Infrared Generalized Uncertainty Principles Applied To LRS Bianchi I Quantum Cosmology

TL;DR

This paper introduces higher order generalized uncertainty principles in quantum cosmology, exploring their effects on LRS Bianchi I models and suggesting potential quantum gravity influences on the universe's geometry and horizon.

Contribution

It proposes new GUPs with minimum momentum and maximum length scales, applying them to quantum cosmology and analyzing their impact on the Wheeler-DeWitt equation solutions.

Findings

Potential IR quantum gravity effects influence universe geometry

GUPs predict minimum momentum and maximal length scales

Quantum effects may select likely cosmological configurations

Abstract

We propose two higher order generalized uncertainty principles(GUPs) which predict a minimum uncertainty in momentum and apply the deformations that they entail of the Heisenberg algebra to one half of the phase space of the LRS Bianchi I models. After numerically solving the resultant Wheeler Dewitt equations we analyze our solutions and provide evidence that potential IR effects of quantum gravity could have played a role in selecting an overwhelmingly likely geometrical configuration that a quantum universe can possess. In addition we propose a GUP which predicts both a minimum uncertainty in momentum and a maximal measurable length scale which can be interpreted as a fixed maximum cosmological horizon. The results contained in this work provide further incentives to study what effects higher order GUP(s) have on quantum cosmology so we can obtain a better understanding of how quantum gravity could have impacted cosmological evolution.