Cosmic Chronometers with Photometry: a new path to $H(z)$

We present a proof-of-principle determination of the Hubble parameter $H(z)$ from photometric data, obtaining a determination at an effective redshift of $z=0.75$ ($0.65<z<0.85$) of $H(0.75) =105.0\pm 7.9(stat)\pm 7.3(sys)$ km s$^{-1}$ Mpc$^{-1}$, with 7.5\% statistical and 7\% systematic (10\% with statistical and systematics combined in quadrature) accuracy. This is obtained in a cosmology model-independent fashion, but assuming a linear age-redshift relation in the relevant redshift range, as such, it can be used to constrain arbitrary cosmologies as long as $H(z)$ can be considered slowly varying over redshift. In particular, we have applied a neural network, trained on a well-studied spectroscopic sample of 140 objects, to the {\tt COSMOS2015} survey to construct a set of 19 thousand near-passively evolving galaxies and build an age-redshift relation. The Hubble parameter is given by the derivative of the red envelope of the age-redshift relation. This is the first time the Hubble parameter is determined from photometry at $\lesssim 10$\% accuracy. Accurate $H(z)$ determinations could help shed light on the Hubble tension; this study shows that photometry, with a reduction of only a factor of two in the uncertainty, could provide a new perspective on the tension.