Addressing the circularity problem in the $E_\text{p}-E_\text{iso}$ correlation of Gamma-Ray Bursts

We here propose a new model-independent technique to overcome the circularity problem affecting the use of Gamma-Ray Bursts (GRBs) as distance indicators through the use of $E_{\rm p}$--$E_{\rm iso}$ correlation. We calibrate the $E_{\rm p}$--$E_{\rm iso}$ correlation and find the GRB distance moduli that can be used to constrain dark energy models. We use observational Hubble data to approximate the cosmic evolution through B\'ezier parametric curve obtained through the linear combination of Bernstein basis polynomials. In so doing, we build up a new data set consisting of 193 GRB distance moduli. We combine this sample with the supernova JLA data set to test the standard $\Lambda$CDM model and its $w$CDM extension. We place observational constraints on the cosmological parameters through Markov Chain Monte Carlo numerical technique. Moreover, we compare the theoretical scenarios by performing the AIC and DIC statistics. For the $\Lambda$CDM model we find $\Omega_m=0.397^{+0.040}_{-0.039}$ at the $2\sigma$ level, while for the $w$CDM model we obtain $\Omega_m=0.34^{+0.13}_{-0.15}$ and $w=-0.86^{+0.36}_{-0.38}$ at the $2\sigma$ level. Our analysis suggests that $\Lambda$CDM model is statistically favoured over the $w$CDM scenario. No evidence for extension of the $\Lambda$CDM model is found.