Covariance of the One-Dimensional Mass Power Spectrum

Abstract

We analyse the covariance of the one-dimensional mass power spectrum along lines of sight. The covariance reveals the correlation between different modes of fluctuations in the cosmic density field and gives the sample variance error for measurements of the mass power spectrum. For Gaussian random fields, the covariance matrix is diagonal. As expected, the variance of the measured one-dimensional mass power spectrum is inversely proportional to the number of lines of sight that are sampled from each random field. The correlation between lines of sight in a single field may alter the covariance. However, lines of sight that are sampled far apart are only weakly correlated, so that they can be treated as independent samples. Using N-body simulations, we find that the covariance matrix of the one-dimensional mass power spectrum is not diagonal for the cosmic density field due to the non-Gaussianity and that the variance is much higher than that of Gaussian random fields. From the covariance, one will be able to determine the cosmic variance in the measured one-dimensional mass power spectrum as well as to estimate how many lines of sight are needed to achieve a target precision.