Precision near-IR spectroscopy for understanding AGN physics and shed light on the H0 tension

The persistent tension between early- and late-Universe measurements of the Hubble constant (H0) remains one of the most significant challenges in modern cosmology. The Spectroastrometry and Reverberation Mapping (SARM) method offers a promising, calibration-independent approach to address this issue by combining time-delay measurements of the Broad-Line Region (BLR) with interferometric angular size determinations. Current implementations of SARM, however, are limited by the difficulty of performing near-infrared reverberation mapping (RM) on the same emission lines observed by GRAVITY, restricting applications to only a few bright AGN. We propose using the capabilities of SHARP, the next-generation near-infrared spectrograph for the Extremely Large Telescope (ELT), to overcome these limitations. SHARP's sensitivity and multi-object spectroscopy will enable (1) efficient long-term monitoring of existing GRAVITY targets with minimal time investment, and (2) systematic RM campaigns for the fainter AGN that will be observed by GRAVITY+. These advances will give us precise infrared lags for tens of AGN, enabling geometric distance measurements and a robust, calibration-free determination of H0. Beyond cosmology, SHARP will allow detailed studies of BLR structure and kinematics in the infrared, advancing our understanding of AGN physics and with repercussions on the measurements of Supermassive Black Holes (SMBH) masses.