Measuring neutrino masses with large-scale structure: Euclid forecast with controlled theoretical error

We present a Markov-Chain Monte-Carlo (MCMC) forecast for the precision of neutrino mass and cosmological parameter measurements with a Euclid-like galaxy clustering survey. We use a complete perturbation theory model for the galaxy one-loop power spectrum and tree-level bispectrum, which includes bias, redshift space distortions, IR resummation for baryon acoustic oscillations and UV counterterms. The latter encapsulate various effects of short-scale dynamics which cannot be modeled within perturbation theory. Our MCMC procedure consistently computes the non-linear power spectra and bispectra as we scan over different cosmologies. The second ingredient of our approach is the theoretical error covariance which captures uncertainties due to higher-order non-linear corrections omitted in our model. Having specified characteristics of a Euclid-like spectroscopic survey, we generate and fit mock galaxy power spectrum and bispectrum likelihoods. Our results suggest that even under very agnostic assumptions about non-linearities and short-scale physics a future Euclid-like survey will be able to measure the sum of neutrino masses with a standard deviation of 28 meV . When combined with the Planck cosmic microwave background likelihood, this uncertainty decreases to 13 meV . Over-optimistically reducing the theoretical error on the bispectrum down to the two-loop level marginally tightens this bound to 11 meV . Moreover, we show that the future large-scale structure (LSS) spectroscopic data will greatly improve constraints on the other cosmological parameters, e.g. reaching a percent (per mille) error on the Hubble constant with LSS alone (LSS + Planck).