Exploring the Cosmological Model Degeneracy with a new evaluate factor G

TL;DR

This work tackles cosmological parameter degeneracy by introducing the G factor as an observational-data quality diagnostic, evaluated on Cosmic Chronometers (CC) and Baryon Acoustic Oscillations (BAO) with MCMC under ΛCDM. The G factor, defined as the sensitivity of the Hubble parameter to density parameters normalized by observational error, is combined across parameters and tested via a Figure of Merit (FoM) to quantify constraining power. Results show CC yields near-linear G(z) while BAO shows a cubic G(z) dependence; high-G data improve FoM and produce parameter constraints closer to Planck results, especially for CC+BAO. Simulated OHD analyses indicate high-G datasets can break degeneracies at high redshift (z > 2.5) and that reducing measurement uncertainties further strengthens this effect, suggesting future high-precision surveys will benefit from G-based data screening and selection.

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.

Figures (10)

• Figure 1: illustrates the posterior distributions from the corresponding MCMC runs in a $3\times2$ matrix layout, representing the data combinations (CC, BAO, CC+BAO) for the two $G$ factor states (Low, High). Within each subplot, the parameters $(H_{0}, \Omega_{\Lambda}, \Omega_{m}, \Omega_{k})$ are uniformly ordered from top to bottom and left to right.
• Figure 2: presents scatter plots with error bars for the three components of the $G$ factor ($G_{\Lambda}$, $G_{m}$, and $G_{k}$) as functions of redshift $z$, derived from the CC+BAO dataset. The corresponding linear fitting curves for each data group and regression coefficient $R$ are also shown in the legend and are distinguished by three different colors.
• Figure 3: is similar to Fig. \ref{['Fig1']} but shows only the scatter plots with error bars for the three components of the $G$ factor ($G_{\Lambda}$, $G_{m}$, and $G_{k}$) as functions of redshift $z$, derived solely from the CC dataset. The legend follows the same format as in Fig. \ref{['Fig1']}.
• Figure 4: differs from Fig. \ref{['Fig1']} in that the dataset is changed to BAO data, and the linear fitting is replaced with a cubic function model, and this adjustment is applied to all components of the $G$ factor ($G_{\Lambda}$, $G_{m}$, and $G_{k}$), leading to a notable improvement in fitting accuracy compared to Fig. \ref{['Fig1']}. The legend format remains the same as in Fig. \ref{['Fig1']}.
• Figure 5: illustrates the cubic fitting curves of the $G$ factor derived using three different methods for cosmological parameter estimation. The blue curve corresponds to parameters obtained from MCMC analysis, the green curve represents results directly provided in Planck2020, and the red curve is constructed based on three parameters defined in the text, which are related to $G$ and its higher-order derivatives with respect to $z$.