Closed universes can satisfy the holographic principle in three dimensions

TL;DR

This paper investigates 2+1 dimensional Friedmann-Robertson-Walker models to determine conditions under which closed universes satisfy the holographic principle, revealing that only exotic matter with negative pressure allows this.

Contribution

It provides a rigorous analysis of holographic principle satisfaction in 2+1D cosmological models, correcting previous assumptions and identifying specific matter conditions needed.

Findings

Closed universes satisfy the holographic principle only with exotic negative-pressure matter.

Previous work's assumptions were found to be erroneous.

Collapse scenarios in flat universes are also analyzed.

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 $\gamma$-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.