Variation of Vacuum Energy if Scale Factor Becomes Infinitely Small, with Fixed Entropy Due to a Non Pathological Big Bang Singularity Accessible to Modified Einstein Equations

Andrew Beckwith

Department of Physics, Chongqing University, Chongqing, China.

DOI: 10.4236/jmp.2012.329171                

Abstract

When initial radius R_{initial 0 if Stoica actually derived Einstein equations in a formalism which remove the big bang singularity pathology, then the reason for Planck length no longer holds. The implications of Rinitial 0 are the first part of this manuscript. Then the resolution is alluded to by work from Muller and Lousto, as to implications of entanglement entropy. We present entanglement entropy in the early universe with a steadily shrinking scale factor, due to work from Muller and Lousto, and show that there are consequences due to initial entanged Sentropy=0.3rH²/a² for a time dependent horizon radius rH in cosmology, with for flat space conditions rH= for conformal time. In the case of a curved, but not flat space version of entropy, we look at vacuum energy as proportional to the inverse of scale factor squared times the inverse of initial entropy, effectively when there is no initial time in line with ~H²/G H≈a^-1. The consequences for this initial entropy being entangled are elaborated in this manuscript. No matter how small the length gets, Sentropy if it is entanglement entropy, will not go to zero. The requirement is that the smallest length of time, t, re scaled does not go to zero. Even if the length goes to zero. This preserves a minimum non zero vacuum energy, and in doing so keep the bits, for computational bits cosmological evolution even if Rinitial 0.}

Keywords

Fjortoft Theorem; Thermodynamic Potential; Matter Creation; Vacuum Energy Non Pathological Singularity Affecting Einstein Equations; Planck Length; Braneworlds

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	C. Stoica, “Beyond the FRWL Big Bang Singularity.” http://arxiv.org/pdf/1203.1819.pdf
[2]	A. W. Beckwith, “Is Quantum Mechanics Involved at the Start of Cosmological Evolution? Does a Machian Relationship between Gravitons and Gravitinos Answer This Question?” http://vixra.org/abs/1206.0023
[3]	J.-W. Lee, “On the Origin of Entropic Gravity and Inertia,” 2012. http://arxiv.org/abs/1003.4464; Foundations of physics,
[4]	R. Muller and A. C. Lousto, “Entanglement Entropy in Curved Space-Times with Event Horizons,” Vol. 1, 28 April, 1995. arXIV gr-qc/9504049
[5]	Y. J. Ng, “Spacetime Foam: From Entropy and Holography to Infinite Statistics and Nonlocality,” Entropy, Vol. 10, No. 4, 2008, pp. 441-461. doi:10.3390/e10040441 Y. J. Ng and H. van Dam, “Measuring the Foaminess of Space-Time with Gravity-Wave Interferometers,” Foundations of Physics, Vol. 30, No. 5, 2000, pp. 795-805. Y. J. Ng, “Quantum Foam and Dark Energy,” Conference International Work Shop on the Dark Side of the Universe. doi:10.1023/A:1003745212871
[6]	A. Mitra, “Why the Big Bang Model Cannot Describe the Observed Universe having Pressure and Radiation”, Journal of Modern Physics, Vol. 2, 2011, pp. 1436-1442.
[7]	G. E. Volovik, “Vacuum Energy: Myths and Realities,” arXIV: gr-qc/0604062 v2, April 16, 2006.
[8]	A. Beckwith, “How to Use the Cosmological Schwinger Principle for Energy Flux, Entropy, and ‘Atoms of Space-Time’ to Create a Thermodynamic Space-Time and Multiverse”, 5th International Workshop DICE2010: Space-Time-Matter—Current Issues in Quantum Mechanics and Beyond, Tuscany, 13-17 September 2010. http://iopscience.iop.org/1742-6596/306/1;jsessionid=A05372A78C18D970BF35F40A9A863B51.c2
[9]	M. Gryzinski, “Classical Theory of Electronic and Ionic Inelastic Collisions,” Physical Review, Vol. 115, No. 2, 1959, pp. 374-383
[10]	U. Bruchholz, “Derivation of Planck’s Constant from Maxwell’s Electrodynamics,” Progress in Physics, Vol. 4, 2009, p. 67. http://www.ptep-online.com/index_files/2009/PP-19-07.PDF
[11]	U. Bruzchholz, “Key Notes on a Geometric Theory of Fields,” Progress in Physics, Vol. 2, 2009, pp. 107-113.
[12]	A. Beckwith, “Octonionic Gravity Formation, Its Connections to Micro Physics,” Open Journal of Microphysics, Vol. 1 No. 1, 2011, pp. 13-18. doi:10.4236/ojm.2011.11002
[13]	J. Pringle and A. King, “Astrophysical Flows,” Cambridge University Press, New York, 2007. doi:10.1017/CBO9780511802201
[14]	T. Padmanabhan, “Lessons from Classical Gravity about the Quantum Structure of Space-Time,” Journal of Physics: Conference Series, Vol. 306, No. 1, Article ID: 012001. http://iopscience.iop.org/1742-6596/306/1/012001
[15]	J. Dickau, “Private Communication to the Author as to Minimum Space-Time ‘Length’,” 7 August 2012.
[16]	A. K. Avessian, “Plancks Constant Evolution as a Cosmological Evolution Test for the Early Universe”, Gravitation and Cosmology, Vol. 15, No. 1, 2009, pp. 10-12
[17]	R. Durrer, et al., “Dynamical Casmir Effect for Gravitons in Bouncing Braneworlds,” 2009. http://theory.physics.unige.ch/~durrer/papers/casimir.pdf;Earlier version http://www.scribd.com/doc/79001898/Ruth-Durrer-and-Macus-Ruser-The-dynamical-Casimir-effect-in-braneworlds ;Version put into PRD Marcus Ruser, Ruth Durrer, “Dynamical Casimir effect for gravitons in bouncing braneworlds”, http://arxiv.org/abs/0704.0790; Phys.Rev.D Vol. 76, 2007, Article ID: 104014,. doi:10.1103/PhysRevD.76.104014
[18]	S. Surya, “In Search of a Covariant Quantum Measure,” 2010. http://iopscience.iop.org/1742-6596/306/1/012018
[19]	A. W. Beckwith, “Identifying a Kaluza Klein Treatment of a Graviton Permitting a Deceleration Parameter Q (Z) as an Alternative to Standard DE,” Journal of Cosmology, Vol. 13, 2011. http://journalofcosmology.com/BeckwithGraviton.pdf