Cosmic Shear Results from the Deep Lens Survey - II: Full Cosmological Parameter Constraints from Tomography

TL;DR

<3-5 sentence high-level summary>This study delivers full cosmological parameter constraints from a deep, five-bin tomographic cosmic shear analysis of the Deep Lens Survey (DLS), leveraging depth to break degeneracies and using stacked redshift distributions for tomography. It couples DLS with external datasets (WMAP9, BAO, SN) and a luminosity-dependent intrinsic alignment model to constrain key parameters, notably |$\Omega_m$, $\sigma_8$, $H_0$, $\Omega_b$, $n_s$, $\Omega_k$, and $w$|, finding results consistent with Planck and LCDM predictions. The analysis includes a rigorous shear calibration via image simulations, a covariance derived from large N-body ray-tracing mocks, and careful handling of small-scale baryonic effects by angular cuts. Overall, the work demonstrates that deep, multi-bin cosmic shear can yield tight cosmological constraints and informs methodologies for upcoming surveys like LSST.

Abstract

We present a tomographic cosmic shear study from the Deep Lens Survey (DLS), which, providing a limiting magnitude r_{lim}~27 (5 sigma), is designed as a pre-cursor Large Synoptic Survey Telescope (LSST) survey with an emphasis on depth. Using five tomographic redshift bins, we study their auto- and cross-correlations to constrain cosmological parameters. We use a luminosity-dependent nonlinear model to account for the astrophysical systematics originating from intrinsic alignments of galaxy shapes. We find that the cosmological leverage of the DLS is among the highest among existing >10 sq. deg cosmic shear surveys. Combining the DLS tomography with the 9-year results of the Wilkinson Microwave Anisotropy Probe (WMAP9) gives Omega_m=0.293_{-0.014}^{+0.012}, sigma_8=0.833_{-0.018}^{+0.011}, H_0=68.6_{-1.2}^{+1.4} km/s/Mpc, and Omega_b=0.0475+-0.0012 for LCDM, reducing the uncertainties of the WMAP9-only constraints by ~50%. When we do not assume flatness for LCDM, we obtain the curvature constraint Omega_k=-0.010_{-0.015}^{+0.013} from the DLS+WMAP9 combination, which however is not well constrained when WMAP9 is used alone. The dark energy equation of state parameter w is tightly constrained when Baryonic Acoustic Oscillation (BAO) data are added, yielding w=-1.02_{-0.09}^{+0.10} with the DLS+WMAP9+BAO joint probe. The addition of supernova constraints further tightens the parameter to w=-1.03+-0.03. Our joint constraints are fully consistent with the final Planck results and also the predictions of a LCDM universe.

Figures (13)

• Figure 1: Redshift distributions in the five DLS tomographic bins. Displayed are the stacked probability $p(z)$ (estimated by BPZ) of sources in each bin. The curves are normalized to unity integrated area. Table 1 lists the total number of sources in each redshift bin and more statistical details.
• Figure 2: Auto- and cross-correlation functions from the five DLS tomographic bins. We display cosmic shear (GG), shear-intrinsic alignment (GI), intrinsic-intrinsic alignment (II), and total (GG+GI+II) signals evaluated at the best-fit cosmology from the Planck2015-CMB result. For constraining cosmological parameters, we use the data points only at $\theta>1\arcmin$ to mitigate baryonic effects (solid blue line). Note that because the GI signals are negative, we artificially flip their signs here to show them in these log-log plots. The two numbers $k,l$ displayed in each panel represent the tomographic bin combination. The contamination of intrinsic alignment to the DLS cosmic shear measurement is mostly negligible. Even when the lowest redshift ($z=0.29$) bin is involved, the amount of the shift in the correlation functions due to the correction is a small ($\lesssim10$%) fraction of their statistical uncertainties. We discuss their impact on our cosmological parameter constraints in §\ref{['section_IA_impact']}. As demonstrated in §\ref{['section_comparison_with_planck2015']}, the DLS cosmic shear signals are fully consistent with the Planck2015-CMB results.
• Figure 3: Compressed representation of our DLS cosmic shear tomography. The 15 data points represent the signal amplitudes of all 15 correlation functions $\xi_{+,-}^{k,l}$ at $\theta=1\arcmin$. The $x$-axis $\xi_{+,-}^{k,l,mod}$ is the model prediction at the reference cosmology (the Planck-CMB result) whereas the y-axis $\xi_{+,-}^{k,l,obs}$ corresponds to the DLS observation (see text for the compression scheme). The solid line is just the equality, not a fit to the data. The error bars include the sample variance.
• Figure 4: Covariance matrix of the DLS tomography. We show the total covariance, which combines the sample variance, shape noise, mixed component, and masking effects. The dimension is 300$\times$300. The element ordering scheme is consistent with the data vector defined in §\ref{['section_data_vector']}. Although the covariance spans from -$1.8\times10^{-9}$ to $+3.6\times10^{-8}$, we truncate the dynamic range as shown in order to highlight low-contrast structures.
• Figure 5: "DLS-ONLY" constraints on $\Omega_m$ and $\sigma_8$ for $\Lambda$CDM. The inner and outer contours represent 68% and 95% confidence regions, resp. Flat priors are used. For the "regular" prior setting, we marginalize over the $0.6 < h < 0.8$, $0.92 < n_s < 1.02$, and $0.03 < \Omega_b < 0.06$ intervals, which bracket the 3$\sigma$ ranges constrained by previous CMB or SNIa+Cepheid studies. The "wide" prior setting refers to the intervals: $0.4 < h < 1.2$, $0.7 < n_s < 1.2$, and $0 <\Omega_b< 0.1$, which are adopted in the CFHTLenS studies.