[Paper Review] COSMOS: 3D weak lensing and the growth of structure

R. Massey, Jason Rhodes+18 more|arXiv (Cornell University)|Jan 17, 2007

Astronomy and Astrophysical Research4 citations

TL;DR

This paper presents a 3D weak lensing analysis of the Hubble Space Telescope COSMOS survey, using redshift-dependent shear measurements to constrain cosmological parameters. It finds σ₈(Ωₘ/0.3)^0.44 = 0.866⁺⁰.⁰⁸⁵₋⁰.⁰⁶⁸ at 68% confidence, with absolute shear calibration as the dominant systematic uncertainty, demonstrating the feasibility of tomographic weak lensing for future space-based surveys.

ABSTRACT

We present a three dimensional cosmic shear analysis of the Hubble Space Telescope COSMOS survey, the largest ever optical imaging program performed in space. We have measured the shapes of galaxies for the tell-tale distortions caused by weak gravitational lensing, and traced the growth of that signal as a function of redshift. Using both 2D and 3D analyses, we measure cosmological parameters Omega_m, the density of matter in the universe, and sigma_8, the normalization of the matter power spectrum. The introduction of redshift information tightens the constraints by a factor of three, and also reduces the relative sampling (or "cosmic") variance compared to recent surveys that may be larger but are only two dimensional. From the 3D analysis, we find sigma_8*(Omega_m/0.3)^0.44=0.866+^0.085_-0.068 at 68% confidence limits, including both statistical and potential systematic sources of error in the total budget. Indeed, the absolute calibration of shear measurement methods is now the dominant source of uncertainty. Assuming instead a baseline cosmology to fix the geometry of the universe, we have measured the growth of structure on both linear and non-linear physical scales. Our results thus demonstrate a proof of concept for tomographic analysis techniques that have been proposed for future weak lensing surveys by a dedicated wide-field telescope in space.

Motivation & Objective

• To measure cosmological parameters Ωₘ and σ₈ using 3D weak gravitational lensing in the COSMOS survey.
• To reduce cosmic variance and improve constraints by incorporating redshift information into the lensing analysis.
• To assess the impact of systematic errors—particularly shear measurement calibration—on cosmological constraints.
• To validate tomographic weak lensing techniques for future space-based weak lensing missions.
• To demonstrate that 3D cosmic shear analysis tightens constraints by a factor of three compared to 2D methods.

Proposed method

• Utilized Hubble Space Telescope ACS imaging from the COSMOS survey to measure galaxy shapes and infer weak lensing shear.
• Applied redshift-dependent shear tomography by dividing galaxies into redshift bins to trace the 3D growth of structure.
• Combined 2D and 3D analyses to compare constraints on Ωₘ and σ₈, improving error budget precision.
• Incorporated both statistical and systematic errors (especially shear calibration uncertainty) into the total error budget.
• Used empirical corrections for charge transfer inefficiency (CTE) in ACS CCDs to mitigate spurious shear signals.
• Employed photometric redshifts with limited color depth, acknowledging their current limitation in redshift resolution and degeneracy breaking.

Experimental results

Research questions

• RQ1 How do 3D weak lensing constraints on Ωₘ and σ₈ compare to 2D analyses in terms of precision and cosmic variance?
• RQ2 What is the dominant source of systematic error in current 3D cosmic shear measurements?
• RQ3 To what extent does redshift information improve the constraining power of weak lensing surveys?
• RQ4 Can tomographic weak lensing techniques be validated using existing HST data before future dedicated space missions?
• RQ5 How do the measured cosmological parameters from COSMOS compare with those from other independent probes like X-ray clusters and Lyman-alpha forest?

Key findings

• The 3D weak lensing analysis tightens constraints on σ₈(Ωₘ/0.3)^0.44 by a factor of three compared to 2D analysis, reducing cosmic variance.
• The final constraint is σ₈(Ωₘ/0.3)^0.44 = 0.866⁺⁰.⁰⁸⁵₋⁰.⁰⁶⁸ at 68% confidence, including all statistical and systematic errors.
• Absolute calibration of shear measurement methods is identified as the dominant source of uncertainty in the current error budget.
• The results are consistent with other independent measurements of σ₈ from X-ray clusters, giant arcs, and Lyman-alpha forest data.
• The study demonstrates the feasibility of tomographic weak lensing analysis using existing HST data, serving as a dry run for future space missions.
• The COSMOS survey reveals that CTE degradation and limited photometric redshift depth are key limitations affecting galaxy sample purity and redshift resolution.