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 Theorem 6.1.2 of 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 Effective  in the Friedman equation. i.e. there are two ways to look at the problem, i.e. after Effective  , set 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  Vac  as proportional to which then would imply using what we call a 5-dimensional contribution to 38 2 ~ 10 GeV Vac   as proportional to 5 ~ cons D t T      . We find that both these models do not work for generating an initial singularity. 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. 