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

Abstract

Accurate measurements of fundamental cosmological parameters, especially the Hubble constant (H_0) and present-day matter density (Ω_{m0}), are crucial for constraining dark energy (DE) evolution. We analyze the sensitivities of cosmological observables (H(z), D_L(z), E_{G}) to Ω_{m0}, w_0, and w_an under different parametrizations. Our results show observables are far more sensitive to Ω_{m0} than to DE equation of state parameters (e.g., at z \sim 0.5, H(z)'s Ω_{m0} sensitivity is \sim 0.7 vs. w_a's \sim 0.04). This hierarchy mandates high-precision Ω_{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 ω(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 Ω_{m0} precision and adopting optimized parametrizations are imperative for future surveys like DESI to fully probe dark energy's nature.

Figures (8)

• Figure 1: Relative deviations of $H$ from the $\Lambda$CDM prediction for different values of cosmological parameters ($H_0,\Omega_{\rm{m} 0}$)=($73,0.3$), ($73,0.25$), and ($68,0.3$) from left to right. Observational data are taken from Jimenez:2003ivStern:2009epGaztanaga:2008xz. The observational data are shown for reference only. No likelihood fit or parameter inference is performed using these data in this figure.
• Figure 2: Logarithmic derivatives of the Hubble parameter with respect to (w.r.t) $\Omega_{\rm{m} 0}$ (left), $\omega_{0}$ (middle), and $\omega_{a}$ (right) as a function of redshift for different DE models: ($\omega_{0}$ ,$\omega_{a}$) = ($-1.0$, $-0.8$) (green, long-dashed), (-1.1, 0.0) (brown, dot-dashed), (-1.0, 0.0) (red, solid), (-0.9, 0.0) (blue, dotted), (-1.0, +0.8) (orange, dashed).
• Figure 3: Logarithmic derivatives of the luminosity distance w.r.t $\Omega_{\rm{m} 0}$ (left), $\omega_{0}$ (middle), and $\omega_{a}$ (right) as a function of redshift for the different DE models. The representation of each curve corresponds to the same DE models used in Figure \ref{['fig2']}.
• Figure 4: Logarithmic derivatives of the $E_{\rm{G}}$ parameter with respect to (w.r.t) $\Omega_{\rm{m} 0}$ (left), $\omega_{0}$ (middle), and $\omega_{a}$ (right) as a function of redshift for the different DE models. The representation of each curve corresponds to the same DE models used in Figure \ref{['fig2']}.
• Figure 5: Logarithmic derivatives of the Hubble parameter w.r.t $\Omega_{\rm{m} 0}$ (left), $\omega_{0}$ (middle), and $\omega_{a}$ (right) as a function of redshift for the different DE models when we use $\omega(z) = \omega_{0} + \omega_{a} \ln(1 + z)$. Note that the DE EOS used here is different from that in Figure \ref{['fig2']} (CPL parametrization), but the ($\omega_{0}$ , $\omega_{a}$) values and the corresponding line styles employed for different DE models are identical to those used in Figure \ref{['fig2']}.