Gravitational-Wave Detector Networks: Standard Sirens on Cosmology and Modified Gravity Theory

We construct the catalogues of standard sirens (StS) based on the future gravitational wave (GW) detector networks, i.e., the second-generation ground-based advanced LIGO+advanced Virgo+KAGRA+LIGO-India (HLVKI), the third-generation ground-based Einstein Telescope+two Cosmic Explorer (ET+2CE), and the space-based LISA+Taiji. From the corresponding electromagnetic (EM) counterpart detectors for each networks, we sample the joint GW+EM detections from the probability to construct the Hubble diagram of standard sirens for 10 years detections of HLVKI, 5 years detections of ET+2CE, and 5 years of detections of LISA+Taiji, which we estimate would be available and released in the 2030s. Thus we construct a combined Hubble diagram from these ground and spaced-based detector networks to explore the expansion history of our Universe from redshift 0 to 7. We give a conservative and realistic estimation of the catalogue and Hubble diagram of GW standard sirens and their potential on studying cosmology and modified gravity theory in the 2030s. We adopt two strategies for the forecasts. One is the traditional model-fitting Markov-Chain Monte-Carlo method (MCMC). The results show that the combined StS alone can constrain the Hubble constant at the precision level of $0.34\%$, 1.76 times more tightly than the current most precise measurement from \textit{Planck}+BAO+Pantheon. The joint StS with current EM experiments will improve the constraints of cosmological parameters significantly. The modified gravity theory can be constrained with $0.46\%$ error from the GW propagation. In the second strategy, we use the machine-learning nonparametric reconstruction techniques, i.e., the Gaussian process (GP) with the Artificial Neural Networks (ANN) as a comparison. GP reconstructions can give comparable results with MCMC. We anticipate more works and research on these topics.