Closed universes can satisfy the holographic principle in three dimensions

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.