Cosmological constraints in extended parameter space from the Planck 2018 Legacy release

TL;DR

This study performs a comprehensive analysis of Planck 2018 data within an extended cosmological parameter space that includes the dark energy equation of state ($w$ and optionally $w_a$), the running of the spectral index ($\alpha_S$), the neutrino sector ($N_{\rm eff}$ and $\Sigma m_{\nu}$), and the lensing amplitude ($A_L$). Using Planck 2018 TT,TE,EE+$lowE$ alongside Planck lensing and external data (BAO, Pantheon, and the $H_0$ prior from Riess 2019), it finds that the $A_L$ lensing anomaly persists across models and strongly influences neutrino-mass bounds. A $w<-1$ solution can reconcile Planck with $H_0$ in the presence of $R19$, but BAO and Pantheon favor $w=-1$, indicating that the tension is dataset-dependent. No compelling evidence for evolving dark energy ($w_a eq 0$) emerges, and $N_{\rm eff}$ remains consistent with the standard three-neutrino value. The results underscore the caution required in interpreting neutrino mass constraints when $A_L$ remains anomalous and highlight the ongoing tension between low- and high-redshift probes within extended cosmologies.

Abstract

We present new constraints on extended cosmological scenarios using the recent data from the Planck 2018 Legacy release. In addition to the six parameters of the standard LCDM model, we also simultaneously vary the dark energy equation of state, the neutrino mass, the neutrino effective number, the running of the spectral index and the lensing amplitude $A_L$. We confirm that a resolution of the Hubble tension is given by a dark energy equation of state with w<-1, ruling out quintessence models at high statistical significance. This solution is, however, not supported by BAO and Pantheon data. We find no evidence for evolving dark energy, i.e. $w_a \neq 0$. The neutrino effective number is always in agreement with the expectations of the standard model based on three active neutrinos. The running of the spectral index also is always consistent with zero. Despite the increase in the number of parameters, the $A_L$ lensing anomaly is still present at more than two standard deviations. The $A_L$ anomaly significantly affects the bounds on the neutrino mass that can be larger by a factor four with respect to those derived under standard $Λ$CDM. While the lensing data reduces the evidence for $A_L>1$, the inclusion of BAO and Pantheon increase its statistical significance.

Figures (3)

• Figure 1: Constraints at the $68\%$ and $95\%$ C.L. on the $w$ vs $H_0$, $\Sigma m_{\nu}$ vs $N_{eff}$, and $S_8$ vs $\alpha_s$ planes for the Planck+Lensing, Planck+R19, Planck+BAO, and Planck+Pantheon datasets (Top). The Planck and DES constraints at the $68\%$ and $95\%$ C.L. on the $\sigma_8$ vs $\Omega_m$ plane are also showed (Bottom). A $10$ parameters model, $\Lambda$CDM+$w$+$\alpha_S$+$N_{eff}$+$\Sigma m_{\nu}$, is assumed in the analysis.
• Figure 2: Top:constraints at the $68\%$ and $95\%$ C.L. on the $w$ vs $H_0$, $\Sigma m_{\nu}$ vs $N_{eff}$, and $S_8$ vs $A_L$ planes for the Planck+Lensing, Planck+R19, Planck+BAO, and Planck+Pantheon datasets. Bottom: constraints at the $68\%$ and $95\%$ C.L. on the $\sigma_8$ vs $\Omega_m$ plane from Planck and DES, separately.A $11$ parameters model, $\Lambda$CDM+$w$+$\alpha_S$+$N_{eff}$+$\Sigma m_{\nu}$+$A_L$, is assumed in the analysis.
• Figure 3: Constraints at the $68\%$ and $95\%$ C.L. on the $w$ vs $H_0$,$w_a$ vs $H_0$ ,and $w$ vs $w_a$ planes for the Planck+Lensing, Planck+R19, Planck+BAO, and Planck+Pantheon datasets. In the bottom right corner we also show the 2D constraints on the $w$ vs $w_a$ plane for the Planck+BAO+R19 and Planck+Pantheon+R19 datasets. A $12$ parameters model, $\Lambda$CDM+$w$+$w_a$+$\alpha_S$+$N_{eff}$+$\Sigma m_{\nu}$+$A_L$, is assumed in the analysis.