Journal Article

Combining weak-lensing tomography and spectroscopic redshift surveys

Yan-Chuan Cai and Gary Bernstein

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 422, issue 2, pages 1045-1056
Published in print May 2012 | ISSN: 0035-8711
Published online April 2012 | e-ISSN: 1365-2966 | DOI:
Combining weak-lensing tomography and spectroscopic redshift surveys

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Redshift space distortion (RSD) is a powerful way of measuring the growth of structure and testing General Relativity, but it is limited by cosmic variance and the degeneracy between the galaxy bias b and the growth rate factor f. The cross-correlation of lensing shear with the galaxy density field can in principle measure b in a manner free from cosmic variance limits, breaking the f - b degeneracy and allowing inference of the matter power spectrum from the galaxy survey. We analyse the growth constraints from a realistic tomographic weak-lensing photo-z survey combined with a spectroscopic galaxy redshift survey over the same sky area. For sky coverage fsky= 0.5, analysis of the transverse modes measures b to 2–3 per cent accuracy per Δz= 0.1 bin at z < 1 when ∼10 galaxies arcmin−2 are measured in the lensing survey and all haloes with M > Mmin= 1013h−1  M have spectra. For the gravitational growth parameter parameter γ (, combining the lensing information with RSD analysis of non-transverse modes yields accuracy σ(γ) ≈ 0.01. Adding lensing information to the RSD survey improves σ(γ) by an amount equivalent to a 3 × (10 ×) increase in the RSD survey area when the spectroscopic survey extends down to halo mass 1013.5 (1014) h−1 M. We also find that the σ(γ) of overlapping surveys is equivalent to that of surveys 1.5–2× larger if they are separated on the sky. This gain is greatest when the spectroscopic mass threshold is 1013–1014h−1 M, similar to Luminous Red Galaxy surveys. The gain of overlapping surveys is reduced for very deep or very shallow spectroscopic surveys, but any practical surveys are more powerful when overlapped than when separated. The gain of overlapped surveys is larger in the case when the primordial power spectrum normalization is uncertain by >0.5 per cent.

Keywords: gravitational lensing: weak – methods: statistical – large-scale structure of Universe

Journal Article.  8208 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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