Updated observational constraints on $φ$CDM dynamical dark energy cosmological models

TL;DR

This study tests the spatially flat φCDM dynamical dark energy model with an inverse power-law potential $V(φ)=V_0 φ^{-α}$ against Planck 2018 CMB data and a comprehensive non-CMB dataset (BAO, Pantheon+ SNIa, $H(z)$, $fσ_8$). Using CAMB/COSMOMC with MCMC, the authors constrain the dark-energy dynamics parameter $α$ (and the lensing amplitude $A_L$ in the extended model) and report that non-CMB data tightens constraints on $α$ to $α=0.055±0.041$ for φCDM and $α=0.095±0.056$ for φCDM+$A_L$ with $H_0≈67.55$ km s$^{-1}$ Mpc$^{-1}$, $Ω_m≈0.31$, and $σ_8≈0.80$. Allowing $A_L$ to vary reduces tensions between CMB and non-CMB data, yielding $A_L≈1.105$ (2.8σ above unity). Overall, φCDM provides a fit comparable to ΛCDM, with mild dynamical dark energy slightly favored in some data combinations, indicating that current observations neither decisively confirm nor exclude evolving quintessence-like dark energy; future precise measurements are needed to break the degeneracy.

Abstract

We present updated observational constraints on the spatially flat $φ$CDM model, where dark energy is described by a minimally coupled scalar field $φ$ with an inverse power-law potential $V=V_0 φ^{-α}$. Using Planck 2018 CMB temperature, polarization (P18), and lensing power spectra (lensing), along with a compilation of non-CMB data including baryon acoustic oscillation, type Ia supernova, Hubble parameter, and growth rate measurements, we constrain $φ$CDM and $φ$CDM+$A_L$ models where $A_L$ is the CMB lensing consistency parameter. The scalar field parameter $α$, which governs dark energy dynamics, is more tightly constrained by non-CMB data than by CMB data alone. For the full dataset, we obtain $α= 0.055 \pm 0.041$ in the $φ$CDM model and $α= 0.095 \pm 0.056$ in the $φ$CDM+$A_L$ model, mildly favoring evolving dark energy over a cosmological constant by $1.3σ$ and $1.7σ$. The Hubble constant is $H_0=67.55_{-0.46}^{+0.53}$ km s$^{-1}$ Mpc$^{-1}$ in the $φ$CDM model, consistent with median statistics and some local determinations, but in tension with other local determinations. The constraints for matter density and clustering amplitude ($Ω_m = 0.3096 \pm 0.0055$, $σ_8 = 0.8013_{-0.0067}^{+0.0077}$) of the flat $φ$CDM model statistically agree with $Λ$CDM model values. Allowing $A_L$ to vary reduces tensions between CMB and non-CMB data, although we find $A_L = 1.105 \pm 0.037$, $2.8σ$ higher than unity, consistent with the excess smoothing seen in Planck data. Model comparison using AIC and DIC indicates that the $φ$CDM model provides a fit comparable to $Λ$CDM, with the $φ$CDM+$A_L$ slightly preferred. Overall, while the $Λ$CDM model remains an excellent fit, current data leave open the possibility of mildly evolving quintessence-like dynamical dark energy.

Figures (6)

• Figure 1: One-dimensional likelihoods and 1$\sigma$ and $2\sigma$ likelihood confidence contours of flat $\phi$CDM model parameters favored by non-CMB (solid curves), P18 (grey), and P18+non-CMB data sets (red contours). For P18 and P18+non-CMB data cases, we include $\tau$ and $n_s$, which are fixed in the non-CMB data analysis. $H_0$ has units of km s$^{-1}$ Mpc$^{-1}$.
• Figure 2: One-dimensional likelihoods and 1$\sigma$ and $2\sigma$ likelihood confidence contours of flat $\phi$CDM model parameters favored by non-CMB (solid curves), P18+lensing (grey), P18+lensing+non-CMB data sets (red contours). For P18 and P18+lensing+non-CMB cases, we include $\tau$ and $n_s$, which are fixed in the non-CMB data analysis. $H_0$ has units of km s$^{-1}$ Mpc$^{-1}$.
• Figure 3: One-dimensional likelihoods and 1$\sigma$ and $2\sigma$ likelihood confidence contours of flat $\phi$CDM$+A_L$ model parameters favored by non-CMB (solid curves), P18 (grey), and P18+non-CMB data sets (red contours). For P18 and P18+non-CMB cases, we include $\tau$ and $n_s$, which are fixed in the non-CMB data analysis. $H_0$ has units of km s$^{-1}$ Mpc$^{-1}$. For the P18 case the prior $\alpha \le 5$ was applied.
• Figure 4: One-dimensional likelihoods and 1$\sigma$ and $2\sigma$ likelihood confidence contours of flat $\phi$CDM$+A_L$ model parameters favored by non-CMB (solid curves), P18+lensing (grey), P18+lensing+non-CMB data sets (red contours). For P18+lensing and P18+lensing+non-CMB cases, we include $\tau$ and $n_s$, which are fixed in the non-CMB data analysis. $H_0$ has units of km s$^{-1}$ Mpc$^{-1}$. For the P18+lensing case the prior $\alpha \le 5$ was applied.
• Figure 5: One-dimensional likelihoods and 1$\sigma$ and $2\sigma$ likelihood confidence contours of flat $\phi$CDM$+A_L$ model parameters favored by non-CMB (solid curves), P18 (grey), and P18+non-CMB data sets (red contours). For P18 and P18+non-CMB cases, we include $\tau$ and $n_s$, which are fixed in the non-CMB data analysis. $H_0$ has units of km s$^{-1}$ Mpc$^{-1}$. For the P18 case the prior $\alpha \le 2$ was applied.