Intermediate redshift calibration of gamma-ray bursts and cosmic constraints in non-flat cosmology

We propose a new method to calibrate gamma-ray burst (GRB) correlations employing intermediate redshift data sets, instead of limiting to z ≃ 0 catalogues, and applied it to the well-consolidated Amati correlation. This model-independent calibration technique is based on the Bézier polynomial interpolation of the most updated observational Hubble data and baryonic acoustic oscillations (BAO) and alleviates de facto the well-known circularity problem affecting GRB correlations. In doing so, we also investigate the influence of the BAO scales r_s, got from Planck results, and rfids⁠, got from the considered fiducial cosmology, by considering the cases (rs/rfids)=1 and (rs/rfids)≠1⁠. We get constraints on the cosmic parameters, using Markov chain–Monte Carlo simulations, first fixing and then leaving free the spatial curvature density parameter Ω_k. Compared to previous literature, we obtain tighter constraints on the mass density parameter Ω_m. In particular, our findings turn out to be highly more compatible with those got from standard candle indicators within the Lambda cold dark matter paradigm. Finally, we critically re-examine the recent H_0 tension in view of our outcomes.