Strong lensing time-delay cosmography in the 2020s

Multiply imaged time-variable sources can be used to measure absolute distances as a function of redshifts and thus determine cosmological parameters, chiefly the Hubble Constant H _0 . In the two decades up to 2020, through a number of observational and conceptual breakthroughs, this so-called time-delay cosmography has reached a precision sufficient to be an important independent voice in the current “Hubble tension” debate between early- and late-universe determinations of H _0 . The 2020s promise to deliver major advances in time-delay cosmography, owing to the large number of lenses to be discovered by new and upcoming surveys and the vastly improved capabilities for follow-up and analysis. In this review, after a brief summary of the foundations of the method and recent advances, we outline the opportunities for the decade and the challenges that will need to be overcome in order to meet the goal of the determination of H _0 from time-delay cosmography with 1