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Astron. Astrophys. 356, 418-434 (2000)

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6. Conclusions

Using the Levenberg-Marquardt [FORMULA] minimization method we have determined the cosmological parameters of spatially flat, tilted [FORMULA]MDM models. We searched for a maximum of 6 parameters: the spectral index n, the matter content [FORMULA] ([FORMULA]), the hot dark matter content [FORMULA], the baryon content [FORMULA], the dimensionless Hubble constant h and the biasing parameter for rich clusters, [FORMULA]. The experimental data set used in the search procedure included the Abell-ACO power spectrum (Retzlaff et al. 1998), the position and amplitude of the first acoustic peak in the angular power spectrum of CMB temperature fluctuations determined from the set of published measurements on different scales, the constraints for the density fluctuation amplitude [FORMULA] derived from the mass function of nearby and distant clusters (Girardi et al. 1998, Bahcall & Fan 1998), the mean peculiar velocity of galaxies in a sphere of radius [FORMULA]Mpc (Kolatt & Dekel 1997), the constraints on amplitude and tilt of the power spectra at small scales obtained from Ly-[FORMULA] clouds at z=2-3 (Gnedin 1998, Croft et al. 1998), the nucleosynthesis constraints (Tytler et al. 1996, Burles et al. 1999) and the COBE data (Bunn and White 1997) which is used to normalize the model power spectra.

We have considered one, two and three species of massive neutrinos. We have studied the influence of a reduction of the number of free parameters. In Table 4 we summarize the parameters which we have determined in 33 different cases. Based on the results presented in Table 4 we conclude:

  • The tilted [FORMULA]MDM model with one sort of massive neutrinos and the best-fit parameters [FORMULA], [FORMULA], [FORMULA], [FORMULA], [FORMULA] and [FORMULA] (standard errors) matches the observational data set best. The 1[FORMULA] (68.3%) confidence limits on each cosmological parameter, obtained by marginalizing over the other parameters, are [FORMULA], [FORMULA], [FORMULA], [FORMULA], [FORMULA] and [FORMULA].

  • The degeneracies in the [FORMULA] and [FORMULA] planes [FORMULA] and [FORMULA] are revealed.

  • For fixed Hubble constant h raising from 0.5 to 0.72, the best-fit value for [FORMULA] decreases from 0.63 to 0.39 for [FORMULA]MDM models with [FORMULA]. For models with [FORMULA] and 3 the value of [FORMULA] raises by [FORMULA] and [FORMULA] respectively. The [FORMULA] is higher for more species of massive neutrinos, [FORMULA] for one sort and [FORMULA] for three, and decreases slowly for growing h. The inclination of initial power spectrum n correlates somewhat with [FORMULA] and grows slightly with h.

  • Fixing a low [FORMULA]=0.3 a [FORMULA]CDM model without HDM matches the observational data set best. In this case the parameters are [FORMULA], [FORMULA] and [FORMULA].

  • For all models the biasing parameter [FORMULA] of rich clusters is in the range 2.2-3.3, for the best model it equals [FORMULA] (standard error). The 1[FORMULA] (68.3%) confidence interval is [FORMULA].

  • CDM models with [FORMULA], scale invariant primordial power spectrum [FORMULA] and [FORMULA] are ruled out at very high confidence level, [FORMULA].

  • Also pure MDM models are ruled out at [FORMULA] C.L.

Finally, we note that the accuracy of present observational data on the large scale structure of the Universe is still too low to constrain the set of cosmological parameters sufficiently, but we believe that our work shows the potential of such studies, which search for parameters including data from different, often complementary observations. It is clear that with sufficiently accurate data, such a study may also reveal an inconsistency of model assumptions.

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© European Southern Observatory (ESO) 2000

Online publication: April 10, 2000