How to Obtain a Mass of a Graviton, and Does This Methodology Lead to Voids?

Abstract

Using the Klauder enhanced quantization as a way to specify the cosmological constant as a baseline for the mass of a graviton, we eventually come up and then we will go to the relationship of a Planck Length to a De Broglie length in order to link how we construct a massive graviton mass, with cosmological constant and to interface that with entropy in the early universe. We then close with a reference to the possible quantum origins of e folding and inflation. This objective once achieved is connected with a possible mechanism for the creation of voids, in the later universe, using a construction of shock fronts from J. P. Onstriker, 1991 and followed up afterwards with Mukhanov's physical foundations to Cosmology book section as to indicate how variable input into self reproduction of the Universe structures may lead to void formation in the present era. A connection with Wesson's 5 dimensional cosmology is brought up in terms of a generalized uncertainty principle which may lead to variations of varying energy input into self reproducing cosmological structures which could enable non uniform structure formation and hence voids. One of the stunning results is that the figure of number of gravitons, about 10 58 , early on, is commensurate with a need for negative pressure, (middle of manuscript) which is a stunning result, partly based on Volovik and weakly interacting Bose gas model for pressure, which is completely unexpected. Note that in quantum physics, the idea statistically is that at large quantum numbers, we have an approach to classical physics results. We will do the same as to our cosmological work. This means that the

We Begin with a “Trivial” Condition on Massive Gravitons, and Use That to Examine Nonsingular Starts to Inflation, for GW, with GW Strength and Possible Polarization States?

“…Whereas if we us [2], and [3] and really look at [4], we can add in the following as to the scale factor used in Equation 1which uses at the surface of a presumed non singular start to the expansion of the universe ( ) min a t a t γ = (2) Leading to [4] the inflaton.…”

“…In our write up of Equation (38) to Equation (42) we are assuming for all general purposes that the scale factor would have a minimum value. 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 10 26 . If this is kept in mind, and say that we have a frequency range of about 10 37 Hertz, as a result of the above, we would then have say 10 11 Hertz for Earth signals taken for GW detection.…”

“…Why this is important? Note that in [3] we made reference to [28], which if d (dimension) is fractal, means that the temperature for the universe, so…”

“…Now, make use of [3] again and this relationship below though will stand the test of time, but it is NOT dependent upon frequency! Here g N is a count of gravitons which may commence from our earlier generation of early universe GW.…”

“…Here g N is a count of gravitons which may commence from our earlier generation of early universe GW. From [3] ( )…”