Constraints on Neutrino Masses from Weak Lensing

TL;DR

Neutrino masses suppress structure formation through free-streaming, leaving measurable signatures in weak lensing and other cosmological probes. The authors model the nonlinear matter power spectrum in a mixed dark matter scenario and account for non-Gaussian covariances in cosmic shear, using CFHTLS data and external datasets (WMAP5, SNe, BAO) to perform a joint MCMC analysis over an eight-parameter space. They obtain progressive upper bounds on the sum of neutrino masses, from <1.1 eV with WL+WMAP5 to <0.54 eV when all probes are combined, demonstrating how geometrical probes break degeneracies with $\Omega_{m0}$ and $\sigma_8$. The results highlight the importance of covariance modeling and suggest that future wide-field surveys with lensing tomography could achieve neutrino-mass detections with percent-level precision, significantly advancing our understanding of neutrino properties and their cosmological impact.

Abstract

The weak lensing (WL) distortions of distant galaxy images are sensitive to neutrino masses by probing the suppression effect on clustering strengths of total matter in large-scale structure. We use the latest measurement of WL correlations, the CFHTLS data, to explore constraints on neutrino masses. We find that, while the WL data alone cannot place a stringent limit on neutrino masses due to parameter degeneracies, the constraint can be significantly improved when combined with other cosmological probes, the WMAP 5-year (WMAP5) data and the distance measurements of type-Ia supernovae (SNe) and baryon acoustic oscillations (BAO). The upper bounds on the sum of neutrino masses are m_tot = 1.1, 0.76 and 0.54 eV (95% CL) for WL+WMAP5, WMAP5+SNe+BAO, and WL+WMAP5+SNe+BAO, respectively, assuming a flat LCDM model with finite-mass neutrinos. In deriving these constraints, our analysis includes the non-Gaussian covariances of the WL correlation functions to properly take into account significant correlations between different angles.

Figures (10)

• Figure 1: Left panel: A fractional difference between the matter power spectra for a concordance $\Lambda$CDM model ($\Omega_{\rm m0}=0.3$) and a model with finite-mass neutrinos ($\Omega_{\rm cb0}=0.27$ and $\Omega_{\nu0}=0.03$). Note that the total matter density $\Omega_{\rm m0}(=\Omega_{\rm cb0}+\Omega_{\nu0})$ and other cosmological parameters are fixed for the two models. The solid curve shows the model prediction including the correction of nonlinear mass clustering (see the text for the details), while the dashed curve shows the linear-theory prediction. The finite-mass neutrinos cause a suppression in the power spectrum amplitudes on scales below the free-streaming scale. The suppression effect is enhanced over transition scales between linear and nonlinear regimes. Right panel: A similar plot, but for the lensing power spectrum as a function of multipoles $l$.
• Figure 2: The data points show the measured shear correlation functions, $\xi_E(\theta)$, at each angular bins, which are taken from the CFHTLS result in 2008AA...479....9F. The error bars around each data points are computed from diagonal terms in the inverse of the covariance matrix that includes contributions from the shot noise of intrinsic galaxy ellipticities and the Gaussian and non-Gaussian sample variances (see the text for the details). The solid curve is the model prediction for the $\Lambda$CDM model with finite-mass neutrinos which best matches the WL measurement. The dotted curve is the best-fitting model prediction for the joint fitting of WL+WMAP5+SNe+BAO as will be shown below. Note that the best-fitting model has the total neutrino mass of $\sum\!m_\nu=0.25$ eV. To demonstrate the effect of finite-mass neutrinos on $\xi_E$, the dashed curve shows the model prediction where the neutrino mass is changed to $\sum m_\nu=0.54~$eV, roughly at two sigma upper bound for the joint fitting, and other cosmological parameters are fixed to their best-fitting values.
• Figure 3: The projection matrix $|S_{im}|$ for the principal component decomposition of the normalized covariance matrix is plotted, for first three eigenmodes that have largest differential contributions to the cumulative signal-to-noise ratio, $(S/N)$, defined by Eqn.(\ref{['eqn:sn']}). The left panel shows the results obtained when using the halo model developed in TJ08 to compute the covariance matrix. The total signal-to-noise ratio $S/N=10.6$. The right panel shows the result when the fitting formula in Semboloni et al. (2007) 2007MNRAS.375L...6S is employed, yielding $(S/N)=8.89$. For the real-space correlation function, the projection matrix for each eigenmodes has a broad tail, reflecting significant correlations between different angles. It is also found that the contributions from each separation angles become different depending on which model of the covariance matrix is used.
• Figure 4: The contours show the marginalized constraints (68% and 95% CL) for the ($\sum m_\nu,\Omega_{\rm m0}$)-subspace, obtained by fitting the WMAP5 data to the $\Lambda$CDM model with finite-mass neutrinos.
• Figure 5: The improvement in parameter constraints for ($\Omega_{m0}, \sum m_{\nu}$) obtained by combining the CFHT WL data with WMAP5 (green-color contours), in comparison with the constraints for WMAP5 alone (black). The accuracy of $\Omega_{m0}$ determination is improved by adding the WL constraint, because the WL amplitude is sensitive to $\Omega_{\rm m0}$ as can be found from Eqn. (\ref{['eq:Pkappa']}). However, the constraint on $\Sigma m_\nu$ remains almost unchanged due to parameter degeneracies in the WL information.