Scarcity of Birds

Uncorrelated modes of the non-linear power spectrum

“…10 points up one defect of the pre‐whitened power spectrum, which is that, surprisingly enough, it does not reproduce the linear power spectrum at the very largest scales (small k ). Indeed, the pre‐whitened power goes negative in the Peacock (1997) case at k ≈0.0023 h Mpc −1 , and in the ΛCDM case at k ≈0.000 21 h Mpc −1 . This turns out to be a generic feature of the pre‐whitened power spectrum if the true power spectrum goes to zero at zero wavenumber, as is true for Harrison–Zel’dovich models, ξ ( k )∝ k as k →0.…”

“…In addition to power‐law power spectra, the present paper shows results for the power spectrum derived from observations by Peacock (1997), and for an observationally concordant ΛCDM model from the fitting formulae of Eisenstein & Hu (1998), non‐linearly evolved according to the procedure of Peacock & Dodds (1996). In these cases the adopted amplitudes are those corresponding to n =−1.2, i.e.…”

“…Fig. 10 shows pre‐whitened non‐linear power spectra X ( k ), along with linear and non‐linear power spectra ξ L ( k ) and ξ ( k ), for the observationally derived power spectrum of Peacock (1997) with Ω m =0.3, and for a ΛCDM model of Eisenstein & Hu (1998) with observationally concordant parameters as indicated on the graph.…”

“… Linear power spectrum ξ L ( k ), non‐linear power spectrum ξ ( k ), and pre‐whitened non‐linear power spectrum X ( k ) for (left) the Ω m =0.3 power spectrum derived from observations by Peacock (1997), and (right) the COBE ‐normalized ΛCDM power spectrum from the fitting formulae of Eisenstein & Hu (1998), with parameters as listed on the graph. The non‐linear power spectra were computed from the linear power spectra according to the formula of Peacock & Dodds (1996).…”

“…The numbered curves are for power‐law power spectra with correlation functions ξ ( r )=( r /5 h −1 Mpc) − γ , the number label being the index γ . The curve labelled P97 is for the Ω m =0.3 power spectrum derived from observations by Peacock (1997), while that labelled ΛCDM is for the ΛCDM power spectrum of Eisenstein & Hu (1998).…”