(untitled) (JOURNAL OF ADVANCES IN MATHEMATICS, 2013)
What happens to the topological entanglement entropy of a system, when it is driven out of its ground state by increasing the temperature? This question is basic, especially if there is an increasing amount of temperature up to the interval of Planck time, in early universe cosmology. The author examines what is possible if a cyclic model is arranged via Penrose cyclic cosmology, which may enable entanglement entropy as a way to transfer essential information from a prior to the present universe. We 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 ïŒ ï‚® ïŒ in the Friedman equation. I.e. there are two ways to look at the problem, i.e. after Effective ïŒ ï‚® ïŒ , set Vac ïŒ as equal to zero, and have the left over ïŒ as scaled to background cosmological temperature, as was postulated by Park (2002) or else have Vac ïŒ as proportional to ïŒVac 1038GeV2which then would imply using what we call a 5 dimensional contribution to ïŒ as proportional to 5 const/ T D ï¢ ïŒ ï‚» ïŒ . We find that both these models do not work for generating an initial singularity. ïŒ removal as a non zero cosmological constant is most easily dealt with by a Bianchi I universe version of the generalized Friedman equation.