Unveiling neutrino masses: Insights from a robust BOSS and eBOSS 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 $\ensuremath{\sum}{m}_{\ensuremath{\nu}}<0.072\text{ }\text{ }\mathrm{eV}$ (95% confidence level), ruling out the inverted hierarchy. 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 on data from BOSS, eBOSS, and synthetic power spectra, we showed that projection effects can significantly influence constraints on neutrino mass, rendering these measurements largely unreliable. Our results highlight the need for better techniques to measure the neutrino mass accurately. 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 relative amplitude of the BAO 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 than those heavily reliant on background evolution.