On measuring the absolute scale of baryon acoustic oscillations

Abstract: The baryon acoustic oscillation (BAO) feature in the distribution of galaxies provides a fundamental standard ruler which is widely used to constrain cosmological parameters. In most analyses, the comoving length of the ruler is inferred from a combination of CMB observations and theory. However, this inferred length may be biased by various non-standard effects in early universe physics; this can lead to biased inferences of cosmological parameters such as H_0, \Omega_m and w, so it would be valuable to measure the absolute BAO length by combining a galaxy redshift survey and a suitable direct low-z distance measurement. One obstacle is that low-redshift BAO surveys mainly constrain the ratio r_S / D_V(z), where D_V is a dilation scale which is not directly observable by standard candles. Here, we find a new approximation D_V(z) \simeq (3/4) D_L(4z/3) (1+ 4z/3)^{-1} (1 - 0.02455 z^3 + 0.0105 z^4) which connects D_V to the standard luminosity distance D_L at a somewhat higher redshift; this is shown to be very accurate (relative error < 0.2 percent) for all WMAP-compatible Friedmann models at z < 0.4, with very weak dependence on cosmological parameters H_0, \Omega_m, \Omega_k, w. This provides a route to measure the absolute BAO length using only observations at z < 0.3, including type-Ia supernovae, and potentially future H_0-free physical distance indicators such as gravitational lenses or gravitational wave standard sirens. This would provide a zero-parameter check of the standard cosmology at 10^3 < z < 10^5, and can constrain the number of relativistic species N_{eff} with fewer degeneracies than the CMB.