Abstract
In a wide class of cosmological models, a positive cosmological constant drives cosmological evolution toward an asymptotically de Sitter phase. Here we connect this behavior to the increase of entropy over time, based on the idea that de Sitter spacetime is a maximum-entropy state. We prove a cosmic no-hair theorem for Robertson-Walker and Bianchi I spacetimes that admit a Q-screen ("quantum" holographic screen) with certain entropic properties: If generalized entropy, in the sense of the cosmological version of the Generalized Second Law conjectured by Bousso and Engelhardt, increases up to a finite maximum value along the screen, then the spacetime is asymptotically de Sitter in the future. Moreover, the limiting value of generalized entropy coincides with the de Sitter horizon entropy. We do not use the Einstein field equations in our proof, nor do we assume the existence of a positive cosmological constant. As such, asymptotic relaxation to a de Sitter phase can, in a precise sense, be thought of as cosmological equilibration.
Highlights
Like black holes, universes have no hair, at least if they have a positive cosmological constant Λ [1,2,3,4,5,6,7,8,9,10]
Assuming the generalized second law (GSL), we show that if a Bianchi I spacetime admits a Q-screen along which generalized entropy monotonically increases up to a finite maximum, the anisotropy necessarily decays and the scale factor approaches de Sitter behavior asymptotically in the future
In a RW spacetime, we demonstrated that the existence of a Q-screen along which entropy monotonically increases to a finite maximum implies that the scale factor tends to the de Sitter scale factor far in the future
Summary
Universes have no hair, at least if they have a positive cosmological constant Λ [1,2,3,4,5,6,7,8,9,10]. In this paper we try to make one aspect of these ideas rigorous, showing that a cosmic no-hair theorem can be derived even without direct reference to Einstein’s equation, by invoking an appropriate formulation of the second law This strategy of deducing properties of spacetime from the behavior of entropy is reminiscent of the thermodynamic and entropic gravity programs [32,33,34,35,36], as well as of the gravity-entanglement connection [37,38,39,40,41,42,43,44]. Assuming the GSL, we show that if a Bianchi I spacetime admits a Q-screen along which generalized entropy monotonically increases up to a finite maximum, the anisotropy necessarily decays and the scale factor approaches de Sitter behavior asymptotically in the future.
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