A general analytical expression for the Gaussian covariance of complex multi-tracer power spectra is derived, applied to multipoles and 2D spectra, and validated against Monte Carlo simulations.
Friedrich et al.,Dark energy survey year 3 results: Covariance modelling and its impact on parameter estimation and quality of fit,2012.08568
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abstract
We describe and test the fiducial covariance matrix model for the combined 2-point function analysis of the Dark Energy Survey Year 3 (DES-Y3) dataset. Using a variety of new ansatzes for covariance modelling and testing we validate the assumptions and approximations of this model. These include the assumption of a Gaussian likelihood, the trispectrum contribution to the covariance, the impact of evaluating the model at a wrong set of parameters, the impact of masking and survey geometry, deviations from Poissonian shot-noise, galaxy weighting schemes and other, sub-dominant effects. We find that our covariance model is robust and that its approximations have little impact on goodness-of-fit and parameter estimation. The largest impact on best-fit figure-of-merit arises from the so-called $f_{\mathrm{sky}}$ approximation for dealing with finite survey area, which on average increases the $\chi^2$ between maximum posterior model and measurement by $3.7\%$ ($\Delta \chi^2 \approx 18.9$). Standard methods to go beyond this approximation fail for DES-Y3, but we derive an approximate scheme to deal with these features. For parameter estimation, our ignorance of the exact parameters at which to evaluate our covariance model causes the dominant effect. We find that it increases the scatter of maximum posterior values for $\Omega_m$ and $\sigma_8$ by about $3\%$ and for the dark energy equation of state parameter by about $5\%$.
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First GI BAO measurement from DES Y3 photometric data yields α = 0.966 ± 0.252, consistent with density BAO α = 0.966 ± 0.037 at 0.86σ detection.
The HI one-point PDF, modelled with large-deviation statistics and validated against simulations including beam and foreground systematics, tightens cosmological constraints and breaks the sigma8-b1 degeneracy beyond the power spectrum.
COLA-based hybrid emulator reproduces nonlinear power spectrum boosts in w0wa models to <2% error vs EuclidEmulator2 and produces <0.3σ shifts in LSST-like cosmic shear parameter constraints.
DES Y3 3x2pt analysis constrains S8=0.776±0.017 and Ωm=0.339±0.032 in flat ΛCDM, consistent with Planck CMB results at p=0.13-0.48.
The improved Narrow Kernel Approximation fails to match simulation-based covariances for real-space cosmic shear 2PCF under survey masks due to off-diagonal harmonic-space errors, while the weighted quartic-counts method agrees better.
citing papers explorer
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Complex yet Hermitian: Gaussian covariance of cross-correlation and multi-tracer power spectra
A general analytical expression for the Gaussian covariance of complex multi-tracer power spectra is derived, applied to multipoles and 2D spectra, and validated against Monte Carlo simulations.
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Density-Shear Baryon Acoustic Oscillation as a Cosmological Consistency Check
First GI BAO measurement from DES Y3 photometric data yields α = 0.966 ± 0.252, consistent with density BAO α = 0.966 ± 0.037 at 0.86σ detection.
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One with HI: Modelling HI Intensity Mapping one-point statistics including systematics
The HI one-point PDF, modelled with large-deviation statistics and validated against simulations including beam and foreground systematics, tightens cosmological constraints and breaks the sigma8-b1 degeneracy beyond the power spectrum.
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Modeling nonlinear scales for dynamical dark energy cosmologies with COLA
COLA-based hybrid emulator reproduces nonlinear power spectrum boosts in w0wa models to <2% error vs EuclidEmulator2 and produces <0.3σ shifts in LSST-like cosmic shear parameter constraints.
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Dark Energy Survey Year 3 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing
DES Y3 3x2pt analysis constrains S8=0.776±0.017 and Ωm=0.339±0.032 in flat ΛCDM, consistent with Planck CMB results at p=0.13-0.48.
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Analytical method for computing the covariance matrix of cosmic shear two-point correlation function
The improved Narrow Kernel Approximation fails to match simulation-based covariances for real-space cosmic shear 2PCF under survey masks due to off-diagonal harmonic-space errors, while the weighted quartic-counts method agrees better.