Noncommutativity in Effective Loop Quantum Cosmology

Abstract

We construct a noncommutative extension of the Loop Quantum Cosmology effective scheme for the open FLRW model with a free scalar field via a theta deformation. Firstly, a deformation is implemented in the configuration sector, among the holonomy variable and the matter degree of freedom. We show that this type of noncommutativity retain, to some degree, key features of the Loop Quantum Cosmology paradigm for a free field. Secondly, a deformation is implemented in the momentum sector, among the momentum associated to the holonomy variable and the momentum associated to the matter field. We show that the density, as in the case of Loop Quantum Cosmology is also bounded, furthermore, its maximum value is the same.

Noncommutative Friedmann Equations in Effective LQC

“…These conclusions were also reached in Ref. 24, but different arguments were given. Finally, we argue that an effective (scalar field) potential is induced due to the presence of noncommutativity, giving rise to an accelerated universe; a compelling reason to investigate a possible inflationary era.…”

“…In the present work, we extend and apply the construction made in Ref. 24, and derive a noncommutative version of the Friedmann equations for each sector of phase space. Analytical solutions of the noncommutative equations of motion (EOM) in the momentum sector are obtained (this could not be achieved in Ref.…”

“…This line of thought led to some of the authors of the present investigation to propose a simple noncommutative framework of the effective LQC for the flat FRW model with a free scalar field. 24 The main conclusion was that a canonical noncommutativity in the momentum sector is more compatible with LQC than its configuration sector counterpart, in the sense that key features of LQC are better retained when noncommutativity is introduced among the momentum variables (e.g., the bounce and the energy density profile).…”

“…Analytical solutions of the noncommutative equations of motion (EOM) in the momentum sector are obtained (this could not be achieved in Ref. 24). It is found that the volume of the flat FRW universe preserves the bounce, and that after the bounce it has a slower growth than its commutative counterpart.…”

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…”