Minisuperspace FLRW oscillator cosmological model and generalized uncertainty principle

Abstract

This paper deals with the effects of the generalized uncertainty principle on the one-dimensional minisuperspace FLRW cosmological model with a mixture of noninteracting dust and radiation. The model is presented in a classical and quantum case. In the classical case, the Lagrangian of the model is reduced by a suitable coordinate transformation to the Lagrangian of a linear harmonic oscillator. Within the standard quantum approach Wheeler–DeWitt equation and its general solution, i.e. a wave function of the model is written. The effects of the modified standard commutation relations on the dynamics of the model are considered in both of the approaches, classical and quantum.