Euclid Mission: Novel Technique for Accurate Angular Power Spectrum Covariances

The Euclid mission aims to map the geometry of the universe and probe the nature of dark matter and dark energy. A critical aspect of this endeavor is the accurate measurement of clustering and weak-lensing angular power spectra. This paper introduces DICES (Debiased Internal Covariance Estimation with Shrinkage), a novel technique for generating accurate and precise internal covariances for these measurements. DICES employs jackknife resampling, dividing the survey area into equal segments using a binary space partition algorithm. This allows for internally derived covariance estimates without relying on assumptions about cosmology or galaxy properties. The method then applies linear shrinkage of the empirical correlation matrix towards the Gaussian prediction, ensuring the covariance is non-singular and invertible, which is essential for likelihood estimation and validation. A delete-2 jackknife bias correction is applied to the diagonal components of the jackknife covariance to remove the tendency for jackknife error estimates to be biased high. Validation on synthetic Euclid-like lognormal catalogues demonstrates that DICES produces accurate, non-singular covariance estimates, with significant improvements in relative error compared to standard jackknife estimates. This advancement is crucial for mitigating observational systematic effects and maximizing the scientific return of the Euclid mission. The development of DICES represents a significant step forward in the field of cosmological data analysis, enabling more precise and reliable constraints on cosmological parameters.

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