Constraints on Spatial Curvature and Dark Energy Dynamics in the $w$CDM Model from DESI DR1 and DR2

TL;DR

The paper investigates constraints on the $w$CDM model with spatial curvature ($\Omega_k$) using DESI DR1 and DR2, in combination with BBN, OHD, and Pantheon Plus. Through MCMC analyses within the $w$CDM$+\Omega_k$ framework and employing distance measures $D_H$, $D_M$, and $D_V$ (scaled by the sound horizon $r_d$), it compares DR1 and DR2 performance and assesses degeneracies between curvature and the dark energy EOS $w_0$. Key findings include a mild open-universe preference (larger for DR1 than DR2), near-flat results for DR2 when including OHD and PP, and a subtle deviation of $w_0$ from $-1$ that depends on the dataset (more pronounced with DR2+PP+OHD). The inferred $H_0$ values remain consistent with Planck, and DR2 yields tighter, more consistent distance constraints, underscoring DR2’s improved constraining power. These results motivate further analyses with upcoming DESI data and complementary probes to decisively test curvature and dynamical dark energy.

Abstract

In this study, we investigate the $w$CDM dynamical dark energy model with spatial curvature utilizing the recently released DESI Collaboration data (DR1 and DR2) in conjunction with other observational probes such as BBN, Observational Hubble Data (OHD), and Pantheon Plus (PP). Our investigation attempts to discover which DESI dataset gives a better match to the $w$CDM framework and assess the impact of spatial curvature on cosmological constraints. We find that the cosmic curvature parameter, $Ω_k$, disfavors the cosmological constant for the DR2+BBN and DR2+BBN+OHD data combinations. However, the deviation from the cosmological constant remains below the $1σ$ level, indicating a mild preference for a open universe. In contrast, when using the DR1 based combinations namely DR1+BBN and DR1+BBN+OHD-the deviation from the cosmological constant increases to approximately $1.2σ$, suggesting a slightly stronger indication of a open geometry. Also, the best-fit values of the Hubble constant ($H_0$) obtained from the DR1+BBN+OHD+PP and DR2+BBN+OHD+PP combinations within the dynamical dark energy model are consistent with the results reported by the Planck Collaboration. Our findings provide constraints on the dark energy EoS parameter $ w_{\mathrm{}0}$, reveal a mild but notable deviation from the vacuum energy ($w = -1$) scenario at a significance level $1.8σ$ from DR2+BBN+OHD+PP and $0.5σ$ from DR1+BBN+OHD+PP, both favoring the quintessence region of dark energy. Furthermore, the key physical distance measures $D_H$, $D_V$, and $D_M$ show better consistency with our model when analyzed with the DR2 data.

Figures (7)

• Figure 1: The left 2D contour cosmic curvature $\Omega_k$ versus EoS of DE $w_{0}$ and the right 2D contour cosmic curvature $\Omega_k$ versus $H_0$ for $w$CDM + $\Omega_k$ with all given combination data sets.
• Figure 2: The posterior distribution functions (PDFs) of the EoS of DE $w_{0}$ for $w$CDM + $\Omega_k$ with all given combination data sets.
• Figure 3: The 2D plot Hubble distance $D_H / (r_d *z^{-2/3})$ versus redshift z for $w$CDM + $\Omega_k$ and $\Lambda$CDM models with DR1+BBN+PP+CC and DR2+BBN+PP+CC data sets.
• Figure 4: The 2D plot comoving angular diameter distance $D_M / (r_d *z^{2/3})$ versus redshift z for $w$CDM + $\Omega_k$ and $\Lambda$CDM models with DR1+BBN+PP+CC and DR2+BBN+PP+CC data sets.
• Figure 5: The 2D plot volume-averaged distance $D_V / (r_d *z^{2/3})$ versus redshift z for $w$CDM + $\Omega_k$ and $\Lambda$CDM models with DR1+BBN+PP+CC and DR2+BBN+PP+CC data sets.