Dark Energy Survey year 1 results: Constraints on extended cosmological models from galaxy clustering and weak lensing

We present constraints on extensions of the minimal cosmological models dominated by dark matter and dark energy, $\mathrm{\Lambda }\mathrm{CDM}$ and $w\mathrm{CDM}$, by using a combined analysis of galaxy clustering and weak gravitational lensing from the first-year data of the Dark Energy Survey (DES Y1) in combination with external data. We consider four extensions of the minimal dark energy-dominated scenarios: (1) nonzero curvature ${\mathrm{\Omega }}_k$, (2) number of relativistic species $N_{\mathrm{eff}}$ different from the standard value of 3.046, (3) time-varying equation-of-state of dark energy described by the parameters $w_0$ and $w_a$ (alternatively quoted by the values at the pivot redshift, $w_p$, and $w_a$), and (4) modified gravity described by the parameters ${\mu }_0$ and ${\mathrm{\Sigma }}_0$ that modify the metric potentials. We also consider external information from Planck cosmic microwave background measurements; baryon acoustic oscillation measurements from SDSS, 6dF, and BOSS; redshift-space distortion measurements from BOSS; and type Ia supernova information from the Pantheon compilation of datasets. Constraints on curvature and the number of relativistic species are dominated by the external data; when these are combined with DES Y1, we find ${\mathrm{\Omega }}_k=0.0020_{-0.0032}^{+0.0037}$ at the 68% confidence level, and the upper limit $N_{\mathrm{eff}}<3.28(3.55)$ at 68% (95%) confidence, assuming a hard prior $N_{\mathrm{eff}}>3.0$. For the time-varying equation-of-state, we find the pivot value $(w_p,w_a)=(-0.91_{-0.23}^{+0.19},-0.57_{-1.11}^{+0.93})$ at pivot redshift $z_p=0.27$ from DES alone, and $(w_p,w_a)=(-1.01_{-0.04}^{+0.04},-0.28_{-0.48}^{+0.37})$ at $z_p=0.20$ from DES Y1 combined with external data; in either case we find no evidence for the temporal variation of the equation of state. For modified gravity, we find the present-day value of the relevant parameters to be ${\mathrm{\Sigma }}_0=0.43_{-0.29}^{+0.28}$ from DES Y1 alone, and $({\mathrm{\Sigma }}_0,{\mu }_0)=(0.06_{-0.07}^{+0.08},-0.11_{-0.46}^{+0.42})$ from DES Y1 combined with external data. These modified-gravity constraints are consistent with predictions from general relativity.

Figure 1

Estimated redshift distributions of the lens and source galaxies used in the analysis. The shaded vertical regions define the bins: galaxies are placed in the bin spanning their mean $\mathrm{photo}\text{−}z$ estimate. We show both the redshift distributions of galaxies in each bin (colored lines) and their overall redshift distributions (black lines).

Figure 2

Impact of assumptions and approximations adopted in our analysis, demonstrated on synthetic data (that is, noiseless DES data centered on the theoretical expectation, along with actual external data). Each column shows one of the cosmological parameters describing $\mathrm{\Lambda }\mathrm{CDM}$ extensions; the dotted vertical line is the true input value of that parameter in the DES data vector (which does not necessarily coincide with the parameter values preferred by the external data). The vertical shaded bands show the marginalized 68% CL constraints in the baseline model for the DES-only synthetic data (blue) and $\mathrm{DES}+\mathrm{external}$. The horizontal error bars show the inferred constraint for each individual addition to the synthetic data vector which are listed in rows; they match the shaded bands for the baseline case. For subsequent rows, they show the inferred constraint for each individual addition to the synthetic data vector as listed on the right. Some cases that appear inconsistent with the baseline analysis are discussed further in Sec. 4a. In cases where the prior is informative, we also include a dashed vertical line to signify the prior edge.

Figure 3

Posterior constraints on the spatial curvature (left panel) and the number of relativistic species (right panel) in two of the extensions to $\mathrm{\Lambda }\mathrm{CDM}$ considered in this paper. Blue contours show DES alone, yellow is external data alone, and red is the combination of the two. The 68% confidence region is shaded. The x-axis ranges in both panels coincide with the priors given to ${\mathrm{\Omega }}_k$ and $N_{\mathrm{eff}}$, respectively. Posteriors’ maxima are normalized to unity for better visibility of the DES only results.

Figure 4

Constraints on dark energy parameters $(w_0,w_a)$ (left panel) and the modified gravity parameters $({\mathrm{\Sigma }}_0,{\mu }_0)$ (right panel). Blue contours show the 68% and 95% confidence regions from DES alone, yellow is external data alone, and red is the combination of the two. The intersection of the horizontal and vertical dashed lines shows the parameter values in the $\mathrm{\Lambda }\mathrm{CDM}$ model (left panel) and in general relativity (right). The x-axis range in the left panel and the y-axis range in the right panel coincide with the respective priors given to $w_0$ and ${\mu }_0$. The cause of the nonintuitive shift in the combined ${\mathrm{\Sigma }}_0$ constraint (red contour) relative to separate constraints is discussed in Sec. 5.

Figure 5

Constraints on the pivot value of the dark energy equation-of-state $w_p$ and the variation with scale factor $w_a$ Blue contours show DES alone, yellow is external data alone, and red is the combination of the two. The intersection of the horizontal and vertical dashed lines shows the parameter values in the $\mathrm{\Lambda }\mathrm{CDM}$ model.

Figure 6

Comparison of constraints on the matter density ${\mathrm{\Omega }}_m$ and $S_8$ to the $\mathrm{\Lambda }\mathrm{CDM}$ case. The panels illustrate how the ${\mathrm{\Omega }}_m\text{−}{S}_8$ constraints broaden and shift as we allow to vary: curvature (top left), number of relativistic species (top right), equation-of-state parameters $w_0$ and $w_a$ (bottom left), and modified gravity parameters ${\mathrm{\Sigma }}_0$ and ${\mu }_0$ (bottom right). In each case, the shaded contours denote DES (blue), external (yellow), and $\mathrm{DES}+\mathrm{external}$ (red) constraints. For comparison, in the DES-only case we also show the constraints in the $\mathrm{\Lambda }\mathrm{CDM}$ model with dashed contours, which are the same in each panel.

Figure 7

Impact of changes in modeling assumptions to the inferred cosmology, using actual (and not synthesized as in Fig. 2) DES data. Each column shows one of the cosmological parameters describing $\mathrm{\Lambda }\mathrm{CDM}$ extensions. The horizontal error bars show the constraints for each individual change in the analysis, listed to the right of the figure. The vertical shaded band coincides with the horizontal error bars in the fiducial-analysis case. The modified-gravity analysis assumes conservative scale cuts as a default, so the corresponding test is left blank in the table.

Figure 8

Constraints on ${\mathrm{\Omega }}_m$, $A_s$, $S_8$, ${\mathrm{\Sigma }}_0$ and ${\mu }_0$ using DES Y1 synthetic data for CosmoSIS (blue contours) and CosmoLike (red).