Measuring neutrino masses and dark energy with weak lensing tomography

TL;DR

This paper assesses how weak lensing tomography can constrain neutrino masses and the dark energy equation of state, emphasizing the sensitivity gains from tomographic binning and the impact of key systematic effects. Using a Fisher matrix forecast that combines Planck CMB data with LSST-like (wide) and SNAP-like (deep) lensing surveys, it shows that $\sigma(\sum m_\nu)$ can reach about $0.043$–$0.047$ eV with five tomography bins, effectively breaking the $\,m_\nu - w\,$ degeneracy. The analysis incorporates photometric redshift errors, shear calibration biases, and nonlinear matter power spectrum modeling via a halo model, highlighting that photometric redshift control is crucial for preserving dark-energy and neutrino-mass sensitivities. The results demonstrate the strong complementarity between weak lensing tomography and CMB data, and indicate that future surveys could probe the neutrino mass hierarchy while tightly constraining the dark energy evolution, with practical impact for planning next-generation cosmological probes.

Abstract

Surveys of weak gravitational lensing of distant galaxies will be one of the key cosmological probes in the future. We study the ability of such surveys to constrain neutrino masses and the equation of state parameter of the dark energy, focussing on how tomographic information can improve the sensitivity to these parameters. We also provide a detailed discussion of systematic effects pertinent to weak lensing surveys, and the possible degradation of sensitivity to cosmological parameters due to these effects. For future probes such as the Large Synoptic Survey Telescope survey, we find that, when combined with cosmic microwave background data from the Planck satellite, a sensitivity to neutrino masses of sigma(sum m_nu) < 0.05 eV can be reached. This results is robust against variations in the running of the scalar spectral index, the time-dependence of dark energy equation of state, and/or the number of relativistic degrees of freedom.

Figures (6)

• Figure 1: Convergence auto and cross power spectra for the standard $\Lambda$CDM model, assuming the galaxy distribution function (\ref{['eq:ngal']}) and two tomography bins at $0 \leq z\leq 1.5$ and $1.5 < z \leq 3$. The $1 \sigma$ error bands are computed for a lensing survey with sky coverage $f_{\rm sky}=0.01$, $\bar{n}_{\rm gal}=30 \ {\rm arcmin}^{-2}$, and $\gamma_{\rm rms}=0.4$, smeared over bands of width $\Delta \ell = \ell/4$. See section \ref{['sec:forecast']} for definitions.
• Figure 2: Top: Distance--redshift relation for four sets of dark energy parameters $\{\Omega_{\rm de},w\}$ listed in the Figure, where $w$ is taken to be constant in time. Middle: Lensing weights $W(\chi)/\Omega_m$, without tomography, for the same four sets of $\{\Omega_{\rm de},w\}$, assuming the galaxy distribution function (\ref{['eq:ngal']}) with $\alpha=2$, $\beta=2$, and $z_0=1$. Bottom: Lensing weights for three tomographic divisions at $0 \leq z \leq 1$, $1 < z \leq 2$, and $2 < z \leq 3$.
• Figure 3: Nonlinear matter power spectra constructed from the halo model for various neutrino masses (solid lines). Also shown are the corresponding power spectra from the linear theory (dotted lines).
• Figure 4: Projected $1\sigma$ contours in the dark energy and neutrino parameter space from an LSST-like ground-based wide lensing survey (with and without tomography) and Planck for an eleven parameter cosmological model. The red (dot-dash), blue (solid), green (dashed), and gray (dotted) lines correspond to one, three, five, and eight tomography bins respectively. Each contour comes from marginalising over the other nine cosmological parameters and all $2\times N_{\rm pz}+n_{\rm t}$ systematic parameters, with Gaussian priors imposed on the latter.
• Figure 5: Same as Figure \ref{['fig:wide']}, but from a SNAP-like space-based deep survey and Planck.