Nonlinear power spectrum in the presence of massive neutrinos: Perturbation theory approach, galaxy bias, and parameter forecasts

Future or ongoing galaxy redshift surveys can put stringent constraints on neutrinos masses via the high-precision measurements of galaxy power spectrum, when combined with CMB information. In this paper we develop a method to model galaxy power spectrum in the weakly nonlinear regime for a mixed dark matter [cold dark matter (CDM) plus finite-mass neutrinos] model, based on perturbation theory (PT) whose validity is well tested by simulations for a CDM model. In doing this we carefully study various aspects of the nonlinear clustering (nonlinear neutrino perturbations and the higher-order growth functions), and then arrive at a useful approximation allowing for a quick computation of the nonlinear power spectrum as in the CDM case. The nonlinear galaxy bias is also included in a self-consistent manner within the PT framework. Thus, the use of our PT model can give a more robust understanding of the measured galaxy power spectrum as well as allow for higher sensitivity to neutrino masses due to the gain of Fourier modes beyond the linear regime. Based on the Fisher matrix formalism, we find that the BOSS or Stage-III type survey, when combined with Planck CMB information, gives a precision of total neutrino mass constraint, sigma(m(v,tot)) similar or equal to 0.1 eV, while the Stage-IV type survey may achieve sigma(m(v,tot)) similar or equal to 0.05 eV, i.e., more than a 1-sigma detection of neutrino masses. We also discuss possible systematic errors on dark energy parameters caused by the neutrino mass uncertainty. The significant correlation between neutrino mass and dark energy parameters is found, if the information on power spectrum amplitude is included. More importantly, for the Stage-IV type survey, a best-fit dark energy model may be biased and falsely away from the underlying true model by more than the 1-sigma statistical errors, if neutrino mass is ignored in the model fitting.