Another Two Dark Energy Models Motivated from Karolyhazy Uncertainty Relation

TL;DR

This paper introduces two novel dark energy models inspired by the Karolyhazy uncertainty relation, linking quantum spacetime fluctuations to cosmic acceleration, and shows they behave like a cosmological constant at late times.

Contribution

The paper proposes two new dark energy models based on quantum spacetime fluctuations derived from the Karolyhazy relation, motivated by minimal detectable cells and energy density considerations.

Findings

Dark energy models mimic a cosmological constant at late times

Models are characterized by the universe's age and conformal age

Quantum spacetime fluctuations can drive cosmic acceleration

Abstract

The K$\acute{\text{a}}$rolyh$\acute{\text{a}}$zy uncertainty relation indicates that there exists the minimal detectable cell $\delta t^{3}$ over the region $t^3$ in Minkowski spacetime. Due to the energy-time uncertainty relation, the energy of the cell $\delta t^3$ can not be less $\delta t^{-1}$. Then we get a new energy density of metric fluctuations of Minkowski spacetime as $\delta t^{-4}$. Motivated by the energy density, we propose two new dark energy models. One model is characterized by the age of the universe and the other is characterized by the conformal age of the universe. We find that in the two models, the dark energy mimics a cosmological constant in the late time.