Cosmology from cosmic shear with Dark Energy Survey Science Verification data

We present the first constraints on cosmology from the Dark Energy Survey (DES), using weak lensing measurements from the preliminary Science Verification (SV) data. We use 139 square degrees of SV data, which is less than 3% of the full DES survey area. Using cosmic shear 2-point measurements over three redshift bins we find ${\sigma }_8({\mathrm{\Omega }}_{\mathrm{m}}/0.3{)}^{0.5}=0.81\pm 0.06$ (68% confidence), after marginalizing over 7 systematics parameters and 3 other cosmological parameters. We examine the robustness of our results to the choice of data vector and systematics assumed, and find them to be stable. About 20% of our error bar comes from marginalizing over shear and photometric redshift calibration uncertainties. The current state-of-the-art cosmic shear measurements from CFHTLenS are mildly discrepant with the cosmological constraints from Planck CMB data; our results are consistent with both data sets. Our uncertainties are $\sim 30\%$ larger than those from CFHTLenS when we carry out a comparable analysis of the two data sets, which we attribute largely to the lower number density of our shear catalogue. We investigate constraints on dark energy and find that, with this small fraction of the full survey, the DES SV constraints make negligible impact on the Planck constraints. The moderate disagreement between the CFHTLenS and Planck values of ${\sigma }_8({\mathrm{\Omega }}_{\mathrm{m}}/0.3{)}^{0.5}$ is present regardless of the value of $w$.

Figure 1

DES SV shear two-point correlation function ${\xi }_{\pm }$ measurements in each of the redshift bin pairings (from Becker et al. [47]). The 3 redshift bins ranges are $0.3<z<0.55$, $0.55<z<0.83$ and $0.83<z<1.3$, and each galaxy is assigned to a redshift bin according to the mean of its photometric redshift probability distribution (or excluded if this value is outside the above ranges). Alternating rows are ${\xi }_{+}$ and ${\xi }_{-}$, and the redshift bin combination is labeled in the upper right corner of each panel. The nontomographic measurement is in the bottom left corner. The solid lines show the correlation functions computed for the best-fit Planck 2015 ($\mathrm{TT}+\mathrm{lowP}$) base $\mathrm{\Lambda }\mathrm{CDM}$ cosmology, using halofit [55, 56] to model the nonlinear matter power spectrum. The blue dashed lines (mostly obscured by the black lines) and red dotted lines assume the same cosmology but model nonlinear scales using FrankenEmu [57] (extended at high $k$ using the “CEp” prescription from Harnois-Déraps et al. [43]) and a prescription based on the OWLS “AGN” simulation [58] respectively. Points lying in grey regions are excluded from the analysis because they may be affected by either small-scale matter power spectrum uncertainty or large-scale additive shear bias, as explained in Sec. 4b.

Figure 2

Constraints on the amplitude of fluctuations ${\sigma }_8$ and the matter density ${\mathrm{\Omega }}_{\mathrm{m}}$ from DES SV cosmic shear (purple filled/outlined contours) compared with constraints from Planck (red filled contours) and CFHTLenS (orange filled, using the correlation functions and covariances presented in Heymans et al. [20], and the “original conservative scale cuts” described in Sec. 6a1). DES SV and CFHTLenS are marginalized over the same astrophysical systematics parameters and DES SV is additionally marginalized over uncertainties in photometric redshifts and shear calibration. Planck is marginalized over the 6 parameters of $\mathrm{\Lambda }\mathrm{CDM}$ (the 5 we vary in our fiducial analysis plus $\tau$). The DES SV and CFHTLenS constraints are marginalized over wide flat priors on $n_s$, ${\mathrm{\Omega }}_{\mathrm{b}}$ and $h$ (see text), assuming a flat universe. For each data set, we show contours which encapsulate 68% and 95% of the probability, as is the case for subsequent contour plots.

Figure 3

Graphical illustration of the 68% confidence limits on $S_8\equiv {\sigma }_8({\mathrm{\Omega }}_{\mathrm{m}}/0.3{)}^{0.5}$ values given in Table 1, showing the robustness of our results (purple) and comparing with the CFHTLenS and Planck lensing results (orange) and Planck (red). The grey vertical band aligns with the fiducial constraints at the top of the plot. Note that Planck lensing in particular, and other non-DES lensing measurements optimally constrain a different quantity than shown above e.g. see the second and third columns of Table 1.

Figure 4

Comparison of constraints on ${\sigma }_8$ and ${\mathrm{\Omega }}_{\mathrm{m}}$ for various choices of data vector: ${\xi }_{\pm }$ with no tomography or systematics (purple filled), $C_{\ell }^{ij}$ bandpowers (dashed red lines) and PolSpice-$C_{\ell }$ bandpowers (solid green lines) (both with no tomography or systematics). We do not show our fiducial constraints, or Planck, since we have not marginalized over systematics for the constraints shown here, so agreement is not necessary or meaningful (although Table 1 suggests there is reasonable agreement).

Figure 5

The fractional bias on ${\sigma }_8$ due to ignoring an OWLS AGN baryon model (solid lines) compared to the statistical uncertainty on ${\sigma }_8$ (dashed lines) as a function of minimum scale used for ${\xi }_{-}$ (${\theta }_{\min }^{-}$, x-axis) or ${\xi }_{+}$ (${\theta }_{\min }^{+}$, colors). Whereas the statistical error is minimized by using small scales, the bias is significant for ${\theta }_{\min }^{-}<30^{\prime }$ and ${\theta }_{\min }^{+}<3^{\prime }$.

Figure 6

Robustness to assumptions about shear measurement. Shaded purple (fiducial case): ngmix, with one shear mulitiplicative bias parameter m for each of the 3 tomographic redshift bins, with an independent Gaussian prior on each $m_i$ with $\sigma =0.05$. Solid blue lines: im3shape with the same assumptions. Planck is shown in red.

Figure 7

Results using different photoz codes. Purple filled contours: fiducial case (SkyNet). Blue dashed lines: ANNz2. Green solid lines: TPZ. Red dash-dotted lines: BPZ w/correction.

Figure 8

Left: Constraints on the clustering amplitude ${\sigma }_8$ and the matter density ${\mathrm{\Omega }}_{\mathrm{m}}$ from DES SV alone. The purple shaded contour shows the constraints when our fiducial NLA model of intrinsic alignments is assumed, the green filled lines shows constraints when the LA model is used, the dot-dashed red lines the CTA model and the blue dashed lines shows constraints when IAs are ignored. Right: Constraints on ${\sigma }_8{\mathrm{\Omega }}_{\mathrm{m}}^{0.5}$ and the intrinsic alignment amplitude $A$ from DES alone. The purple shaded contour shows the constraints when our fiducial NLA model of intrinsic alignments is assumed with three tomographic bins, the red lines shows constraints, again using our fiducial NLA model, but using only a single redshift bin and the green dashed contour shows our fiducial NLA model, with three tomographic bins, but marginalized over an additional power law in redshift, where the power law index is a free parameter. Note that the treatment of IAs in both panels assumes a prior range for the amplitude $A=[-5,5]$.

Figure 9

The effect of AGN feedback on cosmological constraints. The purple shaded region and the red solid lines use the fiducial matter power spectrum (halofit) and the OWLS AGN model respectively. Blue dashed and red dot-dashed lines use a more aggressive data vector, using scales down to 2 arcmin in ${\xi }_{+}$ and ${\xi }_{-}$, again with the fiducial matter power spectrum (halofit) and the OWLS AGN model, respectively.

Figure 10

Joint constraints from a selection of recent data sets on the total matter density ${\mathrm{\Omega }}_m$ and amplitude of matter fluctuations ${\sigma }_8$. From highest layer to lowest layer: $\mathrm{Planck}\mathrm{TT}+\mathrm{lowP}$ (red); X-ray cluster mass counts (Mantz et al. [102], white/grey shading); DES SV (purple); CFHTLenS (H13, orange); Planck CMB lensing (yellow); CMASS $f{\sigma }_8$ (Chuang et al. [103], green).

Figure 11

Nontomographic DES SV (blue circles), CFHTLenS K13 (orange squares) and Planck (red) data points projected onto the matter power spectrum (black line). This projection is cosmology-dependent and assumes the Planck best fit cosmology in $\mathrm{\Lambda }\mathrm{CDM}$. The Planck error bars change size abruptly because the $C_{\ell }\mathrm{s}$ are binned in larger $\ell$ bins above $\ell =50$.

Figure 12

Constraints on the dark energy equation of state $w$ and $S_8\equiv {\sigma }_8({\mathrm{\Omega }}_m/0.3{)}^{0.5}$, from DES SV (purple), Planck (red), CFHTLenS (orange), and $\text{Planck}+\mathrm{ext}$ (grey). DES SV is consistent with Planck at $w=-1$. The constraints on $S_8$ from DES SV alone are also generally robust to variation in $w$.