The high-quality cosmological data, which became available in the last decade, have thrusted upon us a rather preposterous composition for the universe which poses one of the greatest challenges theoretical physics has ever faced: the so-called dark energy. By focusing our attention on specific examples of dark energy scenarios, we discuss three different candidates for this dark component, namely, a decaying vacuum energy or time-varying cosmological constant [lambda(tau)], a rolling homogeneous quintessence field (phi), and modifications in gravity due to extra spatial dimensions. As discussed, all these candidates [along with the vacuum energy or cosmological constant (lambda)] seem somewhat to be able to explain the current observational results, which hampers any definitive conclusion on the actual nature of the dark energy.

Given the wealth of increasingly accurate cosmological observations, especially the recent results from the WMAP, and the development of methods and strategies in the search for cosmic topology, it is reasonable to expect that we should be able to detect the spatial topology of the Universe in the near future. Motivated by this, we examine to what extent a possible detection of a nontrivial topology of positively curved universe may be used to place constraints on the matter content of the Universe. We show through concrete examples that the knowledge of the spatial topology allows to place constraints on the density parameters associated to dark matter (omegam) and dark energy (<FONT FACE=Symbol>W L</FONT>).

We propose a new analytic approximation for the luminosity function of galaxies. The suggested expression behaves like the Schechter function at the faint end (f ~ La) but departs considerably at the bright end (L >> L*). We argue here that such a behavior may provide a better fit for the current observational data than does the Schechter function. Its practical interest is stressed by considering roughly the data set provided by the Stromlo-APM redshift survey. Implications on the estimates of the matter density parameter from mass-to-light ratio are also briefly discussed.

Old high-z galaxies are important tools for understanding the structure formation problem and may become the key to determine the ultimate fate of the Universe. In this paper, the inferred ages of the three oldest galaxies at high redshifts reported in the literature are used to constrain the first epoch of galaxy formation and to reanalyse the high-z time scale crisis. The lower limits on the formation redshift z f depends on the quantity of cold dark matter in the Universe. In particular, if omegam > or = 0.37 these galaxies are not formed in FRW cosmologies with no dark energy. This result is in line with the Supernovae type Ia measurements which suggest that the bulk of energy in the Universe is repulsive and appears like an unknown form of dark energy component. In a complementar analysis, unlike recent claims favoring the end of the age problem, it is shown that the Einstein-de Sitter model is excluded at high-z by 3sigma.