Dj. Eisenstein et M. Zaldarriaga, Correlations in the spatial power spectra inferred from angular clustering: Methods and application to the automated plate measuring survey, ASTROPHYS J, 546(1), 2001, pp. 2-19
We reconsider the inference of spatial power spectra from angular clusterin
g 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
Automated Plate Measuring (APM) survey by over a factor of 2. 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 pow
er spectra without underestimating the errors. Within a parameter space of
the cold dark matter (CDM) shape Gamma and the amplitude sigma (8), we find
that the angular correlations in the APM survey constrain Gamma to be 0.19
-0.37 at 68% confidence when fitted to scales larger than k = 0.2 h Mpc(-1)
. A downturn in power at k < 0.04 h Mpc(-1) is significant at only 1 <sigma
>. These results are optimistic, since we include only Gaussian statistical
errors and neglect any boundary effects.