Dilaton Cosmology, Noncommutativity and Generalized Uncertainty Principle

TL;DR

This paper explores how noncommutativity and a minimal length, modeled by the Generalized Uncertainty Principle, influence classical and quantum cosmological solutions in a dilaton model, revealing new insights into early universe physics.

Contribution

It extends the deformed Heisenberg algebra to a deformed Poisson algebra and provides exact solutions for classical and quantum cases under noncommutativity and GUP.

Findings

Exact classical and quantum solutions for exponential dilaton potential

Comparison between commutative, noncommutative, and GUP cases

Approximate solutions under GUP with insights into minimal length effects

Abstract

The effects of noncommutativity and of the existence of a minimal length on the phase space of a dilatonic cosmological model are investigated. The existence of a minimum length, results in the Generalized Uncertainty Principle (GUP), which is a deformed Heisenberg algebra between the minisuperspace variables and their momenta operators. We extend these deformed commutating relations to the corresponding deformed Poisson algebra. For an exponential dilaton potential, the exact classical and quantum solutions in the commutative and noncommutative cases, and some approximate analytical solutions in the case of GUP, are presented and compared.