Cosmological model-independent measurement of cosmic curvature using distance sum rule with the help of gravitational waves

Abstract

Although the cosmic spatial curvature has been precisely constrained in the standard cosmological model using the observations of cosmic microwave background anisotropies, it is still of great importance to independently measure this key parameter using only the late-universe observations in a cosmological model-independent way. The distance sum rule in strong gravitational lensing (SGL) provides such a way, provided that the three distances in the sum rule can be calibrated by other observations. Usually, such a calibration can be performed by using the type Ia supernovae (SN Ia), which, however, has some drawbacks, e.g., dependence on distance ladder, narrow redshift range, etc. In this paper, we propose that gravitational waves (GWs) can be used to provide the distance calibration in the SGL method, which can avoid the dependence on distance ladder and cover a wider redshift range. Using the simulated GW standard siren observation by the Einstein Telescope as an example, we show that this scheme is feasible and advantageous. We find that ∆Ω k 0.17 with the current SGL data, which is slightly more precise than the case of using SN Ia to calibrate. Furthermore, we consider the forthcoming LSST survey that is expected to observe many SGL systems. We simulate a realistic population of SGL systems that will be observed in the near future, and we find that about 10 4 SGL data could provide the precise measurement of ∆Ω k 10 −2 with the help of GWs. Our work indicates that the observations of SGL and GWs by the next-generation facilities would improve the late-universe measurement of cosmic curvature by one order of magnitude.

A New Way to Explore Cosmological Tensions Using Gravitational Waves and Strong Gravitational Lensing

“…), these three distances are connected by the well-known distance sum rule (Räsänen et al 2015;Xia et al 2017;Li et al 2018;Qi et al 2019aQi et al , 2019cLiao 2019;Wang et al 2020a;Zhou & Li 2020;Wang et al 2021Wang et al , 2022b:…”

Cosmological Parameter Estimation Using Current and Future Observations of Strong Gravitational Lensing

“…In fact, for the galaxy-scale SGL samples, in addition to the time-delay measurements, several observed quantities can be used as the statistical quantities to constrain cosmological parameters, including the distribution of image angular separations [35,36], the distribution of lens redshifts [37][38][39], and the velocity dispersion of lens galaxies [40][41][42][43]. Recently, using the lens velocity dispersion as statistical quantity in cosmology yields a series of achievements [44][45][46][47][48][49][50][51][52][53][54]. With spectroscopic and astrometric data, 161 available samples are obtained with well-defined selection criteria at present [52].…”