LINEARIZING THE OBSERVED POWER SPECTRUM

Semi-analytic treatment of the power spectrum with the approximation o f constant linear bias provides a way to compare cosmological models t o a large amount of data, as Peacock & Dodds have shown, By applying t he appropriate corrections to the observational power spectrum it is p ossible to recover the underlying linear power spectrum for any given cosmological model. Using extensive N-body simulations we carefully te st and calibrate all important corrections. To demonstrate that the me thod is applicable to a wide range of cosmological models, we test the standard Omega = 1 cold dark matter (CDM) model, Omega < 1 models tha t include a cosmological constant (Lambda CDM), and Omega = 1 models w ith a mixture of cold and hot dark matter (CI-IDM), both with one mass ive neutrino and two equal mass neutrinos. The Lambda CDM and CHDM mod els are normalized to COBE and to cluster abundances. Our tests indica te that the improved linear-non-linear mapping recently suggested by P eacock & Dodds for treating CDM-type power spectra works well for a wi de range of scale-dependent power spectra. However, we find that the P eacock & Dodds prescription for the recovery of the linear power spect rum from observations, which is often used to test cosmological models , can be misleading because the corrections are model-dependent. A mod el 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 mod el to the observational power spectrum, we find that no model in our t est group recovers the linear power spectrum well for the bias values suggested by Peacock & Dodds between Abell, radio, optical, and IRAS c atalogues: b(A) : b(R) : b(O) : b(I) = 4.5 : 1.9 : 1.3 : 1.0, with b(I ) = 1.0. The recovered linear Lambda CDM and CHDM power spectra were s ystematically below their respective linear power spectra using bI = 1 .0. When we allow bl to vary (keeping the same bias ratios) we find th at: (i) CHDM models give very good fits to observations if optically s elected galaxies are slightly biased (b(O) similar to 1.1), (ii) Most Lambda CDM models give worse but acceptable fits if blue galaxies are considerably antibiased (0.6 less than or similar to b(O) less than or similar to 0.9) and fail if optical galaxies are biased. (iii) There is a universal shape of the recovered linear power spectrum of all Lam bda CDM models over their entire range of explored wavenumbers, 0.01 l ess than or similar to k less than or similar to 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 Lambda CDM in the region 0.01 less than or similar to k less than or similar to 0.2 h Mpc(-1) but diverge from th is spectrum at higher k. We tabulate the recovered linear spectra, and also the initial linear spectra, for all the models considered.