Minimal length, Friedmann equations and maximum density
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Inspired by Jacobson’s thermodynamic approach , Cai et al. [5, 6] have shown the emergence of Friedmann equations from the first law of thermodynamics. We extend Akbar-Cai derivation  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.
KeywordsSpacetime Singularities Cosmology of Theories beyond the SM Models of Quantum Gravity
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- S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
- E.M. Lifshitz, L.P. Pitaevskii and V.B. Berestetskii, Landau-Lifshitz Course of Theoretical Physics, Volume 4: Quantum Electrodynamics, Reed Educational and Professional Publishing (1982).Google Scholar
- S.H. Strogatz, Nonlinear Dynamics and Chaos, Preseus Books (1994).Google Scholar
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