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

Abstract

ABSTRACT 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 Λ-cold dark matter (ΛCDM) model, 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 per cent, 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-$\mathit{ z}$ 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.