  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.

General Relativity and Quantum Cosmology;High Energy Physics - Theory