Towards a new model-independent calibration of Gamma-Ray Bursts

Current data on baryon acoustic oscillations and Supernovae of Type Ia (SNIa) cover up to $z\sim 2.5$. These low-redshift observations play a very important role in the determination of cosmological parameters and have been widely used to constrain the ΛCDM and models beyond the standard, such as the ones with open curvature. To extend this investigation to higher redshifts, Gamma-Ray Bursts (GRBs) stand out as one of the most promising observables. In spite of being transient, they are extremely energetic and can be used to probe the universe up to $z\sim 9.4$. They exhibit characteristics that suggest they are potentially standardizable candles and this allows their use to extend the distance ladder beyond SNIa. The use of GRB correlations is still a challenge due to the spread in their intrinsic properties. One of the correlations that can be employed for the standardization is the fundamental plane relation between the peak prompt luminosity, the rest-frame end time of the plateau phase, and its corresponding luminosity, also known as the three-dimensional Dainotti correlation. In this work, we propose an innovative method of calibration of the Dainotti relation which is independent of cosmology. We employ state-of-the-art data on Cosmic Chronometers (CCH) at $z\lesssim 2$ and use the Gaussian Processes Bayesian reconstruction tool. To match the CCH redshift range, we select 20 long GRBs in the range $0.553\le z\le 1.96$ from the Platinum sample, which consists of well-defined GRB plateau properties that obey the fundamental plane relation. To ensure the generality of our method, we verify that the choice of priors on the parameters of the Dainotti relation and the modeling of CCH uncertainties and covariance have negligible impact on our results. Moreover, we consider the case in which the redshift evolution of the physical features of the plane is accounted for. We find that the use of CCH allows us to identify a sub-sample of GRBs that adhere even more closely to the fundamental plane relation, with an intrinsic scatter of ${\sigma }_{int}={0.20}_{-0.05}^{+0.03}$ obtained in this analysis when evolutionary effects are considered. In an epoch in which we strive to reduce uncertainties on the variables of the GRB correlations in order to tighten constraints on cosmological parameters, we have found a novel model-independent approach to pinpoint a sub-sample that can thus represent a valuable set of standardizable candles. This allows us to extend the cosmic distance ladder presenting a new catalog of calibrated luminosity distances up to $z=5$.