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

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

*as proportional to Λ*

_{Vac}*～10*

_{Vac}^{38}GeV

^{2}which then would imply using what we call a 5-dimensional contribution to Λ as proportional to Λ≈Λ

_{5D}～-const/

*T*

^{}β. We find that both these models do not work for generating an initial singularity. Λ removal as a non zero cosmological constant is most easily dealt with by a Bianchi I universe version of the generalized Friedman equation. The Bianchi I universe case almost allows for use of Theorem 6.1.2. But this Bianchi 1 Universe model almost in fidelity with Theorem 6.1.2 requires a constant non zero shear for initial fluid flow at the start of inflation which we think is highly unlikely.

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*Applied Mathematics*, Vol. 4 No. 7, 2013, pp. 1038-1042. doi: 10.4236/am.2013.47141.

Conflicts of Interest

The authors declare no conflicts of interest.

[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. |

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