Generalized uncertainty principle in Bianchi type I quantum cosmology

TL;DR

This paper investigates a quantum Bianchi type I cosmological model incorporating a generalized uncertainty principle derived from quantum gravity, providing approximate solutions and comparing them with standard quantum cosmology.

Contribution

It introduces a generalized Heisenberg algebra into quantum cosmology and analyzes its effects on the Wheeler-DeWitt equation solutions.

Findings

Approximate analytical solutions for small universe scale factor

Differences between generalized, standard, and noncommutative quantum cosmology

Insights into minimal length effects in early universe models

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.