Cosmology in Extended Parameter Space with DESI Data Release 2 Baryon Acoustic Oscillations: A 2$\sigma$+ Detection of Nonzero Neutrino Masses with an Update on Dynamical Dark Energy and Lensing Anomaly

We obtain constraints in a 12 parameter cosmological model using the recent Dark Energy Spectroscopic Instrument Data Release (DR) 2 Baryon Acoustic Oscillations (BAO) data, combined with cosmic microwave background (CMB) power spectra (Planck Public Release, PR, 4) and lensing (Planck PR4 + Atacama Cosmology Telescope (ACT) Data Release (DR) 6) data, uncalibrated Type Ia Supernovae (SNe) data from Pantheon+ and Dark Energy Survey (DES) Year 5 (DESY5) samples, and Weak Lensing (WL: DES Year 1) data. The cosmological model consists of six $\mathrm{\Lambda }$CDM parameters, and additionally, the dynamical dark energy parameters ($w_0$, $w_a$), the sum of neutrino masses ($\sum m_{\nu }$), the effective number of non-photon radiation species ($N_{\mathrm{e}\mathrm{f}\mathrm{f}}$), the scaling of the lensing amplitude ($A_{\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{s}}$), and the running of the scalar spectral index (${\alpha }_s$). Our major findings are the following: i) With CMB+BAO+DESY5+WL, we obtain the first 2$\sigma$+ detection of a nonzero $\sum m_{\nu }=0.19_{-0.18}^{+0.15}$ eV (95%). Replacing DESY5 with Pantheon+ still yields a $\sim$1.9$\sigma$ detection. ii) The cosmological constant lies at the edge of the 95% contour with CMB+BAO+Pantheon+, but is excluded at 2$\sigma$+ with DESY5, leaving evidence for dynamical dark energy dataset-dependent and inconclusive. iii) With CMB+BAO+SNe+WL, $A_{\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{s}}=1$ is excluded at $>2\sigma$, while it remains consistent with unity without WL data - suggesting that the existence of lensing anomaly with Planck PR4 likelihoods may depend on non-CMB datasets. iv) The Hubble tension persists at 3.6-4.2$\sigma$ with CMB+BAO+SNe; WL data has minimal impact.