Geometric distances to the super massive black hole in AGNs using Spectroastrometry and Reverberation mapping.

Accurately measuring cosmic distances is fundamental to resolving the $H_0$ tension. Active Galactic Nuclei (AGNs) offer a promising method to estimate distances up to redshift 7 through a geometrical approach. By combining spectro-astrometric measurements of the angular size ($\theta$) and reverberation mapping (RM) of the linear size ($R$) of the Broad-Line Region (BLR), the angular diameter distance ($D_A = R / \theta$) can be determined. We conducted RM observations for seven AGNs using the 3.6m DOT and 2m HCT telescopes. Observations for four sources in the optical and NIR wavelength ranges have been completed, with H$\beta$ BLR sizes estimated within 30 light-days. Time-series analysis further yielded lag measurements, validating these results. RM data also enable supermassive black hole mass estimates and provide insights into BLR geometry and kinematics through dynamical modeling. Additionally, we simulate spectro-astrometric signals analogous to those from large interferometers to enable precise angular diameter distance calculations. In this presentation, we will discuss the implications of these findings for extragalactic distance measurements, the $H_0$ tension, and our understanding of cosmic expansion.