Quantum Gravity and String Theory

   

Review of Weyl Tensor as an Aid to Reviewing the Penrose Weyl Tensor Conjecture Near Start of Inflation. I.e. that no Need to Suppose it is Always Zero at Start of Inflation

Authors: Andrew Beckwith

We review, using our prior work the Weyl tensor as an aid to reviewing the Penrose Weyl Tensor Conjecture near start of Inflation. Our supposition is that this Weyl tensor will not vanish, and this is in tandem with a non- zero initial entropy. In doing so, we make use of two representations of the scale factor, one with , and another in terms of , with the time, scaled as . The second representation of the derivative of will yield a not equal to zero due to initial time step not being zero, i.e. a quantization of time, whereas the first representation of depends upon the initial value assumed and picked. We then afterwards, say something as to Malek’s doctoral thesis rendition of , for n general dimensions as a way to buttress our conclusion, that indeed is non-zero at start of inflation provided certain assumptions are made. Which in turn affects entropy production at the start of the universe. Note . in the case of a Pre Planckian imaginary time , i.e. to have real valued, but nonzero, we have to restrict = 1, as a way of making sense of what happens if we do use purely imaginary time. If not, then the Weyl tensor could be complex valued. If we have real time for , we have far less restrictive conditions, as is given in our document. i.e. This idea of use of a much larger initial value of the cosmological constant in line with [16] leads to a closed form solution for the if we have real time for . We conclude with our buildup to the future works section by the end of our conclusion, which has that a Pre Planckian may be linked to the inverse of the Planckian value of the initial Hubble parameter. With future input from reference [13] of our paper.

Comments: 14 Pages.

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Submission history

[v1] 2017-08-14 16:32:10

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