Abstract
Our Methodology is to construct using a “trivial” solution to massive gravitons, and a nonsingular start for expansion of the universe. Our methodology has many unintended consequences, not the least is a relationship between a small time step, t, the minimum scale factor and even the tension or property values of the initial space-time wall, and that is a consequence of a “trivial” solution taking into account “massive” gravitons. I.e. this solution has a mass term times the partial derivative with respect to time of an expression in brackets. The expression in brackets is the cube of a scale factor minus the square of the scale factor. Bonus that this equation is set to zero. It is deemed trivial due to the insistence of having a singular solution. If that is dropped, we have a different venue. In addition, the Friedman equation for nonsingular cosmology can have a quadratic dependence upon a density (of space-time), leading to a way to incorporate right at the surface of the initial “space-time” bubble an uncertainty principle. From there we suggest a first principle Schrodinger equation, with the caveat that time does not exist, within the space-time nonsingular bubble, but is formed right afterwards. From there we again form solutions for strength of GW signals and suggestions as to polarization states. Our quest is motivated by our last articles question, where “We conclude by stating the following question. Can extra dimensions come from a Multiverse feed into Pre-Planckian space-time? See Theorem at the end of this publication. Our answer is in the affirmative, and it has intellectual similarities to George Chapline’s work with Black hole physics”. From there we next will in future articles postulate conditions for experimental detectors for subsequent data sets to obtain falsifiable data sets.
Highlights
Our Methodology is to construct using a “trivial” solution to massive gravitons, and a nonsingular start for expansion of the universe
Our methodology has many unintended consequences, not the least is a relationship between a small time step, t, the minimum scale factor and even the tension or property values of the initial space-time wall, and that is a consequence of a “trivial” solution taking into account “massive” gravitons
The Friedman equation for nonsingular cosmology can have a quadratic dependence upon a density, leading to a way to incorporate right at the surface of the initial “space-time” bubble an uncertainty principle
Summary
If the initial energy were just at the boundary of the bubble of space time, have the odd situation for which we would have the following, namely at the surface of the bubble, so if one used Planck units with lPlanck ≡ ≡ G ≡ 1 we could have the following weird situation γ − 8πG To put it mildly, we would need a lot more experimental data sets! Keep in mind that the surface of the bubble would be, in fidelity with reference [3] be obeying having the scale factor at a minimum value and that in line with inflationary e folds of 60 [15] [24], or 1.14 times 1026 If this is kept in mind, and say that we have a frequency range of about 1037 Hertz, as a result of the above, we would have say 1011 Hertz for Earth signals taken for GW detection
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