Model-independent Way to Determine the Hubble Constant and the Curvature from the Phase Shift of Gravitational Waves with DECIGO

Abstract In this Letter, we propose a model-independent method to determine the Hubble constant and curvature simultaneously by taking advantage of the possibilities of future spaceborne gravitational-wave detector DECIGO in combination with the radio quasars as standard rulers. Similarly to the redshift drift in the electromagnetic domain, accelerating expansion of the Universe causes a characteristic phase correction to the gravitational waveform detectable by DECIGO. Hence, one would be able to extract the Hubble parameter H ( z ). This could be used to recover a distance–redshift relation supported by the data not relying on any specific cosmological model. Assuming the FLRW metric and using intermediate-luminosity radio quasars as standard rulers, one achieves an interesting opportunity to directly assess the H 0 and Ω k parameters. To test this method, we simulated a set of acceleration parameters achievable by future DECIGO. Based on the existing sample of 120 intermediate-luminosity radio quasars calibrated as standard rulers, we simulated much bigger samples of such standard rulers possible to obtain with very long baseline interferometry (VLBI). In the case of ( N = 100) of radio quasars, which is the size of the currently available sample, the precision of the cosmological parameters determined would be σ H 0 = 2.74 km s −1 Mpc −1 and σ Ω k = 0.175 . In the optimistic scenario ( N = 1000) achievable by VLBI, the precision of H 0 would be improved to 1%, which is comparable to the result of σ H 0 = 0.54 km s −1 Mpc −1 from Planck 2018 TT, TE, EE+lowE+lensing data, and the precision of Ω k would be 0.050. Our results demonstrate that such combined analysis, possible in the future, could be helpful in solving the current cosmological issues concerning the Hubble tension and cosmic curvature tension.