The Dark Side of the Universe after Planck

TL;DR

This study investigates whether extensions to ΛCDM, including dark radiation ($ΔN_{ m eff}$) and dynamical dark energy models, can reconcile Planck CMB data with BAO, SNLS, Union2.1, and HST observations. Using CAMB/CosmoMC with datasets Planck+WP+BAO+Union2.1+HST and Planck+WP+BAO+SNLS+HST, the authors fit ΛCDM, $w$CDM, and (CPL)CDM with/without $ΔN_{ m eff}$ and report that a modest dark radiation component ($ΔN_{ m eff}≈0.3–0.5$) can ease the $H_0$ tension but does not fix the $\,Ω_m$ discrepancy; the $w$CDM extension yields a phantom-like $w$ (≈−1.15 to −1.16) with compatible $Ω_m$, while the CPL model offers little improvement and shows no evidence for evolving $w(a)$. Overall, the data favor $w$CDM over ΛCDM+$ΔN_{ m eff}$ or CPL+$ΔN_{ m eff}$, and there remains no statistically robust detection of dark radiation or evolving dark energy beyond a phantom-like EOS in $w$CDM. The findings highlight that while dark radiation can partially address certain tensions, combining all datasets still points to persistent inconsistencies between Planck and some SN Ia samples.

Abstract

Recently released Planck data implies a smaller Hubble constant $H_0$ than that from Hubble Space Telescope project (HST) and a larger percentage of the matter components $Ω_m$ compared to Supernova Legacy Survey (SNLS) in $Λ$CDM model. In this paper we found that even though the tension on $H_0$ between Planck and HST can be relaxed if the dark radiation is introduced ($ΔN_{\rm eff}=0.536_{-0.224}^{+0.229}$ at $68\%$ CL from the datasets of Planck+WMAP Polarization (WP)+baryon acoustic oscillation (BAO)+the combination of supernova Union2.1 compilation of 580 SNe (Union2.1)+HST), $Ω_m$ from Planck is still not nicely compatible with that from SNLS. The tensions between Planck and other astrophysical datasets can be significantly relaxed in $w$CDM model, and the combination of these datasets prefers a phantom-like dark energy at more than $95\%$ CL: $w=-1.15\pm 0.07$ and $w=-1.16\pm 0.06$ at $68\%$ CL from Planck+WP+BAO+Union2.1+HST and Planck+WP+BAO+SNLS+HST respectively. From the statistical point of view, there is no evidence for a time-evolving equation of state ($Δχ^2=-0.3$ compared to a constant equation of state for the combination of Planck+WP+BAO+SNLS+HST).

Figures (11)

• Figure 1: (color online). Contour plots of $\Omega_m - H_0$ in $\Lambda$CDM (+$\Delta N_{\rm eff}$) model with different datasets in $68\%$ and $95\%$ confidence region. The light grey band indicates the prior of $H_0$ from HST project at $1 \sigma$ level. The black, blue, olive solid and olive dashed contours enclose the $68\%$ and $95\%$ confidence regions from Planck+WP, BAO, Union2.1+HST and SNLS+HST in the base $\Lambda$CDM model. The red shaded region and green contour respectively enclose the $68\%$ and $95\%$ confidence regions from Planck+WP, and Planck+WP+BAO+Union2.1+HST in the $\Lambda$CDM+$\Delta N_{\rm eff}$ model respectively.
• Figure 2: (color online). Distribution of $\Omega_m$ from different datasets and models. The black, olive solid and olive dashed curves indicate the distributions of $\Omega_m$ from Planck+WP, Union2.1 and SNLS in the base $\Lambda$CDM model. The green and red curves are the distributions from Planck+WP, and Planck+WP+BAO+Union2.1+HST in the $\Lambda$CDM+$\Delta N_{\rm eff}$ model.
• Figure 3: (color online). Contour plots of $\Delta N_{\rm eff} - \Omega_m$ and $\Delta N_{\rm eff} - H_0$ from different datasets in the $\Lambda$CDM+$\Delta N_{\rm eff}$ model. The green and red contours correspond to Planck+WP and Planck+WP+BAO+Union2.1+HST respectively.
• Figure 4: (color online). Plot of $\Delta N_{\rm eff} - n_s$ from different datasets in the $\Lambda$CDM+$\Delta N_{\rm eff}$ model. The green and red contours correspond to Planck+WP and Planck+WP+BAO+Union2.1+HST respectively.
• Figure 5: (color online). Contour plots of $\Omega_m - H_0$ in the $w$CDM model with $68\%$ and $95\%$ confidence regions. The black, green, olive solid and olive dashed contours enclose the $68\%$ and $95\%$ confidence regions from Planck+WP, Planck+WP+BAO, Union2.1+HST and SNLS+HST in the $w$CDM model. The red shaded region and yellow contours are the $68\%$ and $95\%$ confidence regions from the combinations Planck+WP+BAO+Union2.1+HST and Planck+WP+BAO+SNLS+HST respectively.