Exploring the Cosmological Model Degeneracy with a new evaluate factor G

Abstract

In the context of fitting cosmological models, parameter degeneracy remains a central issue. This paper critically examines traditional methods for constraining parameters and focuses on the G factor as a tool for evaluating the quality of observational data. To ensure analytical independence, two datasets--Cosmic Chronometers (CC) and Baryon Acoustic Oscillations (BAO)--were utilized as samples for parameter fitting, supplemented by Markov Chain Monte Carlo (MCMC) simulations. The Figure of Merit (FoM) matrix served as the final criterion for assessing fitting performance. The results show that the G factor of the CC dataset increases linearly with redshift z, whereas the G factor of the BAO dataset follows a cubic relationship. Further analysis indicates that the FoM value for datasets with high G factors is significantly higher than that for datasets with low G factors, thereby validating the G factor's effectiveness as a tool for assessing observational data quality and reducing parameter degeneracy. This suggests that the G factor may serve as a diagnostic tool and selection criterion for optimizing observational datasets in future research.