Hubble speed from first principles
Fabrizio Renzi, Alessandra Silvestri
Abstract
We introduce a way of measuring ${H}_{0}$ from a combination of independent geometrical data sets, without the need for calibration or the choice of a cosmological model. We build on the distance duality relation, which sets the ratio of the luminosity and angular diameter distance to a fixed scaling in redshift for any metric theory of gravity with standard photon propagation and constitutes a founding block of any theory describing our Universe. Our method allows us to determine ${H}_{0}$ from first principles, unleashing the measurement of this fundamental constant from calibration and the assumption of a cosmological model. We find ${H}_{0}=69.5\ifmmode\pm\else\textpm\fi{}1.7\text{ }\text{ }\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$ at 68% C.L., showing that the Hubble constant can be constrained at the percent level with minimal assumptions.