Gamma-ray Bursts as Cosmological Probes Calibrated with Strongly Lensed Quasars and Neural Networks

Abstract

Gamma-ray bursts (GRBs) extend distance measurements to redshifts beyond those routinely probed by Type Ia supernovae, but their use in cosmology is limited by calibration circularity and possible redshift-dependent effects. We investigate strongly lensed quasars as external calibrators of the Amati and Combo GRB relations. We reconstruct the luminosity-distance relation using an artificial neural network trained on TDCOSMO strong-lensing distances, with the absolute scale inherited from the lensing-only calibration. To avoid extrapolation, only GRBs within the lens-supported redshift interval are used for calibration. We then infer cosmological parameters through a hierarchical Bayesian analysis of flat $\Lambda$CDM, with $w_0{w}_a$CDM examined as a consistency test. For flat $\Lambda$CDM, Amati yields $H_0=78.26_{-16.30}^{+17.87}\mathrm{km}{\mathrm{s}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-1}$ and ${\Omega }_m=0.670_{-0.276}^{+0.223}$, while Combo yields $H_0=78.71_{-11.29}^{+13.83}\mathrm{km}{\mathrm{s}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-1}$ and ${\Omega }_m=0.635_{-0.242}^{+0.235}$. Amati is relatively insensitive to the phenomenological redshift term, whereas Combo shows a stronger dependence. Injection--recovery tests indicate that an unmodelled positive Combo trend can bias $H_0$ and ${\Omega }_m$ upward. Strong-lens calibration therefore offers a route to extending the GRB Hubble diagram, but the inferred $H_0$ is not an independent GRB measurement: it retains the TDCOSMO distance scale. The precision is limited by GRB scatter, redshift-dependent systematics, and lens-modelling uncertainties.

arXiv comment20 pages, 16 figures, 11 tables