1. INTROUCTION

Our information on the dynamical parameters of the Universe describing the cosmic expansion comes from three different epochs. The earliest is the Big Bang nucleosynthesis which occurred a little over 2 minutes after the Big Bang, and which left its imprint in the abundances of the light elements affecting the baryonic density parameter _b. The discovery of anisotropic temperature fluctuations in the cosmic microwave background radiation at large angular scales (CMBR) by COBE-DMR [1], followed by small scale anisotropies measured in the balloon flights BOOMERANG [2] and MAXIMA [3], by the radio telescopes Cosmic Background Imager (CBI) [4], Very Small Array (VSA) [5] and Degree Angular Scale Interferometer (DASI) [6] testify about the conditions in the Universe at the time of last scattering, about 350000 years after Big Bang. The analyses of the CMBR power spectrum give information about every dynamical parameter, in particular ₀ and its components _b, _m and , and the spectral index n_s. For an extensive review of CMBR detectors and results, see Bersanelli et al. [7]. Very recently, also the expected fluctuations in the CMBR polarization anisotropies has been observed by DASI [8].

The third epoch is the time of matter structures: galaxy clusters, galaxies and stars. Our view is limited to the redshifts we can observe which correspond to times of a few Gyr after Big Bang. This determines the Hubble constant, successfully done by the Hubble Space Telescope (HST) [9], and the difference - _m in the dramatic supernova Ia observations by the High-z Supernova Search Team [10] and the Supernova Cosmology Project [11]. The large scale structure (LSS) and its power spectrum has been studied in the SSRS2 and CfA2 galaxy surveys [12], in the Las Campanas Redshift Survey [13], in the Abell-ACO cluster survey [14], in the IRAS PSCz Survey [15] and in the 2dF Galaxy Redshift Survey [16], [17]. Various sets of CMBR data, supernova data and LSS data have been analyzed jointly. We shall only refer to global analyses of the now most recent CMBR power spectra and large scale distributions of galaxies.

The list of other types of observations is really very long. To mention some, there have been observations on the gas fraction in X-ray clusters [18], on X-ray cluster evolution [19], on the cluster mass function and the Ly forest [20], on gravitational lensing [21], on the Sunyaev-Zel'dovich effect [22], on classical double radio sources [23], on galaxy peculiar velocities [24], on the evolution of galaxies and star creation versus the evolution of galaxy luminosity densities [25].

In this review we shall cover briefly recent observations and results for the dynamical parameters H₀, _b, _m, , ₀, n_s, w and q₀. In Section 2 these parameters are defined in their theoretical context, in Section 3 we turn to the Hubble parameter, and in Section 4 to the baryonic density. The other parameters are discussed in Sections 5 and 6, which are organized according to observational method: supernovæ in Section 5, CMBR and LSS in Section 6. Section 7 summarizes our results.