Abstract
In the action formalism variations of metric tensors usually are limited by the Hubble horizon. On the contrary, variations of quantum fields should be extended up to the event horizon, which is the real boundary of the spacetime. As a result the entanglement energy of quantum particles across the apparent horizon is missed in the cosmological equations written for the Hubble volume. We identify this missing boundary term with the dark energy density and express it (using the zero energy assumption for the finite universe) as the critical density multiplied by the ratio of the Hubble and event horizons radii.
Highlights
Since in General Relativity horizons are unavoidable and horizons block information, entropy and temperature can be introduced for spacetime
Many authors consider so-called emergent theories in which gravity is not a fundamental field, but like thermodynamics or hydrodynamics is defined for the matter in bulk [1,2,3,4,5,6,7]. One such approach is the thermodynamic model of gravity [3,4,5,6,7,8,9,10,11,12,13,14,15], where spacetime emerges from the properties of the “universal” ensemble of quantum particles
The relation of the classical action of a physical system to the thermodynamic entropy translates the condition of entropy neutrality into the zero action principle: the sum of all components of the action for a physical system is zero
Summary
Since in General Relativity horizons are unavoidable and horizons block information, entropy and temperature can be introduced for spacetime. One such approach is the thermodynamic model of gravity [3,4,5,6,7,8,9,10,11,12,13,14,15], where spacetime emerges from the properties of the “universal” ensemble of quantum particles. I.e., the total density of all the forms of energy in the universe, ρU, at any moment of time should be zero.
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