COSMOS: 3D weak lensing and the growth of structure

TL;DR

We present a 3D cosmic shear analysis of the HST COSMOS survey to measure the growth of structure and constrain ${\Omega_m}$ and ${\sigma_8}$ using tomographic redshift information. By combining 2D and 3D statistics, including E/B decompositions and a full covariance treatment, we obtain ${\sigma_8}({{\Omega_m}}/{0.3})^{0.44} = 0.866^{+0.085}_{-0.068}$ (68% CL) after accounting for systematic errors; the 3D analysis tightens constraints by roughly a factor of three relative to the 2D case when relative calibration between redshift slices is properly handled. The work also demonstrates a proof of concept for tomographic techniques in future dedicated space-based weak-lensing surveys and highlights the dominant systematics, such as absolute shear calibration and CTE effects, that must be controlled for robust cosmological inferences.

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.

Figures (15)

• Figure 1: The thin, solid line shows the distribution of the best-fit redshifts returned by the COSMOS photometric redshift code (Mobasher et al. 2006) with a luminosity function prior. The thick, solid line shows the distribution after accounting for the different weights given to galaxies. In both cases, the bin size is $\Delta z=0.02$. Peaks below $z\approx1.2$ correspond to real structures in the field, but the artificial clustering at higher redshift is due to limitations in the finite number of observed near-IR colors. The dashed curve shows the redshift sensitivity function, assuming a $\Lambda$CDM universe with WMAP parameters. The dotted line shows the redshift distribution that would have been expected, with knowledge of only the median photometric redshift and a smailzdist fitting function.
• Figure 2: Correlation functions of the 2D shear field. The open circles indicate negative values. The inner error bars show statistical errors only; the outer error bars, visible only on large scales, also include the contribution of cosmic variance. The six parallel curves show theoretical predictions for a flat $\Lambda$CDM cosmology with $\Omega_m=0.3$ and $\sigma_8$ varying from 0.7 (bottom) to 1.2 (top). The roughly horizontal lines indicate the level of the spurious signal due to CTE trailing before and after correction.
• Figure 3: Comparison of the error bars that we measured from the data, to advance predictions from semvariance, obtained by raytracing through $n$-body simulations of large-scale structure. The two solid lines show the predictions assuming a Gaussianised mass distribution (bottom) and with the full, non-Gaussian distribution (top).
• Figure 4: Covariance matrix for the 2D correlation functions $C_1(\theta)$ and $C_2(\theta)$ shown in figure \ref{['fig:2dcth']}, obtained by splitting the COSMOS field into four quadrants and performing the analysis separately in each. The diagonal elements illustrate the size of the errors in each of the thirteen $\theta$ bins, and the off-diagonal elements illustrate how much the measurements are correlated. The color scale is logarithmic.
• Figure 5: Variance of the 2D shear signal in circular cells of varying size. Solid lines show predictions in a concordance cosmology with $\sigma_8$ varying as in figure \ref{['fig:2dcth']}. Note that adjacent data points are highly correlated.