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

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 Vac as proportional to Λ Vac ～ 10 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.