Sub-percentage measure of distances to redshift of 0.1 by a new cosmic ruler

Distance-redshift diagrams probe expansion history of the Universe. We show that the stellar mass-binding energy (massE) relation of galaxies proposed in our previous study offers a new distance ruler at cosmic scales. By using elliptical galaxies in the main galaxy sample of the Sloan Digital Sky Survey Data Release 7, we construct a distance-redshift diagram over the redshift range from 0.05 to 0.2 with the massE ruler. The best-fit dark energy density is 0.675+-0.079 for flat Lambda-CDM, consistent with those by other probes. At the median redshift of 0.11, the median distance is estimated to have a fractional error of 0.34%, much lower than those by supernova (SN) Ia and baryonic acoustic oscillation (BAO) and even exceeding their future capability at this redshift. The above low-z measurement is useful for probing dark energy that dominates at the late Universe. For a flat dark energy equation of state model (flat wCDM), the massE alone constrains w to an error that is only a factor of 2.2, 1.7 and 1.3 times larger than those by BAO, SN Ia, and cosmic microwave background (CMB), respectively.
Comment: 8 pages, 5 figures, MNRAS in press. The cosmoSIS modules for the massE ruler is at https://astronomy.nju.edu.cn/DFS//file/2022/07/02/20220702161632756vbde28.zip