How an Effective “Cosmological Constant” May Affect a Minimum Scale Factor, to Avoid a Cosmological Singularity (Breakdown of the First Singularity Theorem)

Author(s)
Andrew Walcott Beckwith

ABSTRACT

We once again reference Theorem6.1.2of the book by Ellis, Maartens, and MacCallum in order to argue that if there
is a non zero initial scale factor, that there is a partial breakdown of the
Fundamental Singularity theorem which is due to the Raychaudhuri equation.
Afterwards, we review a construction of what could happen if we put in what
Ellis, Maartens, and MacCallum call the measured effective cosmological constant
and substitute Λ→Λ_{effective} in the Friedman equation. *i.e.* there are two ways to look at the problem, *i.e.* after Λ→Λ_{effective}, set Λ* _{Vac}* as equal to zero, and have the left over as scaled to
background cosmological temperature, as was postulated by Park (2002) or else
have Λ

Cite this paper

A. Beckwith, "How an Effective “Cosmological Constant” May Affect a Minimum Scale Factor, to Avoid a Cosmological Singularity (Breakdown of the First Singularity Theorem),"*Applied Mathematics*, Vol. 4 No. 7, 2013, pp. 1038-1042. doi: 10.4236/am.2013.47141.

A. Beckwith, "How an Effective “Cosmological Constant” May Affect a Minimum Scale Factor, to Avoid a Cosmological Singularity (Breakdown of the First Singularity Theorem),"

References

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[2] A. Beckwith, “How Massive Gravitons (and Gravitinos) May Affect and Modify the Fundamental Singularity Theorem (Irrotational Geodestic Singularities from the Raychaudhuri Equation).” http://vixra.org/abs/1304.0147

[3] G. Ellis, R. Maartens and M. A. H. MacCallum, “Relativistic Cosmology,” Cambridge University Press, Cambridge, 2012. doi:10.1017/CBO9781139014403

[4] E. Kolb and M. Turner, “The Early Universe,” Westview Press, 1994.

[5] D. K. Park, H. Kim and S. Tamarayan, “Nonvanishing Cosmological Constant of Flat Universe in Brane World Scenarios,” Physics Letters, Vol. B535, 2002, pp. 5-10. doi:10.1016/S0370-2693(02)01729-X

[6] R. Penrose, “Cycles of Time,” The Bodley Head, London, 2010.

[1] S. Kauffmann, “ A Self Gravitational Upper Bound on Localized Energy Including That of Virtual Particles and Quantum Fields, Which Yield a Passable Dark Energy Density Estimate.” http://arxiv.org/abs/1212.0426

[2] A. Beckwith, “How Massive Gravitons (and Gravitinos) May Affect and Modify the Fundamental Singularity Theorem (Irrotational Geodestic Singularities from the Raychaudhuri Equation).” http://vixra.org/abs/1304.0147

[3] G. Ellis, R. Maartens and M. A. H. MacCallum, “Relativistic Cosmology,” Cambridge University Press, Cambridge, 2012. doi:10.1017/CBO9781139014403

[4] E. Kolb and M. Turner, “The Early Universe,” Westview Press, 1994.

[5] D. K. Park, H. Kim and S. Tamarayan, “Nonvanishing Cosmological Constant of Flat Universe in Brane World Scenarios,” Physics Letters, Vol. B535, 2002, pp. 5-10. doi:10.1016/S0370-2693(02)01729-X

[6] R. Penrose, “Cycles of Time,” The Bodley Head, London, 2010.