Abstract
We study effects of noncommutativity on the phase space generated by a non-minimal scalar field which is conformally coupled to the background curvature in an isotropic and homogeneous FRW cosmology. These effects are considered in two cases, when the potential of scalar field has zero and nonzero constant values. The investigation is carried out by means of a comparative detailed analysis of mathematical features of the evolution of universe and the most probable universe wave functions in classically commutative and noncommutative frames and quantum counterparts. The influence of noncommutativity is explored by the two noncommutative parameters of space and momentum sectors with a relative focus on the role of the noncommutative parameter of momentum sector. The solutions are presented with some of their numerical diagrams, in the commutative and noncommutative scenarios, and their properties are compared. We find that impose of noncommutativity in the momentum sector causes more ability in tuning time solutions of variables in classical level, and has more probable states of universe in quantum level. We also demonstrate that special solutions in classical and allowed wave functions in quantum models impose bounds on the values of noncommutative parameters.
Highlights
Scalar fields are an integral part of modern models in particle physics [1], and recently play very important roles in cosmology and have become a powerful tool to build cosmological models as well
Scalar fields present degrees of freedom and appear as dynamical variables of corresponding phase space, where this point can be regarded as relevance of noncommutativity in these models
We proceed to quantize the cosmological model given by the action (1) in the case of free potential, such that the canonical quantization of the phase space leads to the Wheeler–DeWitt (WD) equation, HΨ = 0, where His the Hamiltonian operator and Ψ is a wave function of universe
Summary
Scalar fields are an integral part of modern models in particle physics [1], and recently play very important roles in cosmology and have become a powerful tool to build cosmological models as well. Scalar fields present degrees of freedom and appear as dynamical variables of corresponding phase space, where this point can be regarded as relevance of noncommutativity in these models. A novel interest has been developed in considering the NC classical and quantum cosmology In these studies, the influence of noncommutativity has been explored by the formulation of a version of NC cosmology in which a deformation of minisuperspace [9]–[12] or, of phase space [13] is required instead of space–time deformation.
Sign-in/Register to view highlights & summary 
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call