Model-independent way to determine the Hubble constant and the curvature from 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 taking advantage of the possibilities of future space-borne gravitational wave (GW) 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 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 $H_0$ and $\Omega_k$ 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 VLBI. In the case of $(N=100)$ of radio quasars, which is the size of currently available sample, the precision of cosmological parameters determined would be $\sigma_{H_0}=2.74$ ${\mathrm{~km~s^{-1}~Mpc^{-1}}}$ and $\sigma_{\Omega_k}=0.175$. 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 $\sigma_{H_0} =0.54$ ${\mathrm{~km~s^{-1}~Mpc^{-1}}}$ from \emph{Planck} 2018 TT, TE, EE+lowE+lensing data, and the precision of $\Omega_k$ would be 0.050. Our results demonstrate that such combined analysis, possible in the future, could be helpful to solve the current cosmological issues concerning the Hubble tension and cosmic curvature tension.