Weighing Neutrinos: Weak Lensing Approach

TL;DR

The paper investigates weighing neutrinos with weak gravitational lensing by exploiting the suppression of small-scale power in the matter distribution caused by non-zero neutrino masses. It derives the weak lensing convergence power spectrum $P_\kappa(l)$ from the 3D potential power spectrum, incorporating realistic source distributions and noise, and models linear and nonlinear evolution including massive neutrinos with the Ma (1998) fitting function. Using a Fisher information framework with six cosmological parameters and various priors, it forecasts 2σ neutrino-mass limits for surveys of different sizes, showing that 100×100 deg$^2$ surveys could detect $m_ν$ at the few-eV level under conservative assumptions, while Planck-like CMB constraints could push sensitivity to sub-eV scales. The study highlights degeneracies that can mimic neutrino effects (cosmic confusion) and stresses that external parameter constraints are essential for robust neutrino mass measurements from weak lensing, although even small surveys can contribute under favorable priors.

Abstract

We study the possibility for a measurement of neutrino mass using weak gravitational lensing. The presence of non-zero mass neutrinos leads to a suppression of power at small scales and reduces the expected weak lensing signal. The measurement of such a suppression in the weak lensing power spectrum allows a direct measurement of the neutrino mass, in contrast to various other experiments which only allow mass splittings between two neutrino species. Making reasonable assumptions on the accuracy of cosmological parameters, we suggest that a weak lensing survey of 100 sqr. degrees can be easily used to detect neutrinos down to a mass limit of 3.5 eV at the 2 sigma level. This limit is lower than current limits on neutrino mass, such as from the Ly-alpha forest and SN1987A. An ultimate weak lensing survey of pi steradians down to a magnitude limit of 25 can be used to detect neutrinos down to a mass limit of 0.4 eV at the 2 sigma level, provided that other cosmological parameters will be known to an accuracy expected from cosmic microwave background spectrum using the MAP satellite. With improved parameters estimated from the PLANCK satellite, the limit on neutrino mass from weak lensing can be further lowered by another factor of 3 to 4. For much smaller surveys (10 sqr. degrees) that are likely to be first available in the near future with several wide-field cameras, the presence of neutrinos can be safely ignored when deriving conventional cosmological parameters such as the mass density of the Universe. However, armed with cosmological parameter estimates with other techniques, even such small area surveys allow a strong possibility to investigate the presence of non-zero mass neutrinos.

Figures (3)

• Figure 1: Weak Lensing Power Spectrum for two COBE normalized models involving non-zero mass neutrinos. The upper set of curves correspond to a flat cosmological model involving $\Omega_m=0.75$, $\Omega_b=0.05$, $h=0.65$, $n_s=1$, while the lower set of curves are for $\Omega_m=0.35$ with other parameters as above. In grey, we show weak lensing power spectra using Peacock & Dodds (1996) fitting function for nonlinear evolution of the power spectrum, calculated assuming its validity for MDM cosmologies, while dark lines show weak lensing power spectra for recently updated fitting functions for MDM cosmologies by Ma (1998). In dot-dashed lines, we show expected errors in the power spectrum measurement from a weak lensing survey of 25 $\times$ 25 deg$^{2}$ down to the magnitude limits of 25 in R. Such a survey is expected to be available in near future with wide-field cameras such as MEGACAM (Boulade et al. 1998).
• Figure 2: Cosmic confusion: Two alternate models involving changes in the baryon content or the scalar tilt produce essentially the same power spectrum as a model involving 0.7 eV neutrinos. The grey curves are same as Fig. 1.
• Figure 3: Expected 2$\sigma$ detection limit for 100 $\times$ 100 deg.$^2$ weak lensing survey down to a magnitude limit of 25, assuming a spatially flat Universe with a scalar tilt of 1. Solid line represents detection with our conservative errors while the dashed line represent detection with more optimistic errors. The dot-dashed line is for models involving normalizations based on current measurements of $\sigma_8$ and using more optimistic errors.