Dark Energy Survey Year 1 results: Cosmological constraints from cosmic shear

We use $26\times {10}^6$ galaxies from the Dark Energy Survey (DES) Year 1 shape catalogs over $1321{\mathrm{deg}}^2$ of the sky to produce the most significant measurement of cosmic shear in a galaxy survey to date. We constrain cosmological parameters in both the flat $\mathrm{\Lambda }\mathrm{CDM}$ and the $w\mathrm{CDM}$ models, while also varying the neutrino mass density. These results are shown to be robust using two independent shape catalogs, two independent photo-$z$ calibration methods, and two independent analysis pipelines in a blind analysis. We find a 3.5% fractional uncertainty on ${\sigma }_8({\mathrm{\Omega }}_m/0.3{)}^{0.5}=0.782_{-0.027}^{+0.027}$ at 68% C.L., which is a factor of 2.5 improvement over the fractional constraining power of our DES Science Verification results. In $w\mathrm{CDM}$, we find a 4.8% fractional uncertainty on ${\sigma }_8({\mathrm{\Omega }}_m/0.3{)}^{0.5}=0.777_{-0.038}^{+0.036}$ and a dark energy equation-of-state $w=-0.95_{-0.39}^{+0.33}$. We find results that are consistent with previous cosmic shear constraints in ${\sigma }_8$—${\mathrm{\Omega }}_m$, and we see no evidence for disagreement of our weak lensing data with data from the cosmic microwave background. Finally, we find no evidence preferring a $w\mathrm{CDM}$ model allowing $w\ne -1$. We expect further significant improvements with subsequent years of DES data, which will more than triple the sky coverage of our shape catalogs and double the effective integrated exposure time per galaxy.

Figure 1

The footprint of the DES Y1 Metacalibration catalog selection used in this work, covering $1321{\mathrm{deg}}^2$. The joint redMaGiC mask described in Sec. 2a is not included. The raw mean number density of objects drawn by Skymapper in HEALPix cells of $N_{\mathrm{side}}$ 1024 is shown, which is uncorrected for the coverage fraction at subpixel scales. Overlaid are the bounds of the nominal five year DES survey footprint. The full shape catalog footprint, which includes the Stripe 82 region, is shown in [40]. For the Metacalibration catalog, $n_g$ is equivalent to the H12 $n_{\mathrm{eff}}$ in Table 1.

Figure 2

The measured bpz and resampled COSMOS redshift distributions for the Metacalibration shape catalog, binned by the means of the photo-$z$ posteriors into the four tomographic ranges in Table 1 and marked by the color shading. The normalization of each bin reflects their relative $n_{\mathrm{eff}}$. The bpz distributions are corrected by the mean of the redshift bias priors $\mathrm{\Delta }{z}^i$. The contribution of each galaxy is weighted by $W_i{S}_i$, as defined in Sec. 4. The im3shape redshift distributions are similar to those shown for Metacalibration. The second bin is clearly the most different between the resampled COSMOS estimate and BPZ—we explore this further in Sec. 9c and show that it does not significantly impact the inferred cosmological parameters.

Figure 3

The measured nontomographic shear correlation function ${\xi }_{\pm }$ for the DES Y1 shape catalogs. The best-fit $\mathrm{\Lambda }\mathrm{CDM}$ theory line from the fiducial tomographic analysis is shown as the same solid line compared to measurements from both catalogs.

Figure 4

The measured shear correlation function ${\xi }_{+}$ (top triangle) and ${\xi }_{-}$ (bottom triangle) for the DES Y1 Metacalibration catalog. Results are scaled by the angular separation ($\theta$) to emphasize features and differences relative to the best-fit model. The correlation functions are measured in four tomographic bins spanning the redshift ranges listed in Table 1, with labels for each bin combination in the upper left corner of each panel. The assignment of galaxies to tomographic bins is discussed in Sec. 2b. Scales which are not used in the fiducial analysis are shaded (see Sec. 7a). The best-fit $\mathrm{\Lambda }\mathrm{CDM}$ theory line from the full tomographic analysis is shown as the solid line. We find a ${\chi }^2$ of 227 for 211 degrees of freedom (d.o.f.) in the nonshaded regions.

Figure 5

The measured shear correlation function ${\xi }_{+}$ (top triangle) and ${\xi }_{-}$ (bottom triangle) for the DES Y1 im3shape catalog (see caption of Fig. 4). The uncertainty on ${\xi }_{\pm }$ is clearly larger for im3shape compared to Metacalibration in Fig. 4 due to the lower number density of objects. We find a ${\chi }^2$ of 224 for 211 d.o.f. in the nonshaded regions.

Figure 6

The cosmic shear correlation matrix. The fiducial halo model correlation matrix is shown in the lower triangle, while the difference of this with the correlation matrix derived from 1200 flask log-normal simulations with the DES Y1 mask applied is shown in the upper triangle. This shows primarily the noise in the flask covariance, and any differences between the two derived covariance matrices were shown to be entirely negligible in [59]. Elements are ordered to the right (upward) by increasing redshift bin pair index $ij$ with $i\le j$ (i.e., 11, 12, 13,…). Within each $ij$ block, angular scales also increase to the right (upward).

Figure 7

Fiducial constraints on the clustering amplitude ${\sigma }_8$ and $S_8$ with the matter density ${\mathrm{\Omega }}_m$ in $\mathrm{\Lambda }\mathrm{CDM}$. The fiducial DES Y1 cosmic shear constraints are shown by the gray filled contours, with Planck CMB constraints given by the filled green contours, and cosmic shear constraints from KiDS-450 shown by unfilled blue contours. In all cases, 68% and 95% confidence levels are shown. External data have been reanalyzed in our model space, as described in Sec. 8c.

Figure 8

A comparison of the fiducial constraints in $\mathrm{\Lambda }\mathrm{CDM}$ (filled gray contours) to constraints where: (1) we fix ${\mathrm{\Omega }}_{\nu }{h}^2$ (orange contours), (2) we fix all photo-$z$ and shear systematic parameters (green contours), and (3) we fix all systematic parameters and intrinsic alignment (IA) parameters (blue contours). We find no visually significant bias correction or decrease in constraining power including systematics parameters, but varying ${\mathrm{\Omega }}_{\nu }{h}^2$ and IA parameters both shift and enlarge the resulting contours. Both 68% and 95% confidence levels are shown.

Figure 9

Summary of constraints on the 1D peak value of $S_8\equiv {\sigma }_8({\mathrm{\Omega }}_{\mathrm{m}}/0.3{)}^{0.5}$ in $\mathrm{\Lambda }\mathrm{CDM}$. The 68% C.L. are shown as horizontal bars. We distinguish variations on the fiducial setup that are not necessarily required to give consistent results (e.g., by neglecting astrophysical systematics) by an asterisk. The numerical parameter values are listed in Table 3. Especially for external data, it is important to remember that we vary ${\mathrm{\Omega }}_{\nu }{h}^2$ in our fiducial analysis, and thus all results we compare to, and so the central values and uncertainties of parameters may not follow intuition from previous results.

Figure 10

Fiducial constraints on the clustering amplitude ${\sigma }_8$, $S_8$, and $w$ with the matter density ${\mathrm{\Omega }}_m$ in $w\mathrm{CDM}$. The fiducial DES Y1 cosmic shear constraints are shown by the gray filled contours, with Planck CMB constraints given by the filled green contours, and cosmic shear constraints from KiDS-450 by unfilled blue contours. In all cases, 68% and 95% confidence levels are shown. External data have been reanalyzed in our model space, as described in Sec. 8c. A dotted line at $w=-1$ indicates the $\mathrm{\Lambda }\mathrm{CDM}$ value.

Figure 11

A comparison of the DES Y1 constraints on $S_8$ and the matter density ${\mathrm{\Omega }}_m$ in $\mathrm{\Lambda }\mathrm{CDM}$ with external data sets excluding cosmic shear. The fiducial DES Y1 cosmic shear constraints are shown by the gray filled contours, with Planck CMB constraints given by the green contours, the combination of BAO and JLA (SNe) constraints in blue contours, and the combination $\mathrm{Planck}+\mathrm{BAO}+\mathrm{JLA}$ in orange contours. In all cases, 68% and 95% confidence levels are shown.

Figure 12

A comparison of $\mathrm{\Lambda }\mathrm{CDM}$ constraints in the $S_8\text{−}{\mathrm{\Omega }}_m$ plane from the two shape measurement pipelines, Metacalibration (gray filled contours) and im3shape (blue contours). This is a strong test of robustness to assumptions and differences in measurement and calibration methodology. Each pipeline utilizes very different and independent methods of shape measurement and shear calibration. We also compare the DES SV results (from ngmix) in green. Both 68% and 95% confidence levels are shown.

Figure 13

A comparison of $\mathrm{\Lambda }\mathrm{CDM}$ constraints in the $S_8\text{−}{\mathrm{\Omega }}_m$ plane for different photo-$z$ choices. The gray filled contours show the fiducial analysis using the BPZ redshift distribution shown in Fig. 2 with the offset priors listed in Table 2. The green contours are the result of the same analysis, but removing the fourth tomographic bin. The blue contours use the COSMOS $n(z)$ from which part of the BPZ prior is derived. By design, the mean redshift of each tomographic bin agrees between the resampled COSMOS $n(z)$ and the BPZ redshift distribution used in the fiducial analysis, but the shapes of the $n(z)$ are significantly different in some tomographic bins, providing a test of whether parametrizing the photo-$z$ bias as only a shift in the mean redshift is sufficient. Both 68% and 95% confidence levels are shown.

Figure 14

A comparison of $\mathrm{\Lambda }\mathrm{CDM}$ constraints in the $S_8\text{−}{\mathrm{\Omega }}_m$ plane for different data vector choices. The filled gray contours show the fiducial analysis, while the orange contours show small scales outside the fiducial selection, the blue contours use fiducial angular scales for ${\xi }_{+}$ (${\xi }_{-}$) with $\theta >20^{\prime }$ ($\theta >150^{\prime }$), and the green contours use fiducial scales for ${\xi }_{+}$ (${\xi }_{-}$) with $\theta <20^{\prime }$ ($\theta <150^{\prime }$). The orange contours should not necessarily agree with the fiducial case due to the impact of baryonic effects, while we find consistent results using subsets of our fiducial angular scale range. Both 68% and 95% confidence levels are shown.

Figure 15

A comparison of the impact of different IA models on $\mathrm{\Lambda }\mathrm{CDM}$ and $w\mathrm{CDM}$ constraints in the $S_8\text{−}{\mathrm{\Omega }}_m$ plane. The fiducial model ($\mathrm{NLA}+z$-power law—gray contours), is compared to the single-parameter NLA model (green contours), the NLA model with a free amplitude in each tomographic bin (orange contours), and the mixed alignment model (blue contours). There is no significant difference in inferred cosmology among the first three models, which are well tested and have been implemented in the literature before. The mixed alignment model, which includes alignment due to tidal torquing (or other nonlinear contributions), does cause a non-negligible shift in inferred parameters in $w\mathrm{CDM}$, which is discussed further in Sec. 9e. Both 68% and 95% confidence levels are shown.

Figure 16

The constraint on the intrinsic alignment amplitude $A$ as a function of redshift in the four models considered. For all models, we show $A_1$, the amplitude of the TA model, while for the mixed alignment model, we also show the constraint on $A_2$, the amplitude of the TT component of the model. We find good agreement between the redshift evolution of the tidal alignment amplitude in the four models.

Figure 17

The measured correlation functions ${\xi }_{ep}$ [Eq. (a3)] and ${\xi }_{eq}$ [Eq. (a4)]. The resulting model from the best-fit $\alpha$ and $\beta$ from Eqs. (a3) and (a4) for $\alpha$ and $\beta$ is shown as a solid line for each tomographic bin. The best-fit $\alpha$ is consistent with zero, while the values of ${\beta }_{\mathrm{METACALIBRATION}}$ used are shown in Table 5.

Figure 18

The significance of differences in the cosmic shear signal, $\mathrm{\Delta }{\xi }_{\pm }$, between subsets of the shape catalogs split by ten quantities that are most likely to be correlated with residual shear systematics. These are signal-to-noise (S/N), PSF ellipticity (PSF $e_1$, $e_2$), galaxy size ($T$-Metacalibration, $R_{gp}/R_{pp}$-im3shape), $r\text{−}i$ color, dust extinction [$E(B-V)$], sky brightness, PSF FWHM, airmass, and $r$-band limiting magnitude. We report the normalized ${\chi }^2$ of $\mathrm{\Delta }{\xi }_{\pm }$ with the null hypothesis in each case for both ${\xi }_{\pm }$. The most interesting differences occur in the highest redshift bin, and when taking selection biases in the photo-$z$ catalog into account, are not concerning as a contaminant to the cosmic shear signal. In all cases, the cumulative impact on the data vector combining all four autocorrelations is consistent with there being no significant residual systematic effects in the fiducial cosmic shear analysis.

Figure 19

The full 1D posteriors on all 16 parameters in our $\mathrm{\Lambda }\mathrm{CDM}$ model space. Shaded regions show the approximate 68% confidence intervals. The smooth curves show the Gaussian priors on systematic parameters.