Beating Lensing Cosmic Variance with Galaxy Tomography
Ue-Li Pen
TL;DR
This paper addresses the limitation that lensing analyses are limited by cosmic variance and the uncertain, possibly scale- and time-dependent galaxy bias. It proposes cross-correlating distance information from galaxies with projected weak-lensing maps to jointly reconstruct a fully three-dimensional dark matter map and its power spectrum by solving a linear system for a redshift weight function $w(z)$, yielding $w(z)$ approximately equal to $w_L(z)/b(z)$ in the ideal case. By explicitly modeling the scale-dependent bias $b(k,z)$ and the cross-correlation coefficient $r(k,z)$, the framework can quantify stochasticity and, in the linear regime, significantly tighten constraints on $P_{dm}(k,z)$ and the growth factor $D(z)$, with stochasticity bounded via the residual $\chi^2$ of the fit. Demonstrated for CFHT Legacy Survey-like parameters, the method can reduce linear-scale errors by up to a factor of about 3 (and potentially up to 10 when combined with deep spectroscopic data like CLAR), effectively beating cosmic variance and enhancing sensitivity to the cosmic equation of state and neutrino masses. The approach thus provides a practical pathway to high-fidelity 3D dark matter maps from planned and future lensing surveys and redshift surveys.
Abstract
I discuss the use of cross correlations between galaxies with distance information and projected weak lensing dark matter maps to obtain a fully three dimensional dark matter map and power spectrum. On large scales l<100 one expects the galaxies to be biased, but not stochastic. I show that this allows a simultaneous solution of the full 3-D evolving galaxy bias and the dark matter power spectrum simultaneously. Within the photo-z information of the CFH lensing legacy survey, this allows a threefold reduction of statistical error, while a cross correlation with CLAR or other deep spectroscopic surveys allows a tenfold improvement in dark matter power accuracy on linear scales. This makes lensing surveys more sensitive to the cosmic equation of state and the neutrino masses.