Correlations in the Spatial Power Spectra Inferred from Angular Clustering: Methods and Application to APM

We reconsider the inference of spatial power spectra from angular clustering data and show how to include correlations in both the angular correlation function and the spatial power spectrum. Inclusion of the full covariance matrices loosens the constraints on large-scale structure inferred from the APM survey by over a factor of two. We present a new inversion technique based on singular value decomposition that allows one to propagate the covariance matrix on the angular correlation function through to that of the spatial power spectrum and to reconstruct smooth power spectra without underestimating the errors. Within a parameter space of the CDM shape Γ and the amplitude σ8, we find that the angular correlations in the APM survey constrain Γ to be 0.19–0.37 at 68% confidence when fit to scales larger than k = 0.2hMpc. A downturn in power at k < 0.04hMpc is significant at only 1–σ. These results are optimistic as we include only Gaussian statistical errors and neglect any boundary effects. Subject headings: cosmology: theory – large-scale structure of the universe