Uncorrelated Modes of the Nonlinear Power Spectrum

Nonlinear evolution causes the galaxy power spectrum to become broadly correlated over different wavenumbers. It is shown that prewhitening the power spectrum – transforming the power spectrum in such a way that the noise covariance becomes proportional to the unit matrix – greatly narrows the covariance of power. The eigenfunctions of the covariance of the prewhitened nonlinear power spectrum provide a set of almost uncorrelated nonlinear modes somewhat analogous to the Fourier modes of the power spectrum itself in the linear, Gaussian regime. These almost uncorrelated modes make it possible to construct a near minimum variance estimator and Fisher matrix of the prewhitened nonlinear power spectrum analogous to the Feldman-KaiserPeacock estimator of the linear power spectrum. The paper concludes with summary recipes, in gourmet, fine, and fastfood versions, of how to measure the prewhitened nonlinear power spectrum from a galaxy survey in the FKP approximation. An Appendix presents FFTLog, a code for taking the fast Fourier or Hankel transform of a periodic sequence of logarithmically spaced points, which proves useful in some of the manipulations.