DES Y1 results: Splitting growth and geometry to test $\mathrm{\Lambda }\mathrm{CDM}$

We analyze Dark Energy Survey (DES) data to constrain a cosmological model where a subset of parameters—focusing on ${\mathrm{\Omega }}_m$—are split into versions associated with structure growth (e.g., ${\mathrm{\Omega }}_m^{\mathrm{grow}}$) and expansion history (e.g., ${\mathrm{\Omega }}_m^{\mathrm{geo}}$). Once the parameters have been specified for the $\mathrm{\Lambda }\mathrm{CDM}$ cosmological model, which includes general relativity as a theory of gravity, it uniquely predicts the evolution of both geometry (distances) and the growth of structure over cosmic time. Any inconsistency between measurements of geometry and growth could therefore indicate a breakdown of that model. Our growth-geometry split approach therefore serves both as a (largely) model-independent test for beyond-$\mathrm{\Lambda }\mathrm{CDM}$ physics, and as a means to characterize how DES observables provide cosmological information. We analyze the same multiprobe DES data as [Phys. Rev. Lett. 122, 171301 (2019)] : DES Year 1 (Y1) galaxy clustering and weak lensing, which are sensitive to both growth and geometry, as well as Y1 BAO and Y3 supernovae, which probe geometry. We additionally include external geometric information from BOSS DR12 BAO and a compressed Planck 2015 likelihood, and external growth information from BOSS DR12 RSD. We find no significant disagreement with ${\mathrm{\Omega }}_m^{\mathrm{grow}}={\mathrm{\Omega }}_m^{\mathrm{geo}}$. When DES and external data are analyzed separately, degeneracies with neutrino mass and intrinsic alignments limit our ability to measure ${\mathrm{\Omega }}_m^{\mathrm{grow}}$, but combining DES with external data allows us to constrain both growth and geometric quantities. We also consider a parametrization where we split both ${\mathrm{\Omega }}_m$ and $w$, but find that even our most constraining data combination is unable to separately constrain ${\mathrm{\Omega }}_m^{\mathrm{grow}}$ and $w^{\mathrm{grow}}$. Relative to $\mathrm{\Lambda }\mathrm{CDM}$, splitting growth and geometry weakens bounds on ${\sigma }_8$ but does not alter constraints on $h$.

Figure 1

Dependence of the nonlinear matter power spectrum on ${\mathrm{\Omega }}_m^{\mathrm{grow}}$ and ${\mathrm{\Omega }}_m^{\mathrm{geo}}$. Gray lines show the impact of changing ${\mathrm{\Omega }}_m$ by $\pm 20\%$ in $\mathrm{\Lambda }\mathrm{CDM}$, red lines show changes to ${\mathrm{\Omega }}_m^{\mathrm{geo}}$, and blue lines show changes to ${\mathrm{\Omega }}_m^{\mathrm{grow}}$. The fiducial model uses ${\mathrm{\Omega }}_m^{\mathrm{grow}}={\mathrm{\Omega }}_m^{\mathrm{geo}}=0.295$. Solid lines correspond to an increase in the relevant ${\mathrm{\Omega }}_m$ parameter to 0.354, while dotted lines show a decrease to 0.236.

Figure 2

Redshift distribution of source and lens galaxies used in the DES $\mathrm{Y}1\text{−}3\times 2\mathrm{pt}$ analysis. The vertical shaded bands represent the nominal range of the redshift bins, while the solid lines show their estimated true redshift distributions, given their photometric-redshift-based selection.

Figure 3

The 68% and 95% confidence regions for ${\mathrm{\Omega }}_m^{\mathrm{grow}}$ and ${\mathrm{\Omega }}_m^{\mathrm{geo}}$ for our various data combinations. The diagonal gray lines show where ${\mathrm{\Omega }}_m^{\mathrm{grow}}={\mathrm{\Omega }}_m^{\mathrm{geo}}$. Note that the three plots have the same axis ranges, and that the vertical axes cover a much larger range of values than the horizontal axes. The blue outline-only contours in the top plot are the same as the shaded blue contours in the other plots.

Figure 4

Marginalized constraints from DES and external data when both ${\mathrm{\Omega }}_m$ and $w$ are split. The diagonal panels show normalized one-dimensional marginalized posteriors, while the off-diagonal panels show 68% and 95% confidence regions. Solid gray lines show the $w\mathrm{CDM}$ parameter subspace where ${\mathrm{\Omega }}_m^{\mathrm{grow}}={\mathrm{\Omega }}_m^{\mathrm{geo}}$ and $w^{\mathrm{grow}}=w^{\mathrm{geo}}$.

Figure 5

Marginalized posterior of the difference ${\mathrm{\Omega }}_m^{\mathrm{grow}}-{\mathrm{\Omega }}_m^{\mathrm{geo}}$, from fitting the split-${\mathrm{\Omega }}_m$ model to the DES, $\mathrm{DES}+\mathrm{Ext}\text{−}\mathrm{geo}$, and $\mathrm{DES}+\mathrm{Ext}\text{−}\mathrm{all}$ data combinations.

Figure 6

Constraints from the DES and the Ext-all external dataset, which includes the compressed Planck likelihood, BOSS DR12 BAO, and BOSS DR12 RSD. The off-diagonal panels show the 68% and 95% confidence intervals for each data combination, while the diagonal panels show normalized one-dimensional marginalized posteriors on parameters. DES-only results are shown in blue, Ext-all results are pink, and their combination is shown using unshaded purple contours. The gray dashed curves show $\mathrm{DES}+\mathrm{Ext}\text{−}\mathrm{all}$ constraints in $\mathrm{\Lambda }\mathrm{CDM}$, and the gray solid lines show where ${\mathrm{\Omega }}_m^{\mathrm{grow}}={\mathrm{\Omega }}_m^{\mathrm{geo}}$.

Figure 7

Constraints on parameters most relevant for describing late-time growth, shown for the datasets that make up Ext-all. Contours show the 68% and 95% confidence regions for the compressed Planck likelihood in yellow, and those for BOSS DR12 BAO and RSD in orange. The unshaded black contours correspond to Ext-all, and are the same as the pink contours in other figures. Gray dashed contours show $\mathrm{\Lambda }\mathrm{CDM}$ results for Ext-all.

Figure 8

The same combined $\mathrm{DES}+\mathrm{Ext}\text{−}\mathrm{geo}$ (top) and $\mathrm{DES}+\mathrm{Ext}\text{−}\mathrm{all}$ (bottom) constraints as the second and third panels of Fig. 3, but with the sum of neutrino masses fixed to 0.06 eV.

Figure 9

The impact of changing the redshift $z_i$, where growth parameters start controlling the evolution of the matter power spectrum, defined in Eq. (1), for DES-only (top panel) and $\mathrm{DES}+\mathrm{Ext}\text{−}\mathrm{all}$ (bottom panel). Countours show the 68% and 95% confidence regions from the analysis of synthetic data.

Figure 10

Constraints illustrating the parameter degeneracies that are relevant to understanding the parameter space projection effects impacting the DES-only constraints on split ${\mathrm{\Omega }}_m$. Off-diagonal panels show 68% and 95% confidence intervals, with DES-only results in blue, Ext-geo in light green, and $\mathrm{DES}+\mathrm{Ext}\text{−}\mathrm{geo}$ as the dark green unshaded contours. The gray diagonal line shows where ${\mathrm{\Omega }}_m^{\mathrm{grow}}={\mathrm{\Omega }}_m^{\mathrm{geo}}$, and gray dashed contours show $\mathrm{\Lambda }\mathrm{CDM}$ results for $\mathrm{DES}+\mathrm{Ext}\text{−}\mathrm{geo}$.

Figure 11

Robustness of constraints to adding systematics to simulated data, for the split-${\mathrm{\Omega }}_m$ model. Data points and error bars represent the peak and 68% confidence intervals for marginalized one-dimensional posteriors. The vertical shaded regions correspond to the baseline error bars.

Figure 12

Marginalized posteriors for synthetic data vectors contaminated by systematic effects, showing constraints on the difference between growth and geometry parameters. Top row: Split-${\mathrm{\Omega }}_m$ results for DES-only (left) and for $\mathrm{DES}+\mathrm{Ext}\text{−}\mathrm{geo}$ (right). Bottom row: Results from $\mathrm{DES}+\mathrm{Ext}\text{−}\mathrm{all}$ when we split ${\mathrm{\Omega }}_m$ (left), and when we split both ${\mathrm{\Omega }}_m$ and $w$, showing growth-geometry differences for ${\mathrm{\Omega }}_m$ (center) and $w$ (right).

Figure 13

Robustness of real-data constraints to changes in analysis choices when we split ${\mathrm{\Omega }}_m$. Data points and error bars represent the peak and 68% confidence intervals for marginalized one-dimensional posteriors. The vertical shaded regions correspond to the 68% confidence interval of the baseline measurements.

Figure 14

Robustness of results to adding systematics to simulated data for the model splitting ${\mathrm{\Omega }}_m$ and $w$. Data points and error bars represent the peak and 68% confidence intervals for marginalized one-dimensional posteriors. The vertical shaded regions correspond to the baseline error bars.

Figure 15

Robustness of real-data constraints to changes in analysis choices when we split ${\mathrm{\Omega }}_m$ and $w$. Data points and error bars represent the peak and 68% confidence intervals for marginalized one-dimensional posteriors. The vertical shaded regions correspond to the 68% confidence interval of the baseline measurements.

Figure 16

Likelihood profile showing the maximum likelihood for chain samples within narrow bins of ${\mathrm{\Omega }}_m^{\mathrm{grow}}$. The sharp step functions in the DES-only plot show where the sample density decreases significantly due to the $A_{\mathrm{IA}}-{\mathrm{\Omega }}_m^{\mathrm{grow}}$ projection effects discussed in Appendix pp2.

Figure 17

Marginalized constraints from DES and Ext-geo data. This plot is identical to Fig. 6, but uses the external dataset that does not include BOSS RSD.

Figure 18

Ext-all constraints (not including any DES information) showing the effect of fixing neutrino mass for both the split ${\mathrm{\Omega }}_m$ parametrization and $\mathrm{\Lambda }\mathrm{CDM}$.