Probing Time-Varying Dark Energy with DESI: The Crucial Role of Precision Matter Density (\Omega_{m0}) Measurements

TL;DR

Precise measurements of matter density are essential for constraining time-varying dark energy, as current data shows high sensitivity to \\Omega_{m0} but limited ability to detect DE evolution without improved precision and parametrization.

Contribution

This study highlights the critical importance of high-precision \\Omega_{m0} measurements and optimized parametrizations for constraining dynamic dark energy with DESI data.

Findings

Cosmological observables are more sensitive to \\Omega_{m0} than to DE parameters.

Standard CPL parametrization shows low sensitivity to w_a, limiting DE evolution detection.

Combined datasets improve constraints but are affected by parametrization choices.

Abstract

Accurate measurements of fundamental cosmological parameters, especially the Hubble constant (H_0) and present-day matter density (\Omega_{m0}), are crucial for constraining dark energy (DE) evolution. We analyze the sensitivities of cosmological observables (H(z), D_L(z), E_{G}) to \Omega_{m0}, w_0, and w_an under different parametrizations. Our results show observables are far more sensitive to \Omega_{m0} than to DE equation of state parameters (e.g., at z \sim 0.5, H(z)'s \Omega_{m0} sensitivity is \sim 0.7 vs. w_a's \sim 0.04). This hierarchy mandates high-precision \Omega_{m0} measurements to accurately constrain time-varying DE. We also find DE parameter sensitivity highly depends on parametrization; the standard CPL form shows low sensitivity to w_a, but \omega(z) = w_0 + w_a \ln(1+z) significantly enhances it. Our analysis of DESI DR1/DR2 data confirms these theoretical limits: standalone DESI data primarily provides only upper limits for w_a, underscoring insufficient constraining power for a definitive time-varying DE detection. While combined datasets offer tighter constraints, interpretation requires caution due to parametrization influence. We further confirm this point using simulated Supernovae MCMC data. In conclusion, improving \Omega_{m0} precision and adopting optimized parametrizations are imperative for future surveys like DESI to fully probe dark energy's nature.