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

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 2σ, while CMB+BAO+DESY5 excludes it at over 2σ, 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 1σ+ 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 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 Dark Energy Survey Year 3 weak lensing is reduced to 1.4σ, likely due to additional parameters and the Planck PR4 likelihoods.