Abstract
When the initial radius of the universe is set in four dimensions and if there is only ONE repeating universe, then the initial radii of the universe is R → 0 or gets very close to zero if we use the Einstein Equations modified by Stoica. The Einstein Equations are reset by Stoical in a formalism which removes in four dimensions, the big bang singularity pathology. So then the reason for Planck length no longer holds. This manuscript assumes a repeating single universe. We present entanglement entropy in the early universe with a shrinking scale factor, due to Muller and Lousto, and show that there are consequences due to initial entangled for a time dependent horizon radius in cosmology, with (flat space conditions) for conformal time. Even if the 3-dimensional spatial length goes to zero. Our new manuscript presentation sets as a starting point a cosmology with a non-zero Λ vacuum energy. The non-zero Λ vacuum energy, initial configuration of the universe permits us to keep in an information theory stand point (information theory), computational bits for our configuration of cosmological expansion. This assemblage of computational bits occurs in cosmological evolution even if in an initial four-dimensional cosmology, we have the initial radii of the universe R → 0. We also find that in the case of a multiverse, such considerations will not hold and that cosmic singularities have a more different characteristic in the multiverse setting than in the single universe repeated over and over again, i.e. using an argument borrowed and modified from Kauffman, the multiverse will not mandate “perfect” singularities. The existence of a multiverse may allow for non zero singularities in lieu with the Kauffman argument cited at the end of the document, plus the lower pre big bang temperatures which may allow for the survival of gravitons just before the onset of the cosmological expansion phase, if a multiverse exists embedding our present universe.
Highlights
We first examine what is to be expected in the four-dimensional case as to what happens if there is a single repeating universe
When the initial radius of the universe is set in four dimensions and if there is only ONE repeating universe, the initial radii of the universe is R → 0 or gets very close to zero if we use the Einstein Equations modified by Stoica
The Einstein Equations are reset by Stoical in a formalism which removes in four dimensions, the big bang singularity pathology
Summary
We first examine what is to be expected in the four-dimensional case as to what happens if there is a single repeating universe. If the term beta in the coefficient of temperature, T, is not zero, we should take a good look at what is done in Weinberg [2] where there is a concerted effort to mix in background viscosity = But first take note of the Grischuck [36] expression as to GW frequency in the hign end, with Temperature approaching Planck Tempure values, with behavior due to space-time temperature dependence as given by: M = mass of “universe” initially, and R = radius of initial dimensions, with Planck temperature values giving for a single universe, and four dimensions ( ) fPeak ≈. The question to ask is the following reasonable? i.e. as given by Giovannini [37]
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