Constraints on the transition redshift from the calibrated gamma-ray burst Ep–Eiso correlation

We constrain the deceleration–acceleration epoch, namely the transition redshift z_tr, adopting model-independent techniques that utilize a calibrated E_p–E_iso correlation for gamma-ray bursts (GRBs). To do so, in addition to real data points, we employ up to 1000 simulated observational Hubble data (OHD) points. We then calibrate the E_p–E_iso correlation by means of the well-consolidate Bézier polynomial technique, interpolating OHD up to the second order. Once GRB data have been calibrated, we consider two strategies of cosmographic expansions, i.e. first we take a direct Hubble rate expansion around z_tr, and second the expansion of the deceleration parameter around the same redshift, but with a different order. Employing Type Ia supernovae, baryonic acoustic oscillations and GRB data sets, from Monte Carlo analyses we infer tight constraints on z_tr and the jerk parameters at z = z_tr, namely j_tr. Our results are extremely compatible with previous outcomes and confirm the Lambda cold dark matter predictions, being slightly different in terms of the jerk parameter. In this respect, we conjecture which extensions of the concordance paradigm are possible and we compare our findings with expectations provided by generic dark energy models.