Standard rulers, candles, and clocks from the low-redshift Universe

Abstract: We measure the length of the Baryon Acoustic Oscillation (BAO) feature, and the expansion rate of the recent Universe, from low-redshift data only, almost model-independently. We make only the following minimal assumptions: homogeneity and isotropy; a metric theory of gravity; a smooth expansion history, and the existence of standard candles (supernov\ae) and a standard BAO ruler. The rest is determined by the data, which are compilations of recent BAO and Type IA supernova results. Making only these assumptions, we find for the first time that the standard ruler has length $103.9 \pm 2.3\, h^{-1}$ Mpc. The value is a measurement, in contrast to the model-dependent theoretical prediction determined with model parameters set by Planck data ($99.3 \pm 2.1 \, h^{-1}$ Mpc). The latter assumes $\Lambda$CDM, and that the ruler is the sound horizon at radiation drag. Adding passive galaxies as standard clocks or a local Hubble constant measurement allows the absolute BAO scale to be determined ($142.8\pm 3.7$ Mpc), and in the former case the additional information makes the BAO length determination more precise ($101.9\pm 1.9 \, h^{-1}\,$Mpc). The inverse curvature radius of the Universe is weakly constrained and consistent with zero, independently of the gravity model, provided it is metric. We find the effective number of relativistic species to be $N_{\rm eff} = 3.53\pm 0.32$, independent of late-time dark energy or gravity physics.