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We have investigated the emerging conformal field theory behavior on theinterior interface of the region near the cosmological event horizon on anexample of massless Dirac fermions. Indeed, we have constructed and verifiedthe emerging de Sitter/CFT correspondence for the near cosmological eventhorizon region.  It is in this near horizon region where the infinitely thin shell of matterwith the stiffest equation of state (Zeldovich's matter) is placed in the modelfor a thermodynamically stable `would be black hole' which is sometimes calleda gravastar or a dark energy star. We put forward the hypothesis to the effectthat the Zeldovich matter consists of the strongly correlated quanta which arebest described by the emerging conformal field theory in the near `would behorizon' region of a gravastar/dark energy star.

An Optical Geometry Perspective on the Emerging Conformal Field Theory  Behavior on the Cosmological Event Horizon: Massless Fermions on de Sitter  Space