Noncommutativity, Gravity and Cosmology

Dear Colleagues,

Noncommutativity is a long-standing subject in mathematics and physics. The proposal of noncommutativity in spacetime was first put forward by Snyder. 

In addition, noncommutative field theory has also been established. Substantially further motivations for investigating the noncommutative proposals have arisen due to the advances in string and M-theory and interesting predictions made in particle physics such as predictions about the IR/UV mixing, non-locality, Lorentz violation and new physics at very short distance scales. 

Several noncommutative gravitational scenarios have been inspired by noncommutative field theory. Noncommutative cosmology is also an application of noncommutativity between fields. More specifically, noncommutative deformations modify the noncommutative fields, and the effects of non-commutative gravity could be determined by applying mini-superspace variables. 

Such procedures have been constructed by employing the Moyal product of functions in the Wheeler–DeWitt equation as well as the semiclassical approximation of quantum gravity. In addition, classical noncommutative models have been studied by modifying the Poisson brackets.

Noncommutative cosmological models have been employed to describe various aspects of the universe, such as inflation, dark energy and dark matter. As already mentioned, UV/IR mixing is one of the features of noncommutative field theories, by which short scales are effectively mixed with long scales. Therefore, the noncommutative effects could be seen in the current time of the Universe due to the presence of noncommutativity effects at small scale. In analogy to the usual quantum mechanics, the noncommutativity effects are usually related to a minimal size by a generalized uncertainty principle.

Any review and further developments of the noncommutative proposals mentioned above that are relevant to gravity and cosmology are the focus of this special issue and are welcome.

Dr. Seyed Meraj Mousavi Rasouli
Prof. Dr. Paulo Vargas Moniz
Guest Editors

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• noncommutative gravity/cosmology
• noncommutative geometry
• noncommutative quantum mechanics
• Wheeler-DeWitt equation
• Moyal product
• semiclassical approximation of quantum gravity
• noncommutative classical Poisson algebra
• noncommutative minisuperspaces
• minimal length