Noncommutativity in quantum cosmology and the hierarchy problem

Abstract

We study the quantum cosmology of an empty (4+1)-dimensional Kaluza-Klein cosmology with a negative cosmological constant and a FRW type metric with two scale factors, one for 4-D universe and the other for one compact extra dimension. By assuming the noncommutativity in the corresponding mini-superspace we suggest a solution for the Hierarchy problem, at the level of Wheeler-DeWitt equation. PACS: 98.80.Qc

Noncommutativity, Generalized Uncertainty Principle and FRW Cosmology

“…In other words if we assume M EW to be the natural cutoff in the original commutative model, the Planck mass is a cutoff in the noncommutative model. A similar discussion can be found for a classical cosmological model in [12] and at the quantum level in [22].…”

“…Hence, the above equation can be interpreted as a redefinition of the cutoff in the theory due the presence of noncommutativity. In this regard, according to [35] we take…”

Dilaton cosmology, noncommutativity, and generalized uncertainty principle

“…For example, an investigation of the cosmological constant problem can be found in [26]. In [27] the same problem is carried over to the Kaluza-Klein cosmology. The problem of compactification and stabilization of the extra dimensions in multidimensional cosmology may also be addressed using noncommutative ideas in [28].…”

Topics in Supersymmetric and Noncommutative Quantum Cosmology

“…Further development (without pretending to be exhaustive) on this subject can be found in Refs. [54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71]. In Misner's parametrization the metric is written as…”