The Laser Interferometer Space Antenna (LISA) will open the mHz band of the gravitational wave spectrum for exploration. Sensitivity curves are a useful tool for surveying the types of sources that can be detected by the LISA mission. Here we describe how the sensitivity curve is constructed, and how it can be used to compute the signal-to-noise ratio for a wide range of binary systems. We adopt the 2018 LISA mission performance requirement design parameters. We consider both sky-averaged sensitivities, and the sensitivity to sources at particular sky locations. The calculations are included in a publicly available Python notebook.

In this perspective, we outline that a space borne gravitational wave detector network combining LISA and Taiji can be used to measure the Hubble constant with an uncertainty less than 0.5% in ten years, compared with the network of the ground based gravitational wave detectors which can measure the Hubble constant within a 2% uncertainty in the next five years by the standard siren method. Taiji is a Chinese space borne gravitational wave detection mission planned for launch in the early 2030 s. The pilot satellite mission Taiji-1 has been launched in August 2019 to verify the feasibility of Taiji. The results of a few technologies tested on Taiji-1 are presented in this paper.

Gravitational waves (GWs) from tens of millions of compact binaries in our Milky Way enter the millihertz band of space-based detection. The majority of them cannot be resolved individually, resulting in foreground confusion noise for the Laser Interferometer Space Antenna (LISA). The concept of the Taiji mission is similar to LISA’s with slightly better sensitivity, which means that Galactic GW signals will also affect detection with Taiji. Here, we generate GW signals from 29.8 million Galactic binaries for Taiji and subtract the “resolvable” sources. The confusion noise is estimated and fitted in an analytic form with 6-month, 1-year, 2-year, and 4-year observation times. We find that the full sensitivity curve is slightly lower for Taiji than for LISA at frequencies of $\le 0.8\mathrm{mHz}$ and around 2 mHz. For a 4-year lifetime, more than 29 thousand sources are resolvable with Taiji. Compared to LISA, Taiji can subtract $\sim 20\%$ more sources, and the distribution of them in our Milky Way is consistent with that of the resolvable sources with LISA. At frequencies around 2 mHz or with the chirp masses ranging from 0.2 to $0.4M_{\odot }$, more sources become resolvable with Taiji.

The space-based laser interferometers, LISA, Taiji and TianQin, are targeting to observe milliHz gravitational waves (GWs) in the 2030s. The joint observations from multiple space-based detectors yield significant advantages. In this work, we recap the studies and investigations for the joint space-based GW detector networks to highlight: 1) the high precision of sky localization for the massive binary black hole (BBH) coalescences and the GW sirens in the cosmological implication, 2) the effectiveness to test the parity violation in the stochastic GW background observations, 3) the efficiency of subtracting galactic foreground, 4) the improvement in stellar-mass BBH observations. We inspect alternative networks by trading off massive BBH observations and stochastic GW background observation.

Recently, multiple pulsar timing array collaborations have presented compelling evidence for a stochastic signal at nanohertz frequencies, potentially originating from cosmic strings. Cosmic strings are linear topological defects that can arise during phase transitions in the early Universe or as fundamental strings in superstring theory. This paper focuses on investigating the detection capabilities of Taiji, a planned space-based gravitational wave detector, for the gravitational wave background generated by cosmic strings. By analyzing simulated Taiji data and utilizing comprehensive Bayesian parameter estimation techniques, we demonstrate a significant improvement in precision compared to the NANOGrav 15-year data set, surpassing it by an order of magnitude. This highlights the enhanced measurement capabilities of Taiji. Consequently, Taiji can serve as a valuable complementary tool to pulsar timing arrays in validating and exploring the physics of cosmic strings in the early Universe.

Space-based gravitational-wave detectors consist of a triangle of three spacecraft, which makes it possible to detect polarization modes of gravitational waves due to the motion of the detectors in space. In this paper we explore the ability of Taiji to detect the polarization modes in the parametrized post-Einsteinian framework. Assuming massive black hole binaries with the total mass of $M=4\times {10}^5{M}_{\odot }$ at redshift of $z=1$, we find that Taiji can measure the dipole and quadruple emission ($\mathrm{\Delta }{\alpha }_D/{\alpha }_D$ and $\mathrm{\Delta }{\alpha }_Q/{\alpha }_Q$) with the accuracy of up to $\sim 0.04\%$, with the fiducial value of ${\alpha }_D=0.001$, the scalar transverse and longitudinal modes ($\mathrm{\Delta }{\alpha }_B$ and $\mathrm{\Delta }{\alpha }_L$) up to $\sim 0.01$, and the vector modes ($\mathrm{\Delta }{\alpha }_V$) up to $\sim 0.0005$.