%0 Journal Article %T Cosmic Dark Energy from ‘t Hooft’s Dimensional Regularization and Witten’s Topological Quantum Field Pure Gravity %A Mohamed S. El Naschie %J Journal of Quantum Information Science %P 83-91 %@ 2162-576X %D 2014 %I Scientific Research Publishing %R 10.4236/jqis.2014.42008 %X

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) = mc² (21/22) and E(ordinary) = mc²/22. 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 %K Accelerated Cosmic Expansion %K ‘t Hooft-Veltman Dimensional Regularization %K Wilson Renormalization %K Pure Gravity %K Witten’s Topological Quantum Field %K E-Infinity Cantorian Spacetime %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=46062