Cosmological neutrino mass: a frequentist overview in light of DESI (2507.12401v1)

Abstract: We derive constraints on the neutrino mass using a variety of recent cosmological datasets, including DESI BAO, the full-shape analysis of the DESI matter power spectrum and the one-dimensional power spectrum of the Lyman-$\alpha$ forest (P1D) from eBOSS quasars as well as the cosmic microwave background (CMB). The constraints are obtained in the frequentist formalism by constructing profile likelihoods and applying the Feldman-Cousins prescription to compute confidence intervals. This method avoids potential prior and volume effects that may arise in a comparable Bayesian analysis. Parabolic fits to the profiles allow one to distinguish changes in the upper limits from variations in the constraining power $\sigma$ of the different data combinations. We find that all profiles in the $\Lambda$CDM model are cut off by the $\sum m_\nu \geq 0$ bound, meaning that the corresponding parabolas reach their minimum in the unphysical sector. The most stringent 95% C.L. upper limit is obtained by the combination of DESI DR2 BAO, Planck PR4 and CMB lensing at 53 meV, below the minimum of 59 meV set by the normal ordering. Extending $\Lambda$CDM to non-zero curvature and $w_0w_\mathrm{a}$CDM relaxes the constraints past 59 meV again, but only $w_0w_\mathrm{a}$CDM exhibits profiles with a minimum at a positive value. Using a combination of DESI DR1 full-shape, BBN and eBOSS Lyman-$\alpha$ P1D, we successfully constrain the neutrino mass independently of the CMB. This combination yields $\sum m_\nu \leq 285$ meV (95% C.L.). The addition of DESI full-shape or Lyman-$\alpha$ P1D to CMB and DESI BAO results in small but noticeable improvement of the constraining power of the data. Lyman-$\alpha$ free-streaming measurements especially improve the constraint. Since they are based on eBOSS data, this sets a promising precedent for upcoming DESI data.