Inferring the cosmological constant in early Universe only by gravitational waves

The expansion of the Universe is accelerating which can be interpreted as due to the cosmological constant $\Lambda$. In this study, we investigate the behavior of gravitational waves in the presence of a cosmological constant in the early universe. We rigorously analyze the merger rate of binary primordial black holes (PBHs) and the corresponding signal-to-noise ratio within the framework of Laser Interferometer Space Antenna (LISA). We find that binary PBHs with a total mass of $M_{\mathrm{tot}}=1000M_{\odot}$ and a redshift larger than $z=500$ are the ideal system for studying the effect of the cosmological constant through LISA. By computing the fisher information matrix, we establish that the cosmological constant can be effectively constrained.