Revisiting the Concordance $\Lambda$CDM model using Gamma-Ray Bursts together with Supernovae Ia and Planck data

The Hubble constant, $H_0$, tension is the tension among the local probes, Supernovae Ia, and the Cosmic Microwave Background Radiation. It has been almost a decade, and this tension still puzzles the community. Here, we add intermediate redshift probes, such as Gamma-Ray Bursts (GRB) and Quasars (QS0s), to check if and to what extent these higher redshift probes can reduce this tension. We use the three-dimensional fundamental plane relation among the prompt peak luminosity, the luminosity at the end of the plateau emission, and its rest frame duration. We find similar trend in GRB intrinsic parameters as previously seen in Pantheon-Plus intrinsic parameters. We find an apparent $3.14\sigma$ tension for the GRB intrinsic parameter $b$. Indeed, this tension disappears and the parameters are actually compatible within $2.26\sigma$. Another interesting point is that the 3D relation plays an important role in conjunction with Supernovae data with Pantheon Plus and that this apparent discrepancy show how it is important the correction for selection biases and redshift evolution. The incorporation of redshift evolution correction results in a reduction of the GRB tension to $2.26\sigma$ when adjusting correction parameters. We envision that with more data this indication of tension will possibly disappear when the evolutionary parameters of GRBs are computed with increased precision.