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.
Abstract A closed universe containing pressureless dust, a more generally perfect fluid matter with pressure-to-density ratio w in the range ( 1 3 ,− 1 3 ) , violates the holographic principle applied according to the Fischler–Susskind proposal. We show, first for a class of two-fluid solutions and then for the general multifluid case, that the closed universe will obey the holographic principle if it also contains matter with w 1 3 , and if the present value of its total density is sufficiently close to the critical density. It is possible that such matter can be realised by some form of quintessence', much studied recently. Abstract We examine in details Friedmann–Robertson–Walker models in 2+1 dimensions in order to investigate the cosmic holographic principle suggested by Fischler and Susskind. Our results are rigorously derived differing from the previous one found by Wang and Abdalla. We discuss the erroneous assumptions done in this work. The matter content of the models is composed of a perfect fluid, with a γ -law equation of state. We found that closed universes satisfy the holographic principle only for exotic matter with a negative pressure. We also analyze the case of a collapsing flat universe. The holographic bound states that the entropy in a region cannot exceed one quarter of the area (in Planck units) of the bounding surface. A version of the holographic principle that can be applied to cosmological spacetimes has recently been given by Fischler and Susskind. This version can be shown to fail in closed spacetimes and they concluded that the holographic bound may rule out such universes. In this paper I give a modified definition of the holographic bound that holds in a large class of closed universes. Fischler and Susskind also showed that the dominant energy condition follows from the holographic principle applied to cosmological spacetimes with @math . Here I show that the dominant energy condition can be violated by cosmologies satisfying the holographic principle with more general scale factors. We propose that the holographic principle be replaced by the generalized second law of thermodynamics when applied to time-dependent backgrounds. For isotropic open and flat universes with a fixed equation of state, this agrees with the cosmological holographic principle proposed by Fischler and Susskind (hep-th 9806039). However, in more general situations, it does not. copyright ital 1999 ital The American Physical Society A cosmological version of the holographic principle is proposed. Various consequences are discussed including bounds on equation of state and the requirement that the universe be infinite.