Impact of massive neutrinos on nonlinear matter power spectrum

TL;DR

This first attempt to analytically study the nonlinear matter power spectrum for a mixed dark matter model containing neutrinos of total mass ~0.1 eV, based on cosmological perturbation theory, demonstrates that the use of such a nonlinear model may enable a precision of sigma(m(nu,tot)) ~ 0.07 eV in constraining the total neutrino mass for the planned galaxy redshift survey.

Abstract

We present the first attempt to analytically study the nonlinear matter power spectrum for a mixed dark matter (cold dark matter plus neutrinos of total mass ~0.1eV) model based on cosmological perturbation theory. The suppression in the power spectrum amplitudes due to massive neutrinos is, compared to the linear regime, enhanced in the weakly nonlinear regime where standard linear theory ceases to be accurate. We demonstrate that, thanks to this enhanced effect and the gain in the range of wavenumbers to which the PT prediction is applicable, the use of such a nonlinear model may enable a precision of sigma(m_nu,tot) ~ 0.07eV in constraining the total neutrino mass for the planned galaxy redshift survey, a factor of 2 improvement compared to the linear regime.

Figures (2)

• Figure 1: Fractional difference between the mass power spectra at $z=3$ with and without the massive neutrino contributions, where the two cases $f_{\nu}=0.01$ and $0.02$ are considered. The solid and dotted curves show the PT and linear theory results, respectively. The two vertical lines indicate a maximum wavenumber limit $k_{\rm max}$ up to which the two models are expected to be valid (see text). The shaded boxes show the expected $1$-$\sigma$ errors on the power spectrum measurement for the $z\sim 3$ WFMOS survey and the case of $f_\nu=0.01$.
• Figure 2: The marginalized 1-$\sigma$ error on the total neutrino mass as a function of the maximum wavenumber $k_{\rm max}$ used in each redshift slice (see text), for the WFMOS survey combined with the minimal CMB constraints. The fiducial value of $f_\nu=0.01$ is assumed. The solid and dashed curves show the results for the PT and linear theory models, respectively. The light and dark shaded regions represent the range of $k$ where the linear theory and the one-loop PT likely break down due to the stronger nonlinearities.