2025A&A...701A.220L

Context. Model-independent bounds on the Hubble constant H₀ 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 H₀.
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 H₀. 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 1σ level with the H₀ determined from type Ia supernovae (SNe Ia), and at the 2σ level, our findings agree with the measurement derived from the cosmic microwave background (CMB) radiation.
Conclusions. Our method evidences that the bounds on H₀ 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 H₀. 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.