Linearizing the observed power spectrum

Semi-analytic treatment of the power spectrum with the approximation of constant linear bias provides a way to compare cosmological models to a large amount of data, as Peacock &38; Dodds have shown. By applying the appropriate corrections to the observational power spectrum it is possible to recover the underlying linear power spectrum for any given cosmological model. Using extensive N-body simulations we carefully test and calibrate all important corrections. To demonstrate that the method is applicable to a wide range of cosmological models, we test the standard Ω = 1 cold dark matter (CDM) model, Ω < 1 models that include a cosmological constant (ΛCDM), and Ω = 1 models with a mixture of cold and hot dark matter (CHDM), both with one massive neutrino and two equal mass neutrinos. The ΛCDM and CHDM models are normalized to COBE and to cluster abundances. Our tests indicate that the improved linear–non-linear mapping recently suggested by Peacock &38; Dodds for treating CDM-type power spectra works well for a wide range of scale-dependent power spectra. However, we find that the Peacock &38; Dodds prescription for the recovery of the linear power spectrum from observations, which is often used to test cosmological models, can be misleading because the corrections are model-dependent. A model should not be judged based on the linear spectrum recovered by that procedure, but must be compared with the recovered spectrum for that particular model. When we apply the proper corrections for a given model to the observational power spectrum, we find that no model in our test group recovers the linear power spectrum well for the bias values suggested by Peacock &38; Dodds between Abell, radio, optical, and IRAS catalogues: bA : bR : bO : bI = 4.5 : 1.9 : 1.3 : 1.0, with bI = 1.0. The recovered linear ΛCDM and CHDM power spectra were systematically below their respective linear power spectra using bI = 1.0. When we allow bl to vary (keeping the same bias ratios) we find that: (i) CHDM models give very good fits to observations if optically selected galaxies are slightly biased (bO ∼ 1.1). (ii) Most ΛCDM models give worse but acceptable fits if blue galaxies are considerably antibiased (0.6 ≲ bO ≲ 0.9) and fail if optical galaxies are biased. (iii) There is a universal shape of the recovered linear power spectrum of all ΛCDM models over their entire range of explored wavenumbers, 0.01 ≲ k ≲ 0.6 h Mpc−1. For a given bias, recovered linear power spectra of CDM and CHDM models are nearly the same as that of ΛCDM in the region 0.01 ≲ k ≲ 0.2 h Mpc−1 but diverge from this spectrum at higher k. We tabulate the recovered linear spectra, and also the initial linear spectra, for all the models considered.