Year-end Sale % OFF 
Abstract
The cosmological singularity of infinite density, temperature, and spacetime curvature is the classical limit of Friedmann’s general relativity solutions extrapolated to the origin of the standard model of cosmology. Jacob Bekenstein suggests that thermodynamics excludes the possibility of such a singularity in a 1989 paper. We propose a re-examination of his particle horizon approach in the early radiation-dominated universe and verify it as a feasible alternative to the classical inevitability of the singularity. We argue that this minimum-radius particle horizon determined from Bekenstein’s entropy bound, necessarily quantum in nature as a quantum particle horizon (QPH), precludes the singularity, just as quantum mechanics provided the solution for singularities in atomic transitions as radius . An initial radius of zero can never be attained quantum mechanically. This avoids the spacetime singularity, supporting Bekenstein’s assertion that Friedmann models cannot be extrapolated to the very beginning of the universe but only to a boundary that is ‘something like a particle horizon’. The universe may have begun in a 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.
Highlights
In a 1989, paper Jacob Bekenstein questions whether the cosmological singularity is thermodynamically possible [1]
Bekenstein understood that thermodynamics and his entropy bound as in Equation (1) below [2] might provide insight into the nature of the singularity, stating “Thermodynamics has often been used in such dilemmas, and it is proposed to answer the question of whether there was a Friedmann-like singularity in the universe by exploiting the bound on specific entropy that has been established for a finite system” [1]
We suggest that the reference to Planck scale units here takes us naturally to the Planck era of cosmology, where the area of the particle horizon approaches the Planck area as APH → l2P
Summary
In a 1989, paper Jacob Bekenstein questions whether the cosmological singularity is thermodynamically possible [1]. For a cosmology like the Friedmann models, which are spatially homogeneous and spherically symmetric around each point, this is the 2 − D intersection of the past (3 − D) light cone with cosmic time t = 0. Using an idealized Friedmann cosmological model with effectively massless radiation as its matter source, Bekenstein postulates the metric surface area of the particle horizon to define the quantity R in his limit 2πR/(}c) ≥ S/E. In Friedmann cosmology, the apparent horizon coordinates radius r0 → 0 as t0 → 0 , and in singularity theorems [8]; this analysis shows that there is a time t0 before which the universe could not have been Friedmann-like. A particle horizon-like surface at time ~tP is a boundary where, beyond this minimum radius, the Friedmann universe is undefined and not observable. Cosmological horizon; and, lastly, summarize the feasibility of the initial quantum particle horizon
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
