The measurements presented in this work are supported by a number of accompanying infrastructure papers:. i) The construction and validation of the photometrics. Any cosmological interpretation of weak lensing signals requires accurate knowledge of the distribution of distances to the source galaxies used in the measurement[125,126]. COSMOS has ten percent of the redshift information derived from that sample at the faintest magnitudes.
SHEAR CALIBRATION
But a distortion of thenðzÞ is also caused by the response of the measured shape of one galaxy to the shearing of light at the different redshifts of a mixed galaxy, leading to a distortion of the nðzÞ that should be used for lensing analyses. Furthermore, image simulations with an applied redshift-dependent shear impose constraints on the distortion of the mean and the shape of the nðzÞ.
COSMOLOGICAL SIMULATIONS Aspects of this analysis have been validated using the
Constraints on this effect are possible by using several different redshift-dependent ΔγðzÞ in the image simulation. We find that it is significantly different from zero for the DES Y3 analysis choices and accuracy rate [90].
COSMIC-SHEAR MEASUREMENT This section presents the real-space two-point shear
The error bound indicates the square root of the diagonal of the analytic covariance matrix. In the lower panels, the fractional residuals, ðξ−ξtheory Þ=ξtheory, demonstrate the fit of the model to the measurements.
MODELING AND ANALYSIS CHOICES This section outlines the baseline theoretical model for
The term FiðzÞ models the impact on the effective weighting of the discrete sources used to construct niðzÞ, such as (possibly redshift-dependent) multiplicative bias effects. 4 as “no mixing(z).” Using the normalized nðzÞ samples in the analysis pipeline provides this. However, uncertainties in the estimated redshift distributions are not limited to the mean redshift, but rather include, for example, the extent of the tail of a redshift distribution.
The DES Y3 effort has developed techniques to marginalize the entire shape uncertainty of the redshift distribution. HYPERRANK, the primary analysis uses the ensemble mean and the uncertainty approximated as a shift in the mean, with the priors given in Table II. Figure 4 illustrates the impact of the effects of sources of uncertainty in redshift calibration on the expected cosmic shear data vector.
The red line indicates the effect of the mixing redshift mixing effect on the redshift distribution (see Section VII D). Because of the consistency of the impact across scales and bins, it is still warranted to investigate the impact on cosmology, as explored in Sect.
COSMOLOGICAL CONSTRAINTS In this section, we present constraints on cosmological
For parameter inference, the likelihood, L, of a data vector D, given a model T, with parameters p, can be expressed as LðDjpÞ. Therefore, we use MAXLIKEminimizer after bootstrapping the chain to obtain a reliable estimate of the maximum posterior point (MAP). Even in the case of the underlying framework applied to a synthetic, noiseless data vector generated from the same model, the marginalized parameter posteriors may appear biased from the input parameter values due to parameter volume or projection effects that occur when the parameters of interest they are not good - limited by the data or degenerate with other parameters that are known beforehand (see Fig. 2 in ref. [111]).
The analysis has 202 degrees of freedom (227 data points and 28 free parameters), but considering the informative priors used according to Ref. [197], the effective dimensionality of the parameter space is reduced to ~5 if the parameters in the analysis are not fully constrained by the data. For the DES Y3 analysis, we calculate Bayesian suspicion, an evidence-based method that corrects for prior dependence of the constraints in the entire parameter space. It is noticeable that the limit on the value of the S8 parameter is set to be lower than that from Planck by 2.3σ.
In Appendix B, we discuss the extent of the impact of noise on cosmological analyzes by investigating several noisy simulated runs. The gain in S8 restraining power and small displacement can be partially attributed to the removal of the outermost lobes of the a1−a2 fiducial intrinsic alignment posteriorly degenerated by S8 (see Appendix B for further discussion).
INTERNAL CONSISTENCY
In particular, the PPD test addresses the question of the consistency of observations in one redshift bin with FIG. Repeating PPD tests removing both halves, we find that predictions of the low-redshift bins derived from high-redshift observations overpredict the data, albeit with a large uncertainty regarding the loss of constraining power on the intrinsic fitting parameters. In practice, the intrinsic fitting constraint therefore requires accurate knowledge of the redshift distributions and their errors.
Here we inspect the consistency of the small- and large-scale angular contributions to the data vector, by comparing their respective cosmological constraints. We test the consistency of the two components of the two-point function with cosmic shear, ξþ and ξ−. When we consider the S8 parameter, we find consistency within ~0.5σ, with posteriors of these subsets of the data shown in Fig.
In this section, we examine the consistency of the DES Y3 constraints with the DES Y1 cosmic displacement results from [13]. We caution that a comparison of the two results is not straightforward, as analysis choices are different.
ROBUSTNESS TO REDSHIFT CALIBRATION Determination of the true ensemble redshift distribution
At the lowest order, lensing is primarily sensitive to the average redshift and the width of the redshift distribution of each bin [118]. The two extreme choices of the redshift calibration sample, used in the analysis of the red and yellow contours, show no significant difference in cosmological parameters. A comparison for the case of the less restrictive reference analysis is shown in tests 1 and 2 in Figure 7 and Table III.
On the left it is shown compared to "pure" redshift calibration samples, C (red), purely derived from COSMOS and MB (yellow), the "maximum biased" spectroscopic sample, showing the (in)sensitivity of the analysis to spectroscopic vs. In the middle, the levels of the methodology – SOMPZ, WZenSR – are stepped back, showing the consistency of the probabilities of each method. On the right, the fiducial modeling of the uncertainty in the redshift calibration that only considers shifts in the mean of each redshift bin, Δz, is compared to an analysis where the full-form uncertainty is accounted for by nðzÞ realizations with HYPERRANK (red) ).
As a result, the WZ primarily constrains the shape of the redshift distribution rather than the mean, and has relatively little impact on cosmological posteriors. The full-form constraint is only marginally degraded and is unbiased, illustrating that uncertainties in the shape of the redshift distribution are subdominant to cosmic shear at the current statistical precision.
ROBUSTNESS TO BLENDING AND SHEAR CALIBRATION
First, it is shown in [81] that the posteriors in hzi from these methods are stable, before their information is combined at different points in the analysis pipeline, with SR. incorporated into the cosmological likelihood estimation point. We find that the S8 constraints do not change when each method is included and are consistent, and thus our results are robust to these variants in methodology. TheWZanalysis requires the marginalization of flexible models of the redshift evolution of accretion biases of weak lensing sources, which are mostly degenerate withhzi[82,201].
For this analysis, the SR information is effective, finding 25% tighter constraints with the improvement largely attributable to breaking the degeneracies in the TATT internal stretching posterior model, which are bimodal (see Appendix B), rather than a substantially tight posteriors at redshift. distributions[83]. For the fiducial and ΛCDM-optimized analyses, the uncertainty in the redshift estimate is included as an uncorrelated shift in the mean redshift of each bin. As discussed in Section VII E, while the DES Y3 methodology is able to sample full realizations in likelihood analysis with HYPERRANK, thus also capturing variations in the form of thenðzÞ.
Since this modeling choice was made based on a weighing of the impact of this approach on posteriors in a simulated analysis, against increased running time, we test the robustness of the decision here. Comparing this variant with the ΛCDM-optimized analysis (green) in the Ωm−S8 plane, we find consistency.
WHAT LIMITS LENSING COSMOLOGICAL PRECISION?
Uncertainties in the shear and redshift calibration are related due to the limited volume of imaging simulations affecting both. To test the robustness of this assumption, an analysis using HYPERRANK is performed for the sample on nγðzÞrealizations, which of course include both bias-type and nðzÞ-type multiplicative biases, labeled the “full mixture treatment”. The cosmological posteriors from this variant, Test 11, are compared to those in Fig. 11 and shown to be consistent. While the imaging simulations used to inform these choices are in good agreement with the data, they do not account for some effects such as clustering with undetected sources, which may contribute additional mixing effects.
Therefore, the theoretical uncertainties cost about 2=3 of the Y3 force (in terms of variance) on the cosmological parameters, with intrinsic alignment uncertainty contributing slightly more than baryon-driven scale cuts in limiting cosmological precision. The precise balance will depend on how many more modes must be sacrificed to keep the modeling accuracy below the measurement noise, and on how well the intrinsic alignment models can calibrate themselves to data. We note that this is a different scenario than the KiDS-1000 analysis, which appears to be statistically limited [16].
A small improvement over the fixed-theory result is noticeable (×1.9 vs. ×1.8 improvement over the ΛCDM-optimized case), viz. investigation of intrinsic alignment model selection, a similarly performed posterior in Ref. [98], who notes that simpler, less conservative models provide a sufficient fit to the DES Y3 data and could be useful if run before the data were exposed.
CONCLUSIONS
Impact of shift systematics on theξðθÞ signal: The fractional impact,δξ=ξ, of the effects of (i) B-modes (black), (ii) the approximation made in the response correction (red), (iii) the PSF contamination ( yellow), and (iv) the additive correction applied to the shear (blue, dotted). Here we test for the presence of B modes in the shape catalog and potential contamination of the two-point functions used in the cosmological analysis. The impact of this simplification in the calculation of the shear response is shown in red in Fig.13 to be negligible at the current level of accuracy.
We test the impact of SR in the case of the data-preferred NLA-a1 model shown in the figure. The right panel shows the posteriors of the data with permutations of the choice of the intrinsic alignment model (TATT and NLA-no-z) and the inclusion of SR. The inclusion of SR is effective in constraining the intrinsic alignment parameters and, for the case of TATT, in mitigating the impact of bimodality.
This suggests that an uncertainty in the shape of thenðzÞ is compensated for by a more substantial change in the mean of the distribution. To test that such an effect is not occurring in the DES Y3 analysis, we include a detailed description of the full uncertainty in thenðzÞestimates[81]. In this Appendix, the robustness of the analysis results to the elections in the Republic of Croatia is also investigated.
The posteriors for a subset of the ΛCDM cosmological parameters for the fiducial and ΛCDM-optimized analyses.
![FIG. 6. Recent cosmic-shear results: the constraints on Ω m , σ 8 (upper left) and S 8 (upper right) are shown for the DES Y3 Λ CDM- CDM-Optimized analysis (green) and Planck 2018 CMB [19] (with free neutrino mass density, yellow)](https://thumb-ap.123doks.com/thumbv2/azpdfnet/10473720.0/22.918.93.830.344.945/recent-results-constraints-optimized-analysis-planck-neutrino-density.webp)
