约束。这些结果表明，引力波作为探测宇宙学参数的标准警报器可以为现有的实验提供一个独立的和补充的选择。
英文摘要：
We investigate the constraint ability of the gravitational wave (GW) as the standard siren on the cosmological parameters by using the third-generation gravitational wave detector: the Einstein Telescope. We simulate the luminosity distances and redshift measurements from 100 to 1000 GW events. We use two different algorithms to constrain the cosmological parameters. For the Hubble constant $H_0$ and dark matter density parameter $Ω_m$, we adopt the Markov chain Monte Carlo approach. We find that with about 500-600 GW events we can constrain the Hubble constant with an accuracy comparable to \textit{Planck} temperature data and \textit{Planck} lensing combined results, while for the dark matter density, GWs alone seem not able to provide the constraints as good as for the Hubble constant; the sensitivity of 1000 GW events is a little lower than that of \textit{Planck} data. It should require more than 1000 events to match the \textit{Planck} sensitivity. Yet, for analyzing the more complex dynamical property of dark energy, i.e., the equation of state $w$, we adopt a new powerful nonparametric method: the Gaussian process. We can reconstruct $w$ directly from the observational luminosity distance at every redshift. In the low redshift region, we find that about 700 GW events can give the constraints of $w(z)$ comparable to the constraints of a constant $w$ by \textit{Planck} data with type Ia supernovae. Those results show that GWs as the standard sirens to probe the cosmological parameters can provide an independent and complementary alternative to current experiments.
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