Determination of H0 from current and forecasting time-delay lensed quasars at high redshift using cosmological model-independent method

The Hubble constant ([Formula: see text]) remains a critical parameter in cosmology, with persistent discrepancies between measurements from early- and late-universe probes. This study presents a model-independent method to determine [Formula: see text] by combining time-delay distances from strong gravitational lensing systems with distance indicators from gamma-ray bursts (GRBs) calibrated using unanchored Type Ia supernova (SN Ia) distances reconstructed via Gaussian process (GP) regression. Leveraging the wide redshift coverage of GRBs ([Formula: see text]), we extend the cosmological distance ladder beyond the reach of SNe Ia ([Formula: see text]). This approach takes full advantage of the complementary nature of low-redshift SNe Ia and high-redshift GRBs, effectively expanding the redshift range. Using current observational data, we constrain [Formula: see text] to [Formula: see text] [Formula: see text]km s[Formula: see text] [Formula: see text]Mpc[Formula: see text] (3.6% precision) for a nonflat universe and [Formula: see text] [Formula: see text]km s[Formula: see text] [Formula: see text]Mpc[Formula: see text] (1.9% precision) assuming flatness, consistent with previous lensing-based results. Future simulations incorporating 55 mock lens systems and 500 GRBs suggest that [Formula: see text] can be measured with sub-percent precision [Formula: see text] [Formula: see text]km s[Formula: see text] [Formula: see text]Mpc[Formula: see text] for 3% distance uncertainties in a flat universe. Our approach highlights the potential of high-redshift GRBs to enhance [Formula: see text] measurements, offering a pathway to resolve the ongoing Hubble tension and constrain cosmological parameters with upcoming surveys like LSST.