Minimal length, Friedmann equations and maximum density

  • Adel Awad
  • Ahmed Farag AliEmail author
Open Access


Inspired by Jacobson’s thermodynamic approach [4], Cai et al. [5, 6] have shown the emergence of Friedmann equations from the first law of thermodynamics. We extend Akbar-Cai derivation [6] of Friedmann equations to accommodate a general entrop-yarea law. Studying the resulted Friedmann equations using a specific entropy-area law, which is motivated by the generalized uncertainty principle (GUP), reveals the existence of a maximum energy density closed to Planck density. Allowing for a general continuous pressure p(ρ, a) leads to bounded curvature invariants and a general nonsingular evolution. In this case, the maximum energy density is reached in a finite time and there is no cosmological evolution beyond this point which leaves the big bang singularity inaccessible from a spacetime prospective. The existence of maximum energy density and a general nonsingular evolution is independent of the equation of state and the spacial curvature k. As an example we study the evolution of the equation of state p = ωρ through its phase-space diagram to show the existence of a maximum energy which is reachable in a finite time.


Spacetime Singularities Cosmology of Theories beyond the SM Models of Quantum Gravity 


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This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Authors and Affiliations

  1. 1.Center for Theoretical PhysicsBritish University of EgyptSherouk CityEgypt
  2. 2.Centre for Fundamental PhysicsZewail City of Science and TechnologyGizaEgypt
  3. 3.Department of Physics, Faculty of ScienceAin Shams UniversityCairoEgypt
  4. 4.Department of Physics, Faculty of ScienceBenha UniversityBenhaEgypt

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