Generalized uncertainty principle in Bianchi type I quantum cosmology

Abstract

We study a quantum Bianchi type I model in which the dynamical variables of the corresponding minisuperspace obey the generalized Heisenberg algebra. Such a generalized uncertainty principle has its origin in the existence of a minimal length suggested by quantum gravity and sting theory. We present approximate analytical solutions to the corresponding Wheeler-DeWitt equation in the limit where the scale factor of the universe is small and compare the results with the standard commutative and noncommutative quantum cosmology. Similarities and differences of these solutions are also discussed.

A cosmological viewpoint on the correspondence between deformed phase-space and canonical quantization

“…For example, if in a model field theory the fields are taken as noncommutative, as has been done in [35,36], the resulting effective theory predicts the same Lorentz violation as a field theory in which the coordinates are considered as noncommutative [37][38][39]. As a further example, it is well known that string theory can be used to suggest a modification to the bracket structure of coordinates, also known as GUP [34] which is used to modify the phase-space structure [40][41][42][43][44][45]. Over the years, a large number of works on noncommutative fields [25][26][27][28][29] have been inspired by noncommutative geometry model theories [31][32][33].…”

“…(1). Here we will examine a new kind of modification in the phase-space structure inspired by relation (1), much the same as has been done in [25][26][27][28][29][40][41][42][43][44][45]59]. In what follows we introduce noncommutativity based on κ-Minkowskian space and study its consequences on the de Sitter and dusty FRW cosmologies.…”

A fundamental length as a candidate for dark energy: A DSR inspired FRW spacetime

“…In this paper we will examine a new kind of modification in the phase-space structure inspired by relation (1), much the same as what has been done in [16,20,22]. In what follows we introduce noncommutativity based on κ-Minkowskian space and study its consequences on the solutions discussed in the previous section.…”

“…One of these approaches is to modify or deform the algebraic structure of the phase-space. Such deformations may be done in various manners, a few example of which can be found in [16,17,18,19,20,21,22].…”

“…Over the years, a large number of works on noncommutative fields [16,17,18,19] have been inspired by noncommutative geometry model theories [10,11,12]. As a further example, it is well known that string theory can be used to suggest a modification in the bracket structure of coordinates, also known as GUP [32] which is used to modify the phase-space structure [20].…”