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Covariance matrices are important tools for obtaining reliable parameter constraints. Advancements in cosmological surveys lead to larger data vectors and, consequently, increasingly complex covariance matrices, whose number of elements grows as the square of the size of the data vector. The most straightforward way of comparing these matrices, in terms of their ability to produce parameter constraints, involves a full cosmological analysis, which can be very computationally expensive. Using the concept and construction of compression schemes, which have become increasingly popular, we propose a fast and reliable way of comparing covariance matrices. The basic idea is to focus only on the portion of the covariance matrix that is relevant for the parameter constraints and quantify, via a fast Monte Carlo simulation, the difference of a second candidate matrix from the baseline one. To test this method, we apply it to two covariance matrices that were used to analyse the cosmic shear measurements for the Dark Energy Survey Year 1. We found that the uncertainties on the parameters change by 2.6 per cent, a figure in agreement with the full cosmological analysis. While our approximate method cannot replace a full analysis, it may be useful during the development and validation of codes that estimate covariance matrices. Our method takes roughly 100 times less CPUh than a full cosmological analysis. [ABSTRACT FROM AUTHOR]

Using almost one million galaxies from the final Data Release 12 of the SDSS's Baryon Oscillation Spectroscopic Survey (BOSS), we have obtained, albeit with low significance, a first model-independent determination of the radial baryon acoustic oscillation (BAO) peak with 9 per cent error: Δ z BAO(z eff = 0.51) = 0.0456 ± 0.0042. In order to obtain this measurement, the radial correlation function was computed in 7700 angular pixels, from which the mean correlation function and covariance matrix were obtained, making the analysis completely model-independent. This novel method of obtaining the covariance matrix was validated via comparison with 500 BOSS mock catalogues. This Δ z BAO determination can be used to constrain the background expansion of exotic models for which the assumptions adopted in the standard analysis cannot be satisfied. Future galaxy catalogues from J-PAS, DESI, and Euclid are expected to significantly increase the quality and significance of model-independent determinations of the BAO peak, possibly determined at various redshift and angular positions. We stress that it is imperative to test the standard paradigm in a model-independent way in order to test its foundations, maximize the extraction of information from the data, and look for clues regarding the poorly understood dark energy and dark matter. [ABSTRACT FROM AUTHOR]