Modified Brans-Dicke cosmology with Minimum Length Uncertainty

TL;DR

This paper explores a modified Brans-Dicke cosmology incorporating a minimum length uncertainty via the Generalized Uncertainty Principle, analyzing its impact on cosmological evolution compared to the standard theory.

Contribution

It introduces a novel modification to the Brans-Dicke theory inspired by GUP, studying its effects on cosmological dynamics and history.

Findings

Modified scalar field equations due to GUP influence.

Additional degrees of freedom affect cosmological evolution.

Comparison shows differences from standard Brans-Dicke theory.

Abstract

We consider a modification of the Brans-Dicke gravitational Action Integral inspired by the existence of a minimum length uncertainty for the scalar field. In particular, the kinetic part of the Brans-Dicke scalar field is modified such that the equation of motion for the scalar field be modified according to the quadratic Generalized Uncertainty Principle (GUP). For the background geometry, we assume the homogeneous and isotropic Friedmann--Lema\^{\i}tre--Robertson--Walker metric. We investigate the dynamics and the cosmological evolution for the dynamical variables of the theory and we compare the results with the unmodified Brans-Dicke theory. It follows that in consideration because of the additional degrees of freedom in the energy-momentum tensor the dynamical variables describe various aspects of the cosmological history. This is one of the first studies on the effects of GUP in a Machian gravitational theory.