What is Noncommutative Dark Energy? New paper explains as "A Wheeler–DeWitt Non-Commutative Quantum Approach to the Branch-Cut Gravity"

 https://www.mdpi.com/2218-1997/9/10/428

A Wheeler–DeWitt Non-Commutative Quantum Approach to the Branch-Cut Gravity

we propose a phase-space transformation that generates a super-Hamiltonian, expressed in terms of new variables, which describes the behavior of a Wheeler–DeWitt wave function of the Universe within a non-commutative algebraic quantum gravity formulation. ...Our results indicate the acceleration of the early Universe in the context of the non-commutative branch-cut gravity formulation. These results have implications when confronted with information theory; so to accommodate gravitational effects close to the Planck scale, a formulation à la Heisenberg’s Generalized Uncertainty Principle in Quantum Mechanics involving the energy and entropy of the primordial Universe is proposed.

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 The Bekenstein bound states that the entropy of a given region of space-time—where gravity is so strong that nothing, including light or other electromagnetic waves, has enough energy to escape it—is proportional to the number of Planck areas that would be needed to cover the corresponding event horizon. In this sense, there is perfect harmony between the Planck dimensions and the dimensions of the event horizon. In this domain, translating this view to the corresponding BCG [branch-cut gravitation]predictions [7], which indicates a significantly larger range of the branched cosmic scale factor in comparison to the Planck dimensions, this range can be interpreted as quantifying the number of Planck areas that would be necessary to cover the primordial singularity, thus reconciling the BCG predictions with the micro-structure of (quantum) space-time.

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 This conception of information theory reinforces the idea that the entropy at the beginning of the Universe is close to zero and cannot be null since, according to the Bekenstein criterion, it would be impossible for singularities to occur, from a thermodynamic point of view. Recalling that the Bekenstein criterion imposes that the initial state of the Universe is unique, therefore, in a probabilistic conception, the primordial state of the Universe would fit the case of minimum entropy as theorized in the theory of information. In the process of the formation of a black hole, the catalyzed conversion of a pure quantum state to a mixed state occurs, in contradiction with the principle of unitary quantum evolution, thus causing loss of information. To reach a value close to zero, the thermodynamic entropy decreases in the contraction phase, consequently increasing in the expansion phase. This realization has led to the “information paradox”, a topic that has been the scene of fierce conceptual disputes.

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