Constraints on dark energy from the observed density fluctuations spectrum and supernova data

One of the greatest challenges in cosmology today is to determine the nature of dark energy, the source of the observed present acceleration of the universe. High precision experiments are being developed to reduce the uncertainties in the observations. Recently, we showed that the agreement to an accuracy of 10% of measurements of the present density fluctuations (\delta\rho/\rho)^2, derived from galaxy distribution (GD) data and cosmic microwave background (CMB) anisotropies in the \LambdaCDM model, puts very strong limits on the possible decay of the vacuum energy into cold dark matter. Using this agreement, combined with the evidence that the matter density \Omega_M^0=0.28\pm 0.02 and that the universe is approximately flat, we show that the vacuum metamorphosis model (VMM) and the popular brane-world model (BWM), both used to explain dark energy, can be discarded. When we relax the \Omega_M^0 requirement, we find that an agreement within 10% can be obtained only with \Omega_M^0\simeq 0.36 for the VMM and \Omega_M^0\simeq 0.73 for the BWM, both of which are not consistent with observations. The agreement of the CMB and GD data and previous constraints from SNIa data exclude, or put strong limits on, other dark energy models, which have been suggested, that can be described by the parametrized equation of state (EOS) w=p/\rho= w_0 + w_a(1-a), where w_0 and w_a are constants, a is the cosmological scale factor and p (\rho) is the pressure (energy density) of the dark energy. We find that the supergravity (SUGRA) model with w_0=-0.82 and w_a=0.58 can be discarded. In general, we find best values -1.86<w_0<-1.72 with 1.53<w_a<2.0. For redshifts z\sim 0.5-1, where the supernova data is sensitive, w\sim -1 for this parametrized EOS.