Covariance of the one-dimensional mass power spectrum

Citation:

Zhan H, Eisenstein D. Covariance of the one-dimensional mass power spectrum. Monthly Notices of the Royal Astronomical Society. 2005;357 :1387-1398.

Date Published:

March 1, 2005

Abstract:

We analyse the covariance of the one-dimensional mass power spectrumalong lines of sight. The covariance reveals the correlation betweendifferent modes of fluctuations in the cosmic density field and givesthe sample variance error for measurements of the mass power spectrum.For Gaussian random fields, the covariance matrix is diagonal. Asexpected, the variance of the measured one-dimensional mass powerspectrum is inversely proportional to the number of lines of sight thatare sampled from each random field. The correlation between lines ofsight in a single field may alter the covariance. However, lines ofsight that are sampled far apart are only weakly correlated, so thatthey can be treated as independent samples. Using N-body simulations, wefind that the covariance matrix of the one-dimensional mass powerspectrum is not diagonal for the cosmic density field due to thenon-Gaussianity and that the variance is much higher than that ofGaussian random fields. From the covariance, one will be able todetermine the cosmic variance in the measured one-dimensional mass powerspectrum as well as to estimate how many lines of sight are needed toachieve a target precision.

Notes:

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