Updated Cosmological Constraints in Extended Parameter Space with Planck PR4, DESI Baryon Acoustic Oscillations, and Supernovae: Dynamical Dark Energy, Neutrino Masses, Lensing Anomaly, and the Hubble Tension

TL;DR

This study expands the standard $\Lambda$CDM framework to a 12-parameter space by including dynamical dark energy ($w_0$, $w_a$), the sum of neutrino masses $\sum m_\nu$, $N_{\rm eff}$, $A_{\rm lens}$, and $\alpha_s$, analyzed with Planck PR4 (HiLLiPoP/LoLLiPoP) data together with DESI DR1 BAO, Pantheon+ and DESY5 SNe. It finds no robust exclusion of a cosmological constant in some combinations (Pantheon+), while DESY5 alone favors dynamical dark energy, highlighting possible systematics; 1σ hints of $\sum m_\nu$ arise in several cases, but a conservative upper bound of $\sum m_\nu \lesssim 0.3$ eV (95% CL) remains robust. The lensing amplitude remains consistent with unity ($A_{\rm lens} \approx 1$) and the Hubble tension persists at $3.2$–$3.9\sigma$, whereas the $S_8$ tension with DES Year 3 weak lensing is reduced to about $1.4\sigma$ in this extended cosmology. These results underscore the sensitivity of cosmological inferences to dataset choices and modern likelihoods, and they suggest that simple extensions to $\Lambda$CDM are insufficient to fully resolve major cosmological tensions.

Abstract

We present updated constraints on cosmological parameters in a 12-parameter model, extending the standard six-parameter $Λ$CDM by including dynamical dark energy (DE: $w_0$, $w_a$), the sum of neutrino masses ($\sum m_ν$), the effective number of non-photon radiation species ($N_{\rm eff}$), the lensing amplitude scaling ($A_{\rm lens}$), and the running of the scalar spectral index ($α_s$). For CMB data, we use the Planck PR4 (2020) HiLLiPoP and LoLLiPoP likelihoods, Planck PR4+ACT DR6 lensing, and Planck 2018 low-$l$ TT likelihoods, along with DESI DR1 BAO and Pantheon+ and DESY5 uncalibrated type Ia Supernovae (SNe) likelihoods. Key findings are the following: i) Contrary to DESI results, CMB+BAO+Pantheon+ data include a cosmological constant within $2σ$, while CMB+BAO+DESY5 excludes it at over $2σ$, indicating the dynamical nature of dark energy is not yet robust. Potential systematics in the DESY5 sample may drive this exclusion. ii) Some data combinations show a $1σ$+ detection of non-zero $\sum m_ν$, indicating possible future detection. We also provide a robust upper bound of $\sum m_ν \lesssim 0.3$ eV (95% confidence limit (C.L.)). iii) With CMB+BAO+SNe, $A_{\rm lens} = 1$ is included at $2σ$ (albeit not at $1σ$), indicating no significant lensing anomaly in this extended cosmology with Planck PR4 likelihoods. iv) The Hubble tension persists at $3.2$ to $3.9σ$, suggesting these simple extensions do not resolve it. v) The $S_8$ tension with DES Year 3 weak lensing is reduced to $1.4σ$, likely due to additional parameters and the Planck PR4 likelihoods.

Figures (10)

• Figure 1: 68% and 95% marginalised contours in the $w_{0,\rm DE} - w_{a,\rm DE}$ plane for different data combinations. The region at the bottom of the vertical dashed blue line and above the slanted dashed blue line is the parameter space for quintessence-like/non-phantom DE.
• Figure 2: Comparison of 1-D marginalised posterior probability distributions for $w_0$ and $w_a$ for different data combinations.
• Figure 3: Comparison of 1-D marginalised posterior distributions for $\sum m_{\nu}$ [eV] for different data combinations. The two vertical black dashed lines correspond to 0.057 eV and 0.096 eV, which are the minimum masses required by normal and inverted hierarchies respectively.
• Figure 4: 68% and 95% marginalised contours in the $w_{0,\rm DE}-\sum m_{\nu}$ [eV] (top) and $w_{a,\rm DE}-\sum m_{\nu}$ [eV] (bottom) planes for different data combinations.
• Figure 5: The top panel shows the 1-D marginalised posterior probability distributions for $A_{\rm lens}$ for different data combinations. The bottom panel shows the 68% and 95% marginalised contours in the $A_{\rm lens}-\sum m_{\nu}$ [eV] plane for the same data combinations.