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

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1. Introduction

Observations of the large scale structure (LSS) of the Universe carried out during the last years and coming up from current experiments and observational programs allow us to determine the parameters of cosmological models and the nature of dark matter more precisely. The usual cosmological paradigm - a scale free power spectrum of scalar primordial perturbations which evolve in a multicomponent medium to form the large scale structure of the Universe - is compatible with the observed cosmic microwave background (CMB) temperature fluctuations. Most inflationary scenarios predict a scale free primordial power spectrum of scalar density fluctuations [FORMULA] with arbitrary n as well as gravity waves which contribute to the power spectrum of CMB temperature fluctuations [FORMULA] at low spherical harmonics. But models with a minimal number of free parameters, such as the scale invariant ([FORMULA]) standard cold dark matter model (SCDM) or the standard mixed (cold plus hot) dark matter model (SMDM) only marginally match observational data. Better agreement between predictions and observational data can be achieved in models with a larger number of parameters: cold dark matter (CDM) or mixed dark matter (MDM) with baryons, a tilted primordial power spectrum, a spatial curvature ([FORMULA]), a cosmological constant ([FORMULA]) and a tensor contribution to the CMB anisotropy power spectrum.

The neutrino oscillations discovered recently in the Super-Kamiokande experiment (Fukuda et al. 1998) show that at least one species of weakly interacting neutrinos have non-zero rest mass. Assuming that the largest one of them is about [FORMULA] eV we find [FORMULA]. It is also possible that one, two or three species have masses in the eV range and give appreciable contribution to the dark matter content of the Universe.

The presence of rich clusters of galaxies at [FORMULA] (Bahcall & Fan 1998) indicates a low matter density.

In this work we do not include into our analysis the recent observations of distant supernovae (Perlmutter et al. 1998, Riess et al. 1998). The SNeIa measurements support a positive cosmological constant. Assuming a flat Universe, [FORMULA], a value of [FORMULA] is preferred (see also the review by Bahcall et al. 1999), but, in agreement with Valdarnini et al. 1998, Primack & Gross 1998, we find that on the basis of LSS data alone, a non-vanishing cosmological constant is preferred within the class of models analyzed in this work.

Another approach based on the search of best-fit cosmological parameters in open and critical density CDM and [FORMULA]CDM models without gravitational waves for the total combination of observational data on CMB anisotropy has been carried out by Lineweaver & Barbosa 1998. But the CMB data set corresponds to very large scales ([FORMULA]Mpc) and it is not sufficiently sensitive to the existence of a HDM component. The power spectra of density fluctuations obtained from the spatial distribution of Abell-ACO clusters (Einasto et al. 1997, Retzlaff et al. 1998), APM, CfA and IRAS galaxy surveys (Einasto et al. 1999 and references therein) are extended to smaller scales up to galaxy scales which are below the neutrino free streaming scale. On small scales constraints are obtained from absorption features in quasar spectra known as the Ly-[FORMULA] forest (Gnedin 1998, Croft et al. 1998).

The determination of cosmological parameters from some observations of the LSS of the Universe was carried out in many papers (e.g. Atrio-Barandela et al. 1997, Lineweaver & Barbosa 1998, Tegmark 1999a, Bridle et al. 1999, Novosyadlyj 1999 and references therein). Recently, Bridle et al. 1999 have analyzed the cluster abundances, CMB anisotropies and IRAS observations to optimize the four parameters ([FORMULA], h, [FORMULA], and [FORMULA] in a open CDM model. Atrio-Barandela et al. 1997 use the cluster power spectrum together with data of the Saskatoon experiment to discuss the possible existence of a built-in scale in the primordial power spectrum. In this paper a total of 23 measurements from sub-galaxy scales (Ly-[FORMULA] clouds) over cluster scales up to the horizon scale (CMB quadrupole) are used to determine seven cosmological parameters.

Clearly, it is possible that the `correct cosmological model' is not one of those analyzed in this paper. If the data are good enough this can in principle be decided by a [FORMULA]-test. As long as we find a model within the family of models studied here with an acceptable value of [FORMULA], we have no compelling reason to consider other models.

In view of the growing body of observational data, we want to discuss the quantitative differences between theory and observations for the entire class of available models by varying all the input parameters such as the tilt of the primordial spectrum, n, the density of cold dark matter, [FORMULA], hot dark matter, [FORMULA], and baryons, [FORMULA], the vacuum energy or cosmological constant, [FORMULA], and the Hubble parameter h, to find the values which agree best with observations of LSS on all scales (or even to exclude a whole family of models). Here we restrict ourselves to the analysis of spatially flat cosmological models with [FORMULA] ([FORMULA]), where [FORMULA], and to an inflationary scenario without tensor mode. We also neglect the effect of a possible early reionization which could reduce the amplitude of the first acoustic peak in the CMB anisotropy spectrum.

The reason for the restriction of flat models is mainly numerical. However, the new CMB anisotropy data from the Boomerang experiment actually strongly favors spatially flat universes (Melchiorri et al. 1999b). Neglecting the tensor mode which affects the normalization and the height of the first acoustic peak is motivated by the work of Tegmark 1999a, who found that CMB anisotropy data prefer no or a small tensor component, however there are also arguments in favor of the importance of the tensor mode (Arkhipova et al. 1998, Melchiorri et al. 1999a). Furthermore, since the LSS data used in this paper disfavor very blue spectra, the high acoustic peak indicate that reionization cannot be substantial for the class of models analyzed in this paper. Hence we set the optical depth [FORMULA].

The outline of this paper is as follows: In Sect. 2 we describe the observational data which are used. The method of parameter determination and some tests are described in Sect. 3. We present the results obtained under different assumptions about the parameter ranges in Sect. 4. A discussion of our results and the conclusions are given in Sects. 5 and 6 respectively.

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© European Southern Observatory (ESO) 2000

Online publication: April 10, 2000