The length of the low-redshift standard ruler

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 Ia supernovae (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 Λ cold dark matter 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 cosmic microwave background 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 Ia supernovae and baryon acoustic oscillations, and rs = 150.0 ± 4.7 Mpc when using clocks to set the Hubble normalization, while rs = 141.0 ± 5.5 Mpc when using the local Hubble constant determination (using both yields rs = 143.9 ± 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 Planck satellite, which assumes that it is the sound horizon at the end of baryon drag.

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