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**Cosmic Dark Energy from ‘t Hooft’s Dimensional Regularization and Witten’s Topological Quantum Field Pure Gravity** ()

We utilize two different theories to prove that cosmic
dark energy density is the complimentary Legendre transformation of ordinary
energy and vice versa as given by E(dark) = mc^{2} (21/22) and
E(ordinary) = mc^{2}/22. The first theory used is based on G ‘t Hooft’s
remarkably simple renormalization procedure in which a neat mathematical
maneuver is introduced via the dimensionality of our four dimensional
spacetime. Thus, ‘t Hooft used instead of *D* = 4 and then took
at the end of an intricate and subtle computation the limit to obtain the result while avoiding various
problems including the pole singularity at *D* = 4. Here and in contradistinction to the classical form of dimensional and
renormalization we set and do not take the limit where and is the theoretically and experimentally well established
Hardy’s generic quantum entanglement. At the end we see that the dark energy
density is simply the ratio of and the smooth disentangled *D* = 4,* i.e.* (dark) = (4 -*k*)/4 = 3.8196011/4 = 0.9549150275. Consequently where we have ignored the fine structure
details by rounding 21 + *k* to 21 and
22 + *k* to 22 in a manner not that
much different from of the original form of dimensional
regularization theory. The result is subsequently validated by another equally
ingenious approach due mainly to E. Witten and his school of topological
quantum field theory. We notice that in that theory the local degrees of freedom
are zero. Therefore, we are dealing
essentially with pure gravity where are the degrees of freedom and is the corresponding dimension. The results and the conclusion of the paper are summarized in Figure 1-3, Table 1 and Flow Chart 1.

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*Journal of Quantum Information Science*,

**4**, 83-91. doi: 10.4236/jqis.2014.42008.

Conflicts of Interest

The authors declare no conflicts of interest.

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