The Generalized Uncertainty Principle and the Friedmann equations

TL;DR

This paper explores how a generalized uncertainty principle modifies the Friedmann equations and entropy-area relation at Planck scales, revealing new correction terms that could impact early universe cosmology.

Contribution

The paper generalizes the GUP with a linear term and studies its effects on Friedmann equations and entropy corrections in the FRW universe.

Findings

Modified Friedmann equations with GUP effects

New correction terms in entropy-area relation

Leading correction proportional to square root of area

Abstract

The Generalized Uncertainty Principle (or GUP) affects the dynamics in Plank scale. So the known equations of physics are expected to get modified at that very high energy regime. Very recently authors in (Ali et al. 2009) proposed a new Generalized Uncertainty Principle (or GUP) with a linear term in Plank length. In this article, the proposed GUP is expressed in a more general form and the effect is studied for the modification of the Friedmann equations of the FRW universe. In the midway the known entropy-area relation get some new correction terms, the leading order term being proportional to square root of area.