Abstract
Gamma-Ray Bursts (GRBs), the most luminous explosions in the cosmos, are promising tools
for cosmology due to their potential as standardizable candles. Among the empirical correlations
proposed for this purpose, the Yonetoku relation, which connects the intrinsic peak energy (𝐸i,p)
of the 𝜈𝐹𝜈 spectrum to the isotropic peak luminosity (𝐿iso), provides a mean to probe distances
beyond the range of Type Ia supernovae (SNe Ia). In this work, the Yonetoku relation is calibrated
and analyzed using GRBs with measured redshifts and a large sample of GRBs with pseudoredshifts
obtained using Machine Learning (ML). This analysis focuses on estimating the distance
modulus and constraining parameters of a flat ΛCDM cosmology using this relation. A joint
Markov Chain Monte Carlo analysis is applied to simultaneously determine the Yonetoku relation
parameters (𝑘, 𝑚) and cosmological parameters (𝐻0,ΩΛ). This method is applied across the full
redshift range of the GRB samples. This unified fitting strategy avoids the circularity problem
in GRB cosmology, in which adopting fixed cosmological model parameters for calibrating the
correlation parameters can bias subsequent cosmology parameter inference. A total of 116 Fermi-
GBM GRBs with known redshifts are utilized in combination with the pseudo-redshift sample of
1576 GRBs. In addition, a combination with SNe Ia datasets from Union 2.1, the Dark Energy
Survey (DES), and Pantheon+SHOES is employed. This combined approach yields a consistent
value for 𝐻0 and ΩΛ, indicating that GRBs with well-modeled pseudo-redshifts can serve as
effective high-redshift cosmological probes.