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

Abstract We present updated constraints on cosmological parameters in a 12-parameter model, extending the standard six-parameter ΛCDM by including dynamical dark energy (DE ; w 0 , w a ), the sum of neutrino masses (∑ m ν ), the effective number of non-photon radiation species ( N eff ), the lensing amplitude scaling ( A lens ), and the running of the scalar spectral index ( α s ). For cosmic wave background (CMB) data, we use the Planck Public Release (PR) 4 (2020) HiLLiPoP and LoLLiPoP likelihoods, Planck PR4+Atacama Cosmology Telescope (ACT) DR6 lensing, and Planck 2018 low- ℓ TT likelihoods, along with DESI DR1 baryon acoustic oscillations (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 2 σ , while CMB+BAO+DESY5 excludes it at over 2 σ , indicating the dynamical nature of DE is not yet robust. Potential systematics in the DESY5 sample may drive this exclusion. (ii) Some data combinations show a 1 σ + detection of nonzero ∑ m ν , indicating possible future detection. We also provide a robust upper bound of ∑ m ν ≲ 0.3 eV (95% confidence limit (CL)). (iii) With CMB+BAO+SNe, A lens = 1 is included at 2 σ (albeit not at 1 σ ), indicating no significant lensing anomaly in this extended cosmology with Planck PR4 likelihoods. (iv) The Hubble tension persists at 3.2 to 3.9 σ , suggesting these simple extensions do not resolve it. (v) The S 8 tension with Dark Energy Survey Year 3 weak lensing is reduced to 1.4 σ , likely due to additional parameters and the Planck PR4 likelihoods.