Abstract
We study classical and quantum noncommutative cosmology with a Liouville-type scalar degree of freedom. The noncommutativity is imposed on the minisuperspace variables through a deformation of the Poisson algebra. In this paper, we investigate the effects of noncommutativity of minisuperspace variables on the accelerating behavior of the cosmic scale factor. The probability distribution in noncommutative quantum cosmology is also studied and we propose a novel candidate for interpretation of the probability distribution in terms of noncommutative arguments.
Highlights
INTRODUCTIONIn the noncommutative quantum cosmological scenario, the authors considered deformation of the minisuperspace variables instead of deformation of the spacetime algebra, which is a hard task to treat neatly
Almost two decades ago, the noncommutativity of the spacetime coordinates, such as [xμ, xν] = iθμν, (1.1)has been introduced into the study of quantum field theory [1, 2]
The noncommutative variable can be obtained from the linear combination of phase space variables, say, x and py in the two dimensional commutative system. We propose another candidate of probability distribution by using the Wigner function [34, 35] and examine its validity by analysis with our soluble model
Summary
In the noncommutative quantum cosmological scenario, the authors considered deformation of the minisuperspace variables instead of deformation of the spacetime algebra, which is a hard task to treat neatly. We study classical and quantum noncommutative cosmology with a Liouville-type scalar degree of freedom. We investigate the effects of noncommutativity in minisuperspace variables on the accelerating behavior of the cosmic scale factor in exact analytical solutions of the model.
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