Probing neutrino masses with future galaxy redshift surveys

TL;DR

This work forecasts the sensitivity of future CMB and galaxy redshift surveys to the total neutrino mass by incorporating CMB priors into a Fisher-matrix framework that also uses linear-scale galaxy power spectra. It demonstrates that PLANCK+SDSS can detect or bound $\sum m_\nu$ at about $0.21$ eV (2σ) and that next-generation CMB+LSS combinations could reach ~0.10–0.13 eV, with an ideal cosmic-variance-limited scenario possibly reaching ~0.08 eV for the inverted hierarchy. The results show the neutrino mass sensitivity depends subtly on the mass splitting (NH vs IH) at low masses, but the degeneracy with other cosmological parameters is limited in a 9-parameter flat-$\Lambda$CDM framework. Overall, cosmology provides a valuable complementary probe of the absolute neutrino-mass scale, complementing terrestrial experiments and aiding interpretation of potential mass-hierarchy signatures from future data.

Abstract

We perform a new study of future sensitivities of galaxy redshift surveys to the free-streaming effect caused by neutrino masses, adding the information on cosmological parameters from measurements of primary anisotropies of the cosmic microwave background (CMB). Our reference cosmological scenario has nine parameters and three different neutrino masses, with a hierarchy imposed by oscillation experiments. Within the present decade, the combination of the Sloan Digital Sky Survey (SDSS) and CMB data from the PLANCK experiment will have a 2-sigma detection threshold on the total neutrino mass close to 0.2 eV. This estimate is robust against the inclusion of extra free parameters in the reference cosmological model. On a longer term, the next generation of experiments may reach values of order sum m_nu = 0.1 eV at 2-sigma, or better if a galaxy redshift survey significantly larger than SDSS is completed. We also discuss how the small changes on the free-streaming scales in the normal and inverted hierarchy schemes are translated into the expected errors from future cosmological data.

Figures (7)

• Figure 1: The two neutrino schemes allowed if $\Delta m_{\rm atm}^2\gg \Delta m_{\rm sun}^2$: normal hierarchy (NH) and inverted hierarchy (IH).
• Figure 2: Neutrino masses as a function of the total mass in the two schemes for the best-fit values of $\Delta m^2$ in Eq. \ref{['dm2values']}. The vertical line marks the smallest value of $\sum m_\nu$ in the inverted scenario.
• Figure 3: Evolution of the total neutrino energy density as a function of the scale factor of the Universe for models where the same $\sum m_\nu$ ($0.12$ eV) is distributed differently. Each line corresponds to the energy density of 4 different cases (only 1 or 2 massive states, Normal and Inverted Hierarchy) normalized to the case with 3 massive states with mass $m_0=\sum m_\nu/3$.
• Figure 4: Comparison of the matter power spectrum obtained for various models where the same $\sum m_\nu$ ($0.12$ eV) is distributed differently. The four lines correspond to the cases with 1 or 2 massive states, Normal and Inverted Hierarchy, divided each time by that with 3 massive states of equal mass $m_0=\sum m_\nu/3$. Differences in the various individual masses and free-streaming scales affect the position and amplitude of the break in the power spectrum.
• Figure 5: Predicted 2$\sigma$ error on the total neutrino mass $M \equiv \sum m_\nu$ as a function of $M$ in the fiducial model, using PLANCK and SDSS (limited to $k_{\rm max}=0.15~h$ Mpc$^{-1}$). The left plot was obtained with the preferred experimental value of $\Delta m^2_{\rm atm}$, and the right plot with the current 3$\sigma$ upper bound. In each case, we show the results assuming either NH or IH.