Skipping the rungs! Calibrating distance indicators through their clustering with galaxies

Abstract

We show that angular cross-correlations between distance indicators and galaxy redshift catalogues, when interpreted within an assumed cosmological model, can constrain potential biases in distance measurements induced by calibration systematics. As a test case, we consider a simple scenario in which a constant calibration offset $\Delta M$ shifts all observed distances by a multiplicative factor, and we produce Fisher forecasts for the constraining power on $\Delta M$ and $H_0$ from existing and upcoming surveys. In our most optimistic scenario, based on the expected number of SN Ia observed by LSST and the DESI final data release, we find $\sigma_{\Delta M} \approx 0.05$ and $\sigma_{H_0} \approx 1.81~\mathrm{km~s^{-1}~Mpc^{-1}}$. This has important implications for the Hubble tension, since explaining the discrepancy purely as a calibration systematic in low-$z$ measurements would require $\Delta M \approx 0.13$.