Unveiling Neutrino Masses: Insights from Robust (e)BOSS Data Analysis and Prospects for DESI and Beyond

Recent findings from DESI BAO, combined with Planck CMB data, have set an upper limit on the total neutrino mass of ∑ m_ν < 0.072 \, eV (95% confidence level). This rules out the minimum sum for the inverted hierarchy, and interestingly, the most likely value for the total neutrino mass is actually zero. Indeed, methods that rely on the background expansion of the Universe tend to suggest negative neutrino masses. In this work, we contribute to the quest for accurately constraining neutrino mass using cosmological probes. By conducting a full-shape analysis of data from BOSS, eBOSS, and synthetic power spectra, we discovered that constraints on neutrino mass can be significantly influenced by projection effects from the Bayesian marginalization process, rendering these constraints largely unreliable. Our results highlight the need for better techniques to accurately measure the neutrino mass. Based on the large-scale structure suppression, we identified a critical blind spot in the full-shape analysis. By splitting the galaxy power spectrum into broadband and wiggles, we noticed that information on neutrino mass is primarily extracted from the suppressed wiggles rather than broadband suppression. This opens the possibility of developing alternative methods based only on the wiggles of the power spectrum that can be more robust compared to those heavily reliant on background evolution.