Scalar field cosmology modified by the Generalized Uncertainty Principle

TL;DR

This paper explores how the Generalized Uncertainty Principle modifies scalar field cosmology, leading to a model where the equation of state parameter can cross the phantom divide, supported by analytical and numerical analysis.

Contribution

It introduces a modified scalar field cosmology incorporating GUP effects, revealing a new interaction between scalar fields and the possibility of crossing the phantom divide.

Findings

The GUP-modified equation of state parameter can cross w = -1.

Numerical simulations confirm phantom crossing for specific initial conditions.

The model's dynamics are analyzed through a singular perturbation system.

Abstract

We consider quintessence scalar field cosmology in which the Lagrangian of the scalar field is modified by the Generalized Uncertainty Principle. We show that the perturbation terms which arise from the deformed algebra are equivalent with the existence of a second scalar field, where the two fields interact in the kinetic part. Moreover, we consider a spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker spacetime (FLRW), and we derive the gravitational field equations. We show that the modified equation of state parameter $w_{GUP}$ can cross the phantom divide line; that is $w_{GUP}<-1$. Furthermore, we derive the field equations in the dimensionless parameters, the dynamical system which arises is a singular perturbation system in which we study the existence of the fixed points in the slow manifold. Finally, we perform numerical simulations for some well known models and we show that for these models with the specific initial conditions, the parameter $w_{GUP}$ crosses the phantom barrier.