Neutrino masses from large-scale structures: future sensitivity and theory dependence

In the incoming years, cosmological surveys aim at measuring the sum of neutrino masses $\Sigma m_\nu$, complementing the determination of their mass ordering from laboratory experiments. In order to assess the full potential of large-scale structures (LSS), we employ state-of-the-art predictions from the effective field theory of LSS (EFTofLSS) at one loop to perform Fisher forecasts on the sensitivity (combining power spectrum and bispectrum) of ongoing and future surveys (DESI, MegaMapper) in combination with CMB measurements (Planck, Litebird and Stage-4). We find that the 1$\sigma$ sensitivity on $\Sigma m_\nu$ is expected to be 15 meV with Planck+DESI, and 7 meV with S4+MegaMapper, where $\sim 10\%$ and $30\%$ of the constraints are brought by the one-loop bispectrum respectively. To understand how robust are these bounds, we explore how they are relaxed when considering extensions to the standard model, dubbed `new physics'. We find that the shift induced on $\Sigma m_\nu$ by a $1\sigma$ shift on new physics parameters (we consider extra relativistic species, neutrino self-interactions, curvature or a time-evolving electron mass) could be $\mathcal O(10)$ meV for Planck+DESI, but it will be suppressed down to $\mathcal O(1)$ meV in S4+MegaMapper. Our study highlights the quantitative impact of including the bispectrum at one loop in the EFTofLSS, and the robustness of the sensitivity to $\Sigma m_\nu$ against potential new physics thanks to the synergy of cosmological probes.