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

DOI: 10.4236/am.2013.47141   PDF   HTML   XML   2,427 Downloads   3,683 Views  


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→Λeffective in the Friedman equation. i.e. there are two ways to look at the problem, i.e. after Λ→Λeffective, set ΛVac as equal to zero, and have the left over as scaled to background cosmological temperature, as was postulated by Park (2002) or else have ΛVac as proportional to ΛVac1038GeV2 which then would imply using what we call a 5-dimensional contribution to Λ as proportional to Λ≈Λ5D-const/Tβ. 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.

Share and Cite:

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.

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

comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.