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 cosmic microwave background (CMB) information. In this paper we develop a method to model galaxy power spectrum in the weakly nonlinear regime for a mixed 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 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 BOSS or Stage-III type survey, when combined with Planck CMB information, gives a precision of total neutrino mass constraint, sigma(m_nu,tot) 0.1eV, while Stage-IV type survey may achieve sigma(m_nu,tot) 0.05eV, 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 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.Comment: 33 pages, 11 figure

Wave modelling - the state of the art

This paper is the product of the wave modelling community and it tries to make a picture of the present situation in this branch of science, exploring the previous and the most recent results and looking ahead towards the solution of the problems we presently face. Both theory and applications are considered. The many faces of the subject imply separate discussions. This is reflected into the single sections, seven of them, each dealing with a specific topic, the whole providing a broad and solid overview of the present state of the art. After an introduction framing the problem and the approach we followed, we deal in sequence with the following subjects: (Section) 2, generation by wind; 3, nonlinear interactions in deep water; 4, white-capping dissipation; 5, nonlinear interactions in shallow water; 6, dissipation at the sea bottom; 7, wave propagation; 8, numerics. The two final sections, 9 and 10, summarize the present situation from a general point of view and try to look at the future developments