Noncommutative Bianchi Type II Quantum Cosmology

Abstract

In this paper we present the noncommutative Bianchi Class A cosmological models coupled to barotropic perfect fluid. The commutative and noncommutative quantum solution to the Wheeler-DeWitt equation for any factor ordering, to the anisotropic Bianchi type II cosmological model are found, using a stiff fluid (γ = 1). In our toy model, we introduce noncommutative scale factors, is say, we consider that all minisuperspace variables q i does not commute, so the simplectic structure was modified.

Infrared Generalized Uncertainty Principles Applied To LRS Bianchi I Quantum Cosmology

“…The plots in figure (1) are for the three WDW equations ( 24), ( 23 Because multiple peaks are present it is possible that our quantum Bianchi I universe can tunnel between different geometric configurations. This plot is similar to those that were constructed while studying the non-commutative Wheeler Dewitt equation [26][27][28] where the variable related to the scale factor ranged from −∞ to ∞.…”

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…”

Accelerating cosmologies in an integrable model with noncommutative minisuperspace variables

“…Using the variables x, y, π x , and π y which satisfy commutative Poisson brackets (4.1), we can express the noncommutative Poisson algebra (4.10) [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]36]. Here, we develop more generic deformation of variables.…”

“…Since the seminal paper Ref. [3] appeared, many authors have studied noncommutative quantum cosmologies [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. 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.…”