When Fischler and Susskind proposed a holographic prescription based on the particle horizon, they found that spatially closed cosmological models do not verify it due to the apparently unavoidable recontraction of the particle horizon area. In this paper, after a short review of their original work, we expose graphically and analytically that spatially closed cosmological models can avoid this problem if they expand fast enough. It has also been shown that the holographic principle is saturated for a codimension one-brane dominated universe. The Fischler?Susskind prescription is used to obtain the maximum number of degrees of freedom per Planck volume at the Planck era compatible with the holographic principle.
One more remark about observational result comes to support the study of quintessence models. If the fundamental character of the Holographic Principle as a primary principle guiding the behavior of our universe is assumed, it looks reasonable to suppose the saturation of the holographic limit. This is one of the arguments used by T. Banks and W. Fischler @cite_4 @cite_16 to propose a holographic cosmology based on a an early universe, spatially flat, dominated by a fluid with @math Banks and Fischler propose a scenario where black holes of the maximum possible size --the size of the particle horizon-- coalesce saturating the holographic limit; this fluid'' evolves according to @math . . According to ) this value saturates the FS prescription for spatially flat FRW models, but it seems fairly incompatible with observational results. However, for spatially closed FRW cosmological models, it has been found that the saturation of the Holographic Principle is related to the value @math which is compatible with current observations (according to @cite_12 , @math at the 95 Taking @math gives @math in agreement the measured value @cite_32 .
@cite_16 @cite_4 @cite_32 @cite_12
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We present a complete quantum mechanical description of a flat Friedmann-Robertson-Walker universe with equation of state p= rho . We find a detailed correspondence with our heuristic picture of such a universe as a dense black hole fluid. Features of the geometry are derived from purely quantum input. We present a new version of holographic cosmology, which is compatible with present observations. A primordial p = ? phase of the universe is followed by a brief matter dominated era and a brief period of inflation, whose termination heats the universe. The flatness and horizon problems are solved by the p = ? dynamics. The model is characterized by two parameters, which should be calculated in a more fundamental approach to the theory. For a large range in the phenomenologically allowed parameter space, the observed fluctuations in the cosmic microwave background were generated during the p = ? era, and are exactly scale invariant. The scale invariant spectrum cuts off sharply at both upper and lower ends, and this may have observational consequences. We argue that the amplitude of fluctuations is small but cannot yet calculate it precisely. A simple cosmological model with only six parameters (matter density, mh 2 , baryon density, bh 2 , Hubble Constant, H0, amplitude of fluctua We have discovered 16 Type Ia supernovae (SNe Ia) with the Hubble Space Telescope (HST) and have used them to provide the first conclusive evidence for cosmic deceleration that preceded the current epoch of cosmic acceleration. These objects, discovered during the course of the GOODS ACS Treasury program, include 6 of the 7 highest redshift SNe Ia known, all at z > 1.25, and populate the Hubble diagram in unexplored territory. The luminosity distances to these objects and to 170 previously reported SNe Ia have been determined using empirical relations between light-curve shape and luminosity. A purely kinematic interpretation of the SN Ia sample provides evidence at the greater than 99 confidence level for a transition from deceleration to acceleration or, similarly, strong evidence for a cosmic jerk. Using a simple model of the expansion history, the transition between the two epochs is constrained to be at z = 0.46 ± 0.13. The data are consistent with the cosmic concordance model of ΩM ≈ 0.3, ΩΛ ≈ 0.7 (χ = 1.06) and are inconsistent with a simple model of evolution or dust as an alternative to dark energy. For a flat universe with a cosmological constant, we measure ΩM = 0.29 ± (equivalently, ΩΛ = 0.71). When combined with external flat-universe constraints, including the cosmic microwave background and large-scale structure, we find w = -1.02 ± (and w < -0.76 at the 95 confidence level) for an assumed static equation of state of dark energy, P = wρc2. Joint constraints on both the recent equation of state of dark energy, w0, and its time evolution, dw dz, are a factor of 8 more precise than the first estimates and twice as precise as those without the SNe Ia discovered with HST. Our constraints are consistent with the static nature of and value of w expected for a cosmological constant (i.e., w0 = -1.0, dw dz = 0) and are inconsistent with very rapid evolution of dark energy. We address consequences of evolving dark energy for the fate of the universe.