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LISA and Taiji are expected to form a space-based gravitational-wave (GW) detection network in the future. In this work, we make a forecast for the cosmological parameter estimation with the standard siren observation from the LISA-Taiji network. We simulate the standard siren data based on a scenario with configuration angle of 40° between LISA and Taiji. Three models for the population of massive black hole binary (MBHB), i.e., pop III, Q3d, and Q3nod, are considered to predict the events of MBHB mergers. We find that, based on the LISA-Taiji network, the number of electromagnetic (EM) counterparts detected is almost doubled compared with the case of single Taiji mission. Therefore, the LISA-Taiji network’s standard siren observation could provide much tighter constraints on cosmological parameters. For example, solely using the standard sirens from the LISA-Taiji network, the constraint precision of H 0 could reach 1.3%. Moreover, combined with the CMB data, the GW-EM observation based on the LISA-Taiji network could also tightly constrain the equation of state of dark energy, e.g., the constraint precision of w reaches about 4%, which is comparable with the result of CMB+BAO+SN. It is concluded that the GW standard sirens from the LISA-Taiji network will become a useful cosmological probe in understanding the nature of dark energy in the future.

In the coming decades, the space-based gravitational-wave (GW) detectors such as Taiji, TianQin, and LISA are expected to form a network capable of detecting millihertz GWs emitted by the mergers of massive black hole binaries (MBHBs). In this work, we investigate the potential of GW standard sirens from the Taiji-TianQin-LISA network in constraining cosmological parameters. For the optimistic scenario in which electromagnetic (EM) counterparts can be detected, we predict the number of detectable bright sirens based on three different MBHB population models, i.e., pop III, Q3d, and Q3nod. Our results show that the Taiji-TianQin-LISA network alone could achieve a constraint precision of 0.9% for the Hubble constant, meeting the standard of precision cosmology. Moreover, the Taiji-TianQin-LISA network could effectively break the cosmological parameter degeneracies generated by the CMB data, particularly in the dynamical dark energy models. When combined with the CMB data, the joint CMB+Taiji-TianQin-LISA data offer σ ( w ) = 0.036 in the w CDM model, which is close to the latest constraint result obtained from the CMB+SN data. We also consider a conservative scenario in which EM counterparts are not available. Due to the precise sky localizations of MBHBs by the Taiji-TianQin-LISA network, the constraint precision of the Hubble constant is expected to reach 1.2%. In conclusion, the GW standard sirens from the Taiji-TianQin-LISA network will play a critical role in helping solve the Hubble tension and shedding light on the nature of dark energy.

Background Tai chi, also called taiji or tai chi chuan, is a form of mind–body exercise that originated from China. It combines Chinese martial arts and meditative movements that promote balance and healing of the mind and body, involving a series of slowly performed, dance-like postures that flow into one another. As it comprises mental concentration, physical balance, muscle relaxation, and relaxed breathing, tai chi shows great potential for becoming widely integrated into the prevention and rehabilitation of a number of medical and psychological conditions. Purpose A growing body of clinical research has begun to evaluate the efficacy of tai chi as a therapy for a variety of health issues. A systematic review and meta-analysis were carried out on randomized controlled trials (RCTs) and quasi-experimental (Q-E) trials that studied the effects of tai chi on psychological well-being. Method Drawn from English and Chinese databases, 37 RCTs and 5 Q-E studies published up to May 31, 2013 were included in the systematic review. The methodological quality of the RCTs was evaluated based on the following criteria: adequate sequence generation, allocation concealment, blinding, completeness of outcome data, selective reporting, and other potential biases. Statistical analyses were performed using Review Manager version 5.0. Results The studies in this review demonstrated that tai chi interventions have beneficial effects for various populations on a range of psychological well-being measures, including depression, anxiety, general stress management, and exercise self-efficacy. Meta-analysis was performed on three RCTs that used depression as an outcome measure (ES = −5.97; 95 % CI −7.06 to −4.87), with I 2  = 0 %. Conclusion In spite of the positive outcomes, the studies to date generally had significant methodological limitations. More RCTs with rigorous research design are needed to establish the efficacy of tai chi in improving psychological well-being and its potential to be used in interventions for populations with various clinical conditions.

The direct observation of gravitational waves (GWs) opens a new window for exploring new physics from quanta to cosmos and provides a new tool for probing the evolution of universe. GWs detection in space covers a broad spectrum ranging over more than four orders of magnitude and enables us to study rich physical and astronomical phenomena. Taiji is a proposed space-based gravitational wave (GW) detection mission that will be launched in the 2030s. Taiji will be exposed to numerous overlapping and persistent GW signals buried in the foreground and background, posing various data analysis challenges. In order to empower potential scientific discoveries, the Mock Laser Interferometer Space Antenna (LISA) data challenge and the LISA data challenge (LDC) were developed. While LDC provides a baseline framework, the first LDC needs to be updated with more realistic simulations and adjusted detector responses for Taiji’s constellation. In this paper, we review the scientific objectives and the roadmap for Taiji, as well as the technical difficulties in data analysis and the data generation strategy, and present the associated data challenges. In contrast to LDC, we utilize second-order Keplerian orbit and second-generation time delay interferometry techniques. Additionally, we employ a new model for the extreme-mass-ratio inspiral waveform and stochastic GW background spectrum, which enables us to test general relativity and measure the non-Gaussianity of curvature perturbations. Furthermore, we present a comprehensive showcase of parameter estimation using a toy dataset. This showcase not only demonstrates the scientific potential of the Taiji data challenge (TDC) but also serves to validate the effectiveness of the pipeline. As the first data challenge for Taiji, we aim to build an open ground for data analysis related to Taiji sources and sciences. More details can be found on the official website (taiji-tdc.ictp-ap.org).

To increase the interferometric measurement resolution in the Taiji program, we present a noise suppression method in this paper. Taking the specific micro-force perturbation and temperature fluctuation in the Taiji-1 interferometer as an example, we set up and experimentally verified the corresponding transfer function to quantify the effect of both noise sources on the interferometric results. Consistent results were obtained between the numerical and experimental results for the transfer function. It is instructive to eliminate the micro-force perturbations and temperature fluctuations during on-orbit interferometric measurement for as long as the acquisition of the force or temperature distribution of related surfaces and the corresponding transfer functions. This indicates that the method can be used for noise sensing and more in the field of noise elimination and measurement resolution improvement for future Taiji program interferometers.

A kind of full-function two-sided optical bench interferometer (OBI) is designed to meet the practical requirements of the Taiji Program for space gravitational wave detection. The main optical paths are arranged on the A-side for transmission and interference, and other optical paths and electronic devices are placed on the B-side. According to the design scheme, we successfully constructed two OBIs by using hydrogen–oxygen catalytic stress-free bonding technology. When the OBI is installed and adjusted, the position and Angle error of the interference beam are controlled within 30 μm and 50 μrad through the self-designed precision mechanical clamping mechanism and beam position measuring device. The built OBI was placed on the vibration isolation platform in the vacuum tank for the stability test. The test results show that the noise of the OBI is less than 10 pm/√Hz in the frequency band of 0.1 Hz to 1 Hz, which meets the noise budget requirements of the Taiji Pathfinder in the middle- and high-frequency band.

For space-based gravitational wave detection, a laser interferometric measurement system composed of a three-spacecraft formation offers the most rewarding bandwidth of astrophysical sources. There are no oscillators available that are stable enough so that each spacecraft could use its own reference frequency. The conversion between reference frequencies and their distribution between all spacecrafts for the synchronization of the different metrology systems is the job of the inter-spacecraft frequency setting strategy, which is important for continuously acquiring scientific data and suppressing measurement noise. We propose a hierarchical optimization algorithm to solve the frequency setting strategy. The optimization objectives are minimum total readout displacement noise and maximum beat-note frequency feasible range. Multiple feasible parameter combinations were obtained for the Taiji program. These optimized parameters include lower and upper bounds of the beat note, sampling frequency, pilot tone signal frequency, ultrastable clock frequencies, and modulation depth. Among the 20 Pareto optimal solutions, the minimum total readout displacement noise was 4.12 pm/Hz, and the maximum feasible beat-note frequency range was 23 MHz. By adjusting the upper bound of beat-note frequency and laser power transmitted by the telescope, we explored the effects of these parameters on the minimum total readout displacement noise and optimal local laser power in greater depth. Our results may serve as a reference for the optimal design of laser interferometry system instrument parameters and may ultimately improve the detection performance and continuous detection time of the Taiji program.

Gravitational wave (GW) astronomy is witnessing a transformative shift from terrestrial to space-based detection, with missions like Taiji at the forefront. While the transition brings unprecedented opportunities for exploring massive black hole binaries (MBHBs), it also imposes complex challenges in data analysis, particularly in parameter estimation amidst confusion noise. Addressing this gap, we utilize scalable normalizing flow models to achieve rapid and accurate inference within the Taiji environment. Innovatively, our approach simplifies the data’s complexity, employs a transformation mapping to overcome the year-period time-dependent response function, and unveils additional multimodality in the arrival time parameter. Our method estimates MBHBs several orders of magnitude faster than conventional techniques, maintaining high accuracy even in complex backgrounds. These findings significantly enhance the efficiency of GW data analysis, paving the way for rapid detection and alerting systems and enriching our ability to explore the universe through space-based GW observation.

The emergence of the “Three Caverns” 三洞 thought was a critical step in the formation of medieval Daoism. It proposed the first viable approach to integrating emerging Daoist scriptural traditions, enabling the creation of the first canonical Daoist catalog, and laying the foundation for the compilation of the Daozang and the establishment of the Ordination Ranks 法位 system. Scholars generally agree that the Shangqing taiji yinzhu yujing baojue 上清太極隱注玉經寶訣 played a significant role in the development of the Three Caverns thought. However, research on the formation of this scripture remains lacking. This study fills this gap by confirming the composition of the scripture through two independent lines of evidence. Then, based on new insights into its composition, this study discusses the historical context of the Three Caverns concept in this scripture and its direct impact on Lu Xiujing 陸修靜 (406–477)’s cataloging work. These discussions illustrate that, when confronted with the challenge posed by the newly composed Shangqing scriptures, the authors of the Shangqing taiji yinzhu yujing baojue employed the integrative approach commonly found in the Ancient Lingbao Scriptures to propose a more inclusive scriptural system. This approach played a crucial role in providing a theoretical foundation for the formation of medieval Daoism.

A supermassive binary black-hole candidate SDSS J1430+2303 reported recently motivates us to investigate an imminent binary of supermassive black holes as potential gravitational wave source, and the radiated gravitational waves at the end of the merger are shown to be in the band of space-borne detectors. We provide a general analysis on the required detecting sensitivity needed for probing such type gravitational wave sources and make a full discussion by considering two typically designed configurations of space-borne antennas. If a source is so close, it is possible to be detected with Taiji pathfinder-plus which is proposed to be an extension for the planned Taiji pathfinder by just adding an additional satellite to the initial two satellites. The gravitational wave detection on such kind of source enables us to explore the properties of supermassive black holes and the nature of gravity.