The length of the low-redshift standard ruler

Abstract

Assuming the existence of standard rulers, standard candles and standard clocks, requiring only the cosmological principle, a metric theory of gravity, a smooth expansion history, and using state-of-the-art observations, we determine the length of the "low-redshift standard ruler". The data we use are a compilation of recent Baryon acoustic oscillation data (relying on the standard ruler), Type 1A supernov\ae\ (as standard candles), ages of early type galaxies (as standard clocks) and local determinations of the Hubble constant (as a local anchor of the cosmic distance scale). In a standard $\Lambda$CDM cosmology the "low-redshift standard ruler" coincides with the sound horizon at radiation drag, which can also be determined --in a model dependent way-- from CMB observations. However, in general, the two quantities need not coincide. We obtain constraints on the length of the low-redshift standard ruler: $r^h_{\rm s}=101.0 \pm 2.3 h^{-1}$ Mpc, when using only Type 1A supernov\ae\ and Baryon acoustic oscillations, and $r_{\rm s}=150.0\pm 4.7 $ Mpc when using clocks to set the Hubble normalisation, while $r_{\rm s}=141.0\pm 5.5 $ Mpc when using the local Hubble constant determination (using both yields $r_{\rm s}=143.9\pm 3.1 $ Mpc). The low-redshift determination of the standard ruler has an error which is competitive with the model-dependent determination from cosmic microwave background measurements made with the {\em Planck} satellite, which assumes it is the sound horizon at the end of baryon drag.