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The $S$-matrix formulation indicates that a consistent embedding of de Sitterstate in quantum gravity is possible exclusively as an excited quantum stateconstructed on top of a valid $S$-matrix vacuum such as Minkowski. In thepresent paper we offer such a construction of de Sitter in the form of acoherent state of gravitons. Unlike previous realizations of this idea, wefocus on BRST invariance as the guiding principle for physicality. In order toestablish the universal rules of gauge consistency, we study the BRST-invariantconstruction of coherent states created by classical and quantum sources in QEDand in linearized gravity. Introduction of $N$ copies of scalar matter coupledto gravity allows us to take a special double scaling limit, a so-calledspecies limit, in which our construction of de Sitter becomes exact. In thislimit, the irrelevant quantum gravitational effects vanish whereas thecollective phenomena, such as Gibbons-Hawking radiation, are calculable.

De Sitter space as BRST invariant coherent state of gravitons