Gamma Ray Bursts (GRBs) are immensely energetic explosions radiating up to 1054 erg of energy isotropically (Eiso) and they are observed within a wide range of redshift (from ∼ 0.01 up to ∼ 9). Such enormous power and high redshift point at these phenomena being highly favorable to investigate the history and evolution of our universe. The major obstacle in their application as cosmological study-tools is to find a way to standardize the GRBs, for instance similar to SNe Ia. With respect to this goal, the correlation between spectral peak energy (Ep,i) and the "intensity" is a positively useful and investigated criterion. Moreover, it has been demonstrated that, through the Ep,i - Eiso correlation, the current data set of GRBs can already contribute to the independent evidence of the matter density ΩM being ∼ 0.3 for a flat universe scenario. We try to inspect and compare the correlations of Ep,i with different intensity indicators (e.g., radiated energy, average and peak luminosity, bolometric vs. monochromatic quantities, etc.) both in terms of intrinsic dispersion and precise estimation of ΩM. The outcome of such studies are further analyzed in verifying the reliability of the correlations for both GRB physics and their standardization for cosmology.