Bianchi type I cyclic cosmology from Lie-algebraically deformed phase space

TL;DR

This paper explores how Lie-algebraically deformed phase space affects Bianchi type I cosmology, revealing conditions for cyclic universe solutions with endless contractions and re-expansions, both analytically and numerically.

Contribution

It introduces two types of noncommutative phase space structures and demonstrates their impact on cyclic cosmological models, extending classical solutions with new noncommutative effects.

Findings

Exact solutions for commutative and noncommutative cases are provided.

Cyclic behavior of the universe is possible in deformed phase space models.

Numerical solutions confirm repeated cyclic behavior in type II noncommutative structure.

Abstract

We study the effects of noncommutativity, in the form of a Lie-algebraically deformed Poisson commutation relations, on the evolution of a Bianchi type I cosmological model with a positive cosmological constant. The phase space variables turn out to correspond to the scale factors of this model in $x$, $y$ and $z$ directions. According to the conditions that the structure constants (deformation parameters) should satisfy, we argue that there are two types of noncommutative phase space with Lie-algebraic structure. The exact classical solutions in commutative and type I noncommutative cases are presented. In the framework of this type of deformed phase space, we investigate the possibility of building a Bianchi I model with cyclic scale factors in which the size of the universe in each direction experiences an endless sequence of contractions and re-expansions. We also obtain some approximate solutions for the type II noncommutative structure by numerical methods and show that the cyclic behavior is repeated as well. These results are compared with the standard commutative case, and similarities and differences of these solutions are discussed.