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 1058, 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 , in our last set of equations, which as we indicate has the surprise condition that for Pre-Planckian space-time that a very large value for initial Pre Planckian dimensions dmin which is the dimensional input into the Pre Planckian state, prior to emergence into Planckian cosmology conditions. 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.
Highlights
We close with a reference to the possible quantum origins of e folding and inflation
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 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
1, in our last set of equations, which as we indicate has the surprise condition that for Pre-Planckian space-time that a very large value for initial Pre Planckian dimensions ddim which is the dimensional input into the Pre Planckian state, prior to emergence into Planckian cosmology conditions
Summary
We use the Padmanabhan 1st integral [1], of the form, with the third entry of Equation (1) having a Ricci scalar defined via [2] and usually the curvature א is set as extremely small, with the general relativity [3] [4]. The long and short of it is, to tie this value of the cosmological constant, and the production of gravitons due to early universe conditions, to a relationship between De Broglie wavelength, Planck length, and if the velocity v gets to a partial value close to the speed of light, that, we have, say by using [10] as given by Diosi, in Dice (2018) for quantum systems, if we have instead of a velocity much smaller than the speed of light, a situation where the particle moves very quickly (a fraction of the speed of light) that instead of the slow massive particle postulated in [10]. We will be looking at how we can equate out a negative energy and a negative pressure for this Pre Planckian to Planckian physics transition. We will transition to Reference [14] by Volovik, 2003 which has the following expression for pressure in a vacuumstate of weakly interacting Bose Gases. i.e. We use Equation (21) for pressure, if we use the following approximations ( ) EPlan= ck mc2 , EPlan= ck c =Θ 3 n (particle density) , and so we have a pressure for Bose pressure ( ) p + Bose fluid pressure
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