Uncorrelated modes of the non‐linear power spectrum

Non‐linear evolution causes the galaxy power spectrum to become broadly correlated over different wavenumbers. It is shown that pre‐whitening 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 pre‐whitened non‐linear power spectrum provide a set of almost uncorrelated non‐linear 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 pre‐whitened non‐linear power spectrum analogous to the Feldman–Kaiser–Peacock (FKP) estimator of the linear power spectrum. The paper concludes with summary recipes, in gourmet, fine and fastfood versions, of how to measure the pre‐whitened non‐linear power spectrum from a galaxy survey in the FKP approximation. An appendix presents FFTL og , 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.