Cosmology with High-redshift Galaxy Survey: Neutrino Mass and Inflation

TL;DR

This work demonstrates that high-redshift galaxy surveys, when combined with Planck CMB data, can tightly constrain the total neutrino mass and the shape of the primordial power spectrum by exploiting the two-dimensional linear power spectrum in angular and redshift space. Using Fisher-matrix forecasts for three 300 deg^2 survey designs spanning 0.5<z<6.5, the authors show potential detections of m_{ν,tot} with σ ≈ 0.025–0.059 eV and substantial improvements in n_s and alpha_s, particularly from the highest-redshift survey SG. The redshift-space distortion and geometric distortion information play crucial roles in breaking degeneracies with galaxy bias and other cosmological parameters, enabling near-orders-of-magnitude improvements over current constraints. While the analysis is conservative (e.g., neglecting baryonic oscillations), the results highlight the significant impact of high-z clustering on both neutrino physics and inflationary model selection, and point to future refinements including systematics, bispectrum analyses, and joint probes with weak lensing or clusters.

Abstract

(abridged) High-z galaxy redshift surveys open up exciting possibilities for precision determinations of neutrino masses and inflationary models. The high-z surveys are more useful for cosmology than low-z ones owing to much weaker non-linearities in matter clustering, redshift-space distortion and galaxy bias. We can then utilize the two-dimensional information of the linear power spectrum in angular and redshift space to measure the scale-dependent suppression of matter clustering due to neutrino free-streaming as well as the shape of the primordial power spectrum. To illustrate capabilities of high-z surveys for constraining neutrino masses and the primordial power spectrum, we compare three future redshift surveys covering 300 square degrees at 0.5<z<2, 2<z<4, and 3.5<z<6.5. We find that, combined with the cosmic microwave background data expected from the Planck satellite, these surveys allow precision determination of the total neutrino mass with the projected errors of sigma(m_nu)=0.059, 0.043, and 0.025 eV, respectively, thus yielding a positive detection of the neutrino mass rather than an upper limit, as sigma(m_nu) is smaller than the lower limits to the neutrino masses implied from the neutrino oscillation experiments. The accuracies of constraining the tilt and running index of the primordial power spectrum, sigma(n_s)=(3.8, 3.7, 3.0)x10^-3, and sigma(alpha_s)=(5.9, 5.7, 2.4)x10^-3, respectively, are smaller than the current uncertainties by more than an order of magnitude, which will allow us to discriminate between candidate inflationary models. In particular, the error on alpha_s from the highest redshift survey is not very far away from the prediction of a class of simple inflationary models driven by a massive scalar field with self-coupling, alpha_s=-(0.8-1.2)x10^-3.

Figures (8)

• Figure 1: Suppression in the growth rate of total matter perturbations (CDM, baryons and non-relativistic neutrinos), $D_{cb\nu}(a)$, due to neutrino free-streaming. ($a=(1+z)^{-1}$ is the scale factor.) Upper panel: $D_{cb\nu}(a)/D_{\nu=0}(a)$ for the neutrino mass fraction of $f_\nu=\Omega_\nu/\Omega_{\rm m}=0.05$. The number of non-relativistic neutrino species is varied from $N_\nu^{\rm nr}=1$, 2, and 3 (from thick to thin lines), respectively. The solid, dashed, and dotted lines represent $k=0.01$, 0.1, and 1 $h$Mpc$^{-1}$, respectively. Lower panel: $D_{cb\nu}(a)/D_{\nu=0}(a)$ for a smaller neutrino mass fraction, $f_\nu=0.01$. Note that the total mass of non-relativistic neutrinos is fixed to $m_{\nu,{\rm tot}}=N_\nu^{\rm nr}m_\nu=0.66$ eV and 0.13 eV in the upper and lower panels, respectively.
• Figure 2: Upper panel: A fractional suppression of power in the linear power spectrum at $z=4$ due to free-streaming of non-relativistic neutrinos. We fix the total mass of non-relativistic neutrinos by $f_{\rm \nu}=\Omega_\nu/\Omega_{\rm m}=0.05$, and vary the number of non-relativistic neutrino species (which have equal masses, $m_\nu$) as $N^{\rm nr}_\nu=1$ (solid), 2 (dashed), and 3 (dot-dashed). The mass of individual neutrino species therefore varies as $m_\nu=0.66$, 0.33, and 0.22 eV, respectively (see Eq. [\ref{['eq:fnu']}]). The shaded regions represent the 1-$\sigma$ measurement errors on $P(k)$ in each $k$-bin, expected from a galaxy redshift survey observing galaxies at $3.5\le z\le 4.5$ (see Table \ref{['tab:survey']} for definition of the survey). Note that the errors are for the spherically averaged power spectrum over the shell of $k$ in each bin. Different $N_\nu^{\rm nr}$ could be discriminated in this case. Middle panel: Same as in the upper panel, but for a smaller neutrino mass fraction, $f_\nu=0.01$. While it is not possible to discriminate between different $N_\nu^{\rm nr}$, the overall suppression on small scales is clearly seen. Lower panel: Dependences of the shape of $P(k)$ on the other cosmological parameters.
• Figure 3: Upper panel: Projected 68$\%$ error ellipses in the neutrino parameter, ($f_\nu$-$N^{\rm nr}_\nu$) plane, expected from the high-$z$ galaxy survey data combined with the Planck data (see Table \ref{['tab:survey']} for the survey definition). The two fiducial models for $f_\nu$ and $N^{\rm nr}_\nu$ are considered: the left contours assume $(f_{\nu,{\rm fid}}, N^{\rm nr}_{\nu,{\rm fid}})=(0.01,1)$, while the right contours assume $(f_{\nu,{\rm fid}}, N^{\rm nr}_{\nu,{\rm fid}})=(0.05,3)$. The outer thin lines and the middle light-gray contours are the forecasts for SG (the space-based mission at $3.5<z<6.5$) plus Planck, without and with a prior on the running spectral index, $\alpha_s=0$, respectively. The innermost, dark gray contours show the forecasts when all the galaxy surveys (two ground-based surveys and SG) and Planck are combined. The vertical dashed and dotted lines show the lower limits on $f_\nu$ implied from the neutrino oscillation experiments assuming the normal and inverted mass hierarchy models, respectively. The dashed and dotted curves then show the effective number of non-relativistic neutrino species, $N_{\rm eff}$, for the two hierarchy models (see Eq. [\ref{['eq:neff']}] for the definition). Lower panel: The projected 68% on $N^{\rm nr}_{\nu}$ as a function of the fiducial value of $f_\nu$. The thick solid, dashed, and dotted lines use the fiducial values of $N^{\rm nr}_{\nu,{\rm fid}}=1$, 2, and 3, respectively. The dot-dashed curve shows the difference between $N_{\rm eff}$ for the normal and inverted mass hierarchy models. The leftmost thin solid line shows the error expected from a hypothetical full-sky SG survey for $N^{\rm nr}_{\nu,{\rm fid}}=1$.
• Figure 4: The projected 68% error on $f_\nu$ (upper panel) and $N^{\rm nr}_\nu$ (lower panel) against the maximum wavenumber, $k_{\rm max}$, assuming the information in the linear power spectrum at $k\le k_{\rm max}$ can be used in the Fisher matrix analysis. The arrows in the above $x$-axis indicate our nominal $k_{\rm max}$ used in the analysis at each redshift (see Table \ref{['tab:survey']}). Note that $f_{\nu,{\rm fid}}=0.05$ and $N_{\nu,{\rm fid}}^{\rm nr}=3$ are assumed.
• Figure 5: The projected 68% error on $n_s$ (upper panel) and $\alpha_s$ against $k_{\rm max}$, as in Figure \ref{['fig:kmax']}.