%0 Journal Article
%T Variation of Vacuum Energy if Scale Factor Becomes Infinitely Small, with Fixed Entropy Due to a Non Pathological Big Bang Singularity Accessible to Modified Einstein Equations
%A Andrew Beckwith
%J Journal of Modern Physics
%P 1336-1341
%@ 2153-120X
%D 2012
%I Scientific Research Publishing
%R 10.4236/jmp.2012.329171
%X When initial radius R<sub>initial <img src=\"http://chart.googleapis.com/chart?cht=tx&amp;chl=%5Crightarrow%20\" style=\"border:none;\" />0 if Stoica actually derived Einstein equations in a formalism which remove the big bang singularity pathology, then the reason for Planck length no longer holds. The implications of R<sub>initial <img src=\"http://chart.googleapis.com/chart?cht=tx&amp;chl=%5Crightarrow%20\" style=\"border:none;\" />0  are the first part of this manuscript. Then the resolution is alluded to by work from Muller and Lousto, as to implications of entanglement entropy. We present entanglement entropy in the early universe with a steadily shrinking scale factor, due to work from Muller and Lousto, and show that there are consequences due to initial entanged S<sub>entropy</sub>=0.3r<sub>H</sub><sup>2</sup>/a<sup>2</sup> for a time dependent horizon radius r<sub>H</sub> in cosmology, with for flat space conditions r<sub>H</sub>=<img src=\"http://chart.googleapis.com/chart?cht=tx&amp;chl=%5Ceta%20\" style=\"border:none;\" /> for conformal time. In the case of a curved, but not flat space version of entropy, we look at vacuum energy as proportional to the inverse of scale factor squared times the inverse of initial entropy, effectively when there is no initial time in line with <img src=\"http://chart.googleapis.com/chart?cht=tx&amp;chl=%5Crho%20\" style=\"border:none;\" />~H<sup>2</sup>/G <img src=\"http://chart.googleapis.com/chart?cht=tx&amp;chl=%5CLeftrightarrow%20\" style=\"border:none;\" />H¡Öa<sup>-1</sup>. The consequences for this initial entropy being entangled are elaborated in this manuscript. No matter how small the length gets, S<sub>entropy</sub> if it is entanglement entropy, will not go to zero. The requirement is that the smallest length of time, t, re scaled does not go to zero. Even if the length goes to zero. This preserves a minimum non zero   vacuum energy, and in doing so keep the bits, for computational bits cosmological evolution even if R<sub>initial <img src=\"http://chart.googleapis.com/chart?cht=tx&amp;chl=%5Crightarrow%20\" style=\"border:none;\" />0.</sub></sub></sub>
%K Fjortoft Theorem
%K Thermodynamic Potential
%K Matter Creation
%K Vacuum Energy Non Pathological Singularity Affecting Einstein Equations
%K Planck Length
%K Braneworlds
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=23135