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

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.