TITLE:
How an Effective “Cosmological Constant” May Affect a Minimum Scale Factor, to Avoid a Cosmological Singularity (Breakdown of the First Singularity Theorem)
AUTHORS:
Andrew Walcott Beckwith
KEYWORDS:
Raychaudhuri Equation; Fundamental Singularity Theorem; Bianchi I Universe; Effective Cosmological Parameter
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.7,
July
11,
2013
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→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 ΛVac～1038GeV2 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.