Improving sampling and calibration of GRBs as distance indicators

We present a sample of 74 Gamma-Ray Bursts (GRBs) from the Fermi-GBM catalogue for which we compute the distance moduli and use them to constrain effective dark energy models. To overcome the circularity problem affecting GRBs as distance indicators, we calibrate the Amati relation of our sample with a cosmology-independent technique. Specifically, we use the latest observational Hubble parameter data, including associated systematics, to approximate the cosmic expansion through a Bezier parametric curve. We subsequently obtain the distance moduli of the GRBs and include the data in a suite of recent cosmological observations of the expansion history (Planck Compressed 2018, 2012 BOSS release of BAO data and Pantheon SNIa), to compute Bayesian posterior constraints for the standard cosmological model $\Lambda$CDM, as well as $\omega$CDM, and the CPL parametrization. Throughout the analysis we strive to keep under control the error propagation and limit our GRBs sample to avoid observational bias. As a result, we find no evidence in favour of the alternatives to $\Lambda$CDM model. The latter agrees very well with our calibrated sample of GRBs and presently available luminosity distance probes.