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Beckwith, A. How a Minimum Time Step Leads to a Causal Structure Used to Form Initial Entropy Production and High Frequency Gravitons, with 7 Subsequent Open Questions. http://vixra.org/abs/1703.0166

has been cited by the following article:

• TITLE: Isolating a Minimum Radius of the Universe Consistent with the Production of at Least 1 Unit of Entropy, at the Start of Inflation

  AUTHORS: Andrew Walcott Beckwith

  KEYWORDS: Causal Barrier, Inflaton, Mininum Entropy (Non Zero), Initial Radii (of Universe)

  JOURNAL NAME: Journal of High Energy Physics, Gravitation and Cosmology, Vol.3 No.3, July 28, 2017

  ABSTRACT: We begin by examining a general expression of entropy, and its links to a minimum radius of the universe. We derive an expression for the production of at least 1 unit of entropy, which translates to a value of Planck length in radii to 1000 times Planck radii, for the quantum bubble of space-time which depends upon, of all things, the initial Hubble expansion rate value. If the Hubble parameter has the value of 10^19 GeV, we see a minimum radial length of the Universe of about 1 billion times Planck length. If the Hubble parameter is of 10^19 GeV, the minimum radial length of the universe would be about one Planck length, which is surprising to put it mildly. The higher the initial temperate is, up to a point, the more likely the initial entropy is closer to the Causal barrier mentioned in an earlier publication by the author.