## The Bekenstein Quantum Particle Horizon Approach to Avoid the Cosmological Singularity

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The cosmological singularity of infinite density, temperature, and spacetime curvature is the classical limit of Friedmann's general relativity models extrapolated to the origin of the standard model of cosmology. Jacob Bekenstein questions whether the singularity is thermodynamically possible in a 1989 paper in which he outlines four approaches to eliminate the singularity from cosmology. He concludes that none of these is satisfactory, and then reexamines the particle horizon in the early radiation-dominated universe suggesting it holds the key as a feasible alternative to the classical inevitability of the singularity. This minimum-radius particle horizon determined from Bekenstein's entropy bound, and necessarily quantum in nature precludes the singularity just as quantum mechanics provided the solution for singularities in atomic transitions as r → 0. An initial cosmological radius of zero may never be attained quantum mechanically, avoiding the spacetime singularity, and supporting Bekenstein's argument that Friedmann models cannot be extrapolated to the very beginning of the universe but only to a boundary which is 'something like a particle horizon'. The universe may have begun in the bright flash and quantum flux of radiation and particles at a minimum, irreducible quantum particle horizon rather than at the classical mathematical limit and unrealizable state of an infinite singularity.