A unified pseudo- C ℓ framework Alonso, David; Sanchez, Javier; Slosar, Anže
Monthly notices of the Royal Astronomical Society,
04/2019, Letnik:
484, Številka:
3
Journal Article
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The pseudo-Cℓ is an algorithm for estimating the angular power and cross-power spectra that is very fast and in realistic cases also nearly optimal. The algorithm can be extended to deal with ...contaminant deprojection and E/B purification, and can therefore be applied in a wide variety of scenarios of interest for current and future cosmological observations. This paper presents NAMASTER, a public, validated, accurate, and easy-to-use software package that, for the first time, provides a unified framework to compute angular cross-power spectra of any pair of spin-0 or spin-2 fields, contaminated by an arbitrary number of linear systematics and requiring B- or E-mode purification, both on the sphere or in the flat-sky approximation. We describe the mathematical background of the estimator, including all the features above, and its software implementation in NAMASTER. We construct a validation suite that aims to resemble the types of observations that next-generation large-scale structure and ground-based cosmic microwave background experiments will face, and use it to show that the code is able to recover the input power spectra in the most complex scenarios with no detectable bias. NAMASTER can be found at https://github.com/LSSTDESC/NaMaster, and is provided with comprehensive documentation and a number of code examples.
We compare a large suite of theoretical cosmological models to observational data from the cosmic microwave background, baryon acoustic oscillation measurements of expansion, Type Ia supernova ...measurements of expansion, redshift space distortion measurements of the growth of structure, and the local Hubble constant. Our theoretical models include parametrizations of dark energy as well as physical models of dark energy and modified gravity. We determine the constraints on the model parameters, incorporating the redshift space distortion data directly in the analysis. To determine whether models can be ruled out, we evaluate the p-value (the probability under the model of obtaining data as bad or worse than the observed data). In our comparison, we find the well-known tension of H0 with the other data; no model resolves this tension successfully. Among the models we consider, the large-scale growth of structure data does not affect the modified gravity models as a category particularly differently from dark energy models; it matters for some modified gravity models but not others, and the same is true for dark energy models. We compute predicted observables for each model under current observational constraints, and identify models for which future observational constraints will be particularly informative.
Abstract
We study the covariance properties of real space correlation function estimators – primarily galaxy–shear correlations, or galaxy–galaxy lensing – using SDSS data for both shear catalogues ...and lenses (specifically the BOSS LOWZ sample). Using mock catalogues of lenses and sources, we disentangle the various contributions to the covariance matrix and compare them with a simple analytical model. We show that not subtracting the lensing measurement around random points from the measurement around the lens sample is equivalent to performing the measurement using the lens density field instead of the lens overdensity field. While the measurement using the lens density field is unbiased (in the absence of systematics), its error is significantly larger due to an additional term in the covariance. Therefore, this subtraction should be performed regardless of its beneficial effects on systematics. Comparing the error estimates from data and mocks for estimators that involve the overdensity, we find that the errors are dominated by the shape noise and lens clustering, which empirically estimated covariances (jackknife and standard deviation across mocks) that are consistent with theoretical estimates, and that both the connected parts of the four-point function and the supersample covariance can be neglected for the current levels of noise. While the trade-off between different terms in the covariance depends on the survey configuration (area, source number density), the diagnostics that we use in this work should be useful for future works to test their empirically determined covariances.
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