Holographic principle in the closed universe: a resolution with negative pressure matter

A closed universe containing pressureless dust, a more generally perfect fluid matter with pressure-to-density ratio w in the range (13,−13), violates the 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<−13, 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 `quintessenceʹ, much studied recently.