Inferring the cosmological constant in early Universe only by gravitational waves

A bstract Gravitational waves (GWs) from compact binary coalescence (CBC) can directly determine the luminosity distance but usually can not obtain information about the redshift. This assumes that the GW source is at the flat background. However, if the GWs are generated in a not flat but accelerating universe, the GWs should carry the information of the curvature spacetime. The expansion of the Universe is accelerating can be interpreted as the existence of the cosmological constant Λ. 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 space-borne interferometers (like Laser Interferometer Space Antenn, TAIJI and Tian-Qin). We find that binary PBHs with a total mass of M tot = 1000 M ⊙ 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.