Effects of GUP in Quantum Cosmological Perfect Fluid Models

TL;DR

This paper investigates how a new form of the Generalized Uncertainty Principle affects quantum cosmological models with perfect fluids, revealing non-unitary evolution due to non-Hermitian Hamiltonians.

Contribution

It introduces the impact of a linear-term GUP on quantum cosmology, highlighting the resulting non-Hermitian Hamiltonian and non-unitary wave packet evolution.

Findings

Wave packets become non-unitary over time.

Presence of linear GUP term leads to non-Hermitian Hamiltonian.

Model exhibits time-dependent wave packet norms.

Abstract

Very recently authors in [5] proposed a new Generalized Uncertainty Principle (or GUP) with a linear term in Plank length. In this Letter the effect of this GUP is studied in quantum cosmological models with dust and cosmic string as the perfect fluid. For the quantum mechanical description it is possible to find the wave packet which resulted from the superposition of the stationary wave functions of the Wheeler-deWitt equation. However the norm of the wave packets turned out to be time dependent and hence the model became non-unitary. The loss of unitarity is due to the fact that the presence of the linear term in Plank length in the Generalized Uncertainty Principle made the Hamiltonian non-Hermitian.