Classical formulation of the cosmological horizon and the weak equivalence principle

Abstract

We derive the classical equations of motion from the quantum formulation of the extended uncertainty principle. We show that a generalized deformation function due to the cosmological horizon poses a violation to the weak formulation of the equivalence principle. We then construct a second order nonlinear differential equation used to solve the set of modified autonomous differential equations representing the dynamical variables. With this, a modification to the position-time evolution of a free-fall particle in a uniform gravitational field has been discussed.