Holographic Principle in the Closed Universe : a Resolution with Negative Pressure Matter

TL;DR

This paper demonstrates that a closed universe can satisfy the holographic principle if it contains matter with negative pressure (w < -1/3), potentially realizable as quintessence, especially near critical density.

Contribution

It shows that including matter with negative pressure in a closed universe resolves violations of the holographic principle.

Findings

Closed universe obeys holographic principle with negative pressure matter.

Presence of matter with w < -1/3 is essential for holographic compliance.

Near-critical density enhances holographic consistency.

Abstract

A closed universe containing pressureless dust, more generally perfect fluid matter with pressure-to-density ratio w in the range (1/3, - 1/3), violates 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.