Closed universes can satisfy the holographic principle in three dimensions

We examine in details Friedmann-Robertson-Walk-er models in 2 + 1 dimension s in order to investigate the cosmic holographic principle suggested by Fis chler and Susskind. Our results are rigorously derived differing from the p revious 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 perfe ct fluid, with a gamma -law equation of state. We found that closed univers es satisfy the holographic principle only for exotic matter with a negative pressure. We also analyze the case of a collapsing flat universe. (C) 2001 Elsevier Science B.V. All rights reserved.