Determining <i>H</i>₀ from a distance sum rule that combines gamma-ray bursts with observational Hubble data and strong gravitational lensing

Context. Model-independent bounds on the Hubble constant H 0 are important for gaining insight into cosmological tensions. Aims. We work out a model-independent analysis based on the sum rule, which is applied to late- and early-time data catalogs to determine H 0 . Methods. Through the model-independent Bézier interpolation of the observational Hubble data and assuming a flat universe, we reconstructed the dimensionless distances of the sum rule and applied them to strong lensing data to derive constraints on H 0 . We then extended this method to the high-redshift domain, and in two separate analyses, we included gamma-ray burst (GRB) data sets from the well-established Amati and Combo correlations. Results. In all three analyses, our findings agree at the 1 σ level with the H 0 determined from type Ia supernovae (SNe Ia), and at the 2 σ level, our findings agree with the measurement derived from the cosmic microwave background (CMB) radiation. Conclusions. Our method evidences that the bounds on H 0 are significantly affected by strong lensing data, which favor the local measurement from SNe Ia. Including GRBs causes only a negligible decrease in the value of H 0 . This may indicate that GRBs can be used to trace the expansion history, and in conjunction with CMB measurements, GRBs may reconcile the Hubble tension and accommodate the flat ΛCDM paradigm purported by CMB data.