Pre-Planckian Space-time Research Articles

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

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.

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?

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.

Setting Time as Purely Imaginary in Regime of Space-Time before Causal Barrier and Planckian Space-Time

We start where we use an inflaton value due to use of a scale factor . In doing so, using the approximations brought up in the case of an early universe generation of a magnetic field, we come up with the stunning datum of a Pre Planckian space-time with purely imaginary time. The consequences of such are brought up in our document. We use what is brought up in a prior article as to Pre Planckian to Planckian generation of Magnetic fields to make our point. Here, we assume, in the Pre Planckian space-time, a singular injection of space-time, which we argue, if there is no spatial variation of the Inflaton field, so used, and we just have ONE Pre Planckian time instant that this will be imaginary valued time, hence leading to pure Tunneling behavior. Whatever we are assuming, using a Penrose cosmology to initiate CCC universe recycling, in terms of energy, is transferred to Planckian space-time.

How Does a Setting of the Vacuum Energy Density, as Given Today, Lead to an Initial Hubble Radius for the Early Universe, i.e. How Does the Early Universe Partly Mimic a Black Hole?

First we review what was done by Klauber, in his quantum field theory calculation of the Vacuum energy density, and in doing so, use, instead of Planck Mass, which has 1019 GeV, which leads to an answer 10122 times too large, a cut-off value of instead, a number, N, of gravitons, times graviton mass (assumed to be about 10°43 GeV) to get a number, N, count of about 1031 if the vacuum energy is to avoid an overshoot of 10122, and instead have a vacuum energy 10°47 GeV4. Afterwards, we use the results of Mueller and Lousto, to compare the number N, of 1031, assumed to be entropy using Ng’s infinite quantum statistics, to the ratio of the square of (the Hubble (observational) radius over a calculated grid size which we call a), here, a ~ a minimum time step we call delta t, times, the speed of light. Now in doing so, we use a root finder procedure to obtain where we use an inflaton value due to use of a scale factor if we furthermore use as the variation of the time component of the metric tensor in Pre-Planckian Space-time up to the Planckian space-time initial values.

How a Minimum Time Step and Formation of Initial Causal Structure in Space-Time Is Linked to an Enormous Initial Cosmological Constant

We use a root finder procedure to obtain and an inflaton value due to use of a scale factor if we furthermore use as the variation of the time component of the metric tensor in Pre-Planckian Space-time up to the Planckian space-time initial values. In doing so, we obtain, due to the very restricted values for which are of the order of less than Planck time, results leading to an enormous value for the initial Cosmological constant.

How to Determine a Jump in Energy Prior to a Causal Barrier, with an Attendant Current, for an Effective Initial Magnetic Field. In the Pre Planckian to Planckian Space-Time

We start where we use an inflaton value due to use of a scale factor . Also we use as the variation of the time component of the metric tensor in Pre-Planckian space-time. Our objective is to find an effective magnetic field, to obtain the minimum scale factor in line with Non Linear Electrodynamics as given by Camara, et al., 2004. Our suggestion is based upon a new procedure for an effective current based upon an inflaton time exp (i times (frequency) times (cosmological time)) factor as a new rescaled inflaton which is then placed right into a Noether Current scalar field expression as given by Peskins, 1995. This is before the Causal surface with which is, right next to a quantum bounce, determined by , with the next shift in the Hubble parameter as set up to be then . And is an initial degree of freedom value of about 110. Upon calculation of the current, and a resulting magnetic field, for the space time bubble, we then next obtain a shift in energy, leading to a transition from too. We argue then that the delineation of the term is a precursor to filling in information as to the Weyl Tensor for near singularity measurements of starting space-time. Furthermore, as evidenced in Equations ((26) and (27)) of this document, we focus upon a “first order” that checks into if a cosmological “constant” would be invariant in time, or would be along the trajectory of the time, varying Quinessence models. We close this document, with Maxwell equations as to Post Newtonian theory, for Gravity, with our candidates as to a magnetic field included in, with what we think this pertains to, as far as Gravo Electric and Gravo Magnetic fields, and then make suggestions as to a quantum version of this methodology for future gravitational wave physics research. This is Appendix G, this last topic, and deliberately set up future works paradigm which will be investigated in the coming year. It is based upon a Gravo Electric potential, and we make suggestions as to its upgrade in our future works, in early universe cosmology. In the reference by Poisson, and Will, they write and in this last section we come up with a value of U, based in part on the comparison with the alteration of velocity, due to a massive graviton, namely via the substitution, we write as , so as to come up with a post Newtonian approximation result for a magnetic field. We compare this magnetic field, as far as the Inflaton magnetic field, and use it to come up with observations with regards to the phenomenology of gravity in Pre Planckian to Planckian regime limits. We close, then with the observation given in Appendix H, of the inhomogeneity of Pre Planckian-to Planckian space time as a necessary condition for a Gravi-Magnetic field. We also reference an Appendix I, which does a summary of a 5th force calculation, and we then compare those results, with our temporary results of a Gravi Magneitc field, as we have tried to start up as a future works project.

How to Determine Initial Starting Time Step with an Initial Hubble Parameter H = 0 after Formation of Causal Structure Leading to Investigation of the Penrose Weyl Tensor Conjecture

We start where we use an inflaton value due to use of a scale factor . Also we use as the variation of the time component of the metric tensor in Pre-Planckian Space-time. In doing so, what we lead up to using the Huang Superfluid universe model, which is by the modified superfluid cosmology model leading to examining within the Pre Planckian regime, Curvature, small but non zero, and energy density . The Potential energy is given by what it would be if leading to a relationship of , where we will isolate conditions for the initial time and compare them against a root finder procedure given in another paper written by the author. Then, afterwards, assuming a modified Hubble parameter, with an initial Hubble parameter after the Causal surface with, right after a quantum bounce, determined by , is then . And is an initial degree of freedom value of about 110. Then, the graviton production rate is a function of time leading to a temperature T dependence, with M here is a chosen Mass scale, M of about 30 TeV, with d greater than or equal to zero, representing the Kaluza Klein dimensions assumed with the number of gravitons produced after the onset of Causal structure given by . This by Infinite quantum statistics is proportional to entropy. We close with a caveat as far as the implications of all this to the Penrose Conjecture about the vanishing of the Weyl tensor, in the neighborhood of a cosmological initial singularity. And what we think should be put in place instead of the Penrose Weyl tensor hypothesis near a “cosmological” singularity. And we close with a comment about the Weyl curvature tensor, in Pre Planckian to Planckian physics, and also a final appendix on the Mach’s principle as written by Sciama, in defining the initial space-time non-singular “bubble”.

Gedankenexperiment, Assuming Nonsingular Quantum Bounce Friedman Equations Leading to a Causal Discontinuity between Pre Planckian to Planckian Physics Space-Time Regime

This paper is to address using what a fluctuation of a metric tensor leads to, in pre Planckian physics. If so then, we pick the conditions for an equality, with a small δgn, to come up with restraints which are in line with modifications of the Friedman equation in a quantum bounce, with removal of the Penrose theorem initial singularity. In line with super negative pressure being applied, so as to understand what we can present as far as H = 0 (quantum bounce) in terms of density of the Universe. And also considering what to expect when P = wΔρ ~ (-1+e+)Δρ, i.e. we have a negative energy density in Pre Planckian space-time. This leads to a causal discontinuity between Pre Planckian to Planckian space-time due to the sign of the inflaton changing from minus to positive, for reasons brought up in this manuscript, i.e. looking at Equations (9)-(11) of this document, with explanations as to what is going on physically.

The Transition from Pre-Octonionic to Octonionic Gravity and How It May Be Pertinent to a Re-Do of the HUP for Metric Tensors

The quantum gravity problem that the notion of a quantum state, representing the structure of space-time at some instant, and the notion of the evolution of the state, does not get traction, since there are no real “instants”, is avoided by having initial Octonionic geometry embedded in a larger, nonlinear “pilot model” (semi classical) embedding structure. The Penrose suggestion of recycled space time avoiding a “big crunch” is picked as the embedding structure, so as to avoid the “instants” of time issue. Getting Octionic gravity as embedded in a larger, Pilot theory embedding structure may restore Quantum Gravity to its rightful place in early cosmology without the complication of then afterwards “Schrodinger equation” states of the universe, and the transformation of Octonionic gravity to existing space-time is explored via its possible linkage to a new version of the HUP involving metric tensors. We conclude with how specific properties of Octonion numbers algebra influence the structure and behavior of the early-cosmology model. This last point is raised in Section 14, and is akin to a phase transition from Pre-Octonionic geometry, in pre-Planckian space-time, to Octonionic geometry in Planckian space-time. A simple phase transition is alluded to; making this clear is as simple as realizing that Pre-Octonionic is for Pre-Planckian Space-time and Octonionic is for Planckian Space-time. We state that the Standard Model of physics occurs during Planckian Space-time. We also argue that the Standard Model does not apply to Pre Planckian Space-time. This is commensurate with the Octonion number system NOT applying in pre-Planckian space-time, but applying in Plankian space-time. And the last line of Equation (54) gives a minimum time step in pre-Planckian space-time when we do NOT have the Standard Model of physics, or Octonionic Geometry.

How a Minimum Time Step and Formation of Initial Causal Structure in Space-Time Is Linked to an Enormous Initial Cosmological Constant

We use a root finder procedure to obtain . We use an inflaton value due to use of a scale factor if we furthermore use as the variation of the time component of the metric tensor in Pre-Planckian Space-time up to the Planckian space-time initial values. In doing so, it concludes with very restricted limit values for of the order of less than Planck time, leading to an enormous value for the initial Cosmological constant.

Constraints, in Pre-Planckian Space-Time via Padmabhan’s Λ<sub>initial</sub>·<i>H</i><sup style="margin-left:4px;">-2</sup><sub style="margin-left:-17px;">initial</sub>≈<i>o</i>(1) Approximation Leading to Initial Inflaton Constraints and Its Relation to Early Universe Graviton Production

We are looking at what if the initial cosmological constant is due to if we furthermore use as the variation of the time component of the metric tensor in Pre-Planckian Space-time up to the Planckian space-time initial values. This assumes as an initial inflaton value, as well as employing Non-Linear Electrodynamics to the scale factor in , and the upshot is an expression for as an initial inflaton value/squared which supports Corda’s assumptions in the Gravity’s breath Electronic Journal of theoretical physics article. We close with an idea to be worked in further detail as to density matrices and how it may relate to gravitons traversing from a Pre-Planckian to Planckian space-time regime. We will write up an idea in far greater detail in a future publication.

How a Minimum Time Step Leads to a Causal Structure Used to Form Initial Entropy Production and High Frequency Gravitons, with 7 Subsequent Open Questions

We start where we use an inflaton value due to use of a scale factor . Also we use as the variation of the time component of the metric tensor in Pre-Planckian Space-time up to the Planckian spacetime initial values. In doing so, we come up with a polynomial expression for a minimum time step; we can call which leads to a development of the arrow of time. We show an inter relationship between the formation of the Arrow of time, and Causal structure, assuming the setting of H = 0 in the Friedman equation This in turn leads to entropy production at the start of causal structure in the onset of inflation. This then leads to three and a quarter pages of 7 open questions we think have to be answered, subsequently. It is noted that high frequency gravitational waves as specified are due to the 1/delta t entry in Equation (45) of the document which comes out to about 44 Hertz, and certainly is high frequency gravitational waves for the initial cosmological conditions, so this is definitely about high frequency gravitational wave focused initial conditions.

Examination of <i>h</i>(<i>x</i>) Real Field of Higgs Boson as Originating in Pre-Planckian Space-Time Early Universe

We initiate working with Peskin and Schroder’s quantum field theory (1995) write up of the Higgs boson, which has a scalar field write up for Phi , with “lower part” of the spinor having h(x) as a real field, with in spatial averaging. Our treatment is to look at the time component of this h(x) as a real field in Pre-Planckian space-time to Planckian Space-time evolution, in a unitarity gauge specified potential , using a fluctuation evolution equation of the form which is in turn using with this being a modified form of the Heisenberg Uncertainty principle in Pre-Planckian space-time. From here, we can identify the formation of in the Planckian space-time regime. The inflaton is based upon Padmanabhan’s treatment of early universe models, in the case that the scale factor, and t a time factor. The initial value of the scale factor is supposed to represent a quantum bounce, along the lines of Camara, de Garcia Maia, Carvalho, and Lima, (2004) as a non zero initial starting point for expansion of the universe, using the ideas of nonlinear electrodynamics (NLED). And from there isolating .

Creating a (Quantum?) Constraint, in Pre Planckian Space-Time Early Universe via the Einstein Cosmological Constant in a One to One and Onto Comparison between Two Action Integrals

We are looking at comparison of two action integrals and we identify the Lagrangian multiplier as setting up a constraint equation (on cosmological expansion). Two action integrals, one which is connected with quantum gravity is called equivalent to another action integral, and the 2nd action integral has a Lagrangian multiplier in it. Using the idea of a Lagrangian multiplier as a constraint equation, we draw our conclusions in a 1 to 1 and onto assumed equivalence between the two action integrals. The viability of the 1 to 1 and onto linkage between the two action integrals is open to question, but if this procedure is legitimate, the conclusions so assumed are fundamentally important.

Pre-Octonionic to Octonionic Gravity and Could Kinetic Energy Be Larger than Potential Energy before Inflation?

We look at early universe space-time which is characterized by a transition from Pre-Planckian to Planckian space-time. In doing so we also invoke the geometry of Octonionic non-commutative structure and when it breaks down. Doing so is also equivalent to a speculation given earlier by the author as to the kinetic energy of Pre-Planckian space-time being significantly larger than the Potential energy, which is the opposite of what happens after the onset of Inflation, with the assumption as to how this is justified given in a (Pre- Planckian) Hubble Parameter set as of Equation (16), and we close with a comparison of this proposal with string cosmology, as represented in the 2nd reference in this paper.

Gedanken Experiment for Initial Expansion of the Universe and Effects of a Nearly Zero Inflaton in Pre-Planckian Physics Space-Time Satisfying Traditional Slow Roll Formulas Which Happens in Pre-Planckian Regimes Even If φ<sup style="margin-left:-12px;">⋅2</sup>»V<sub>SUSY</sub>

We first of all consider what if the initial inflaton was nearly zero instead of proportional to a Planck mass, in a SUSY type potential. Using the construction of Padmanabhan about general inflaton physics and the conditions of what are usual constituent slow roll requirements for inflation, and also of Kolb, Pi and Raby about a SUSY potential, we come up with the counter intuitive formulation of how usual tests for slow roll give the standard answers even if the inflaton in the SUSY potential as given by Kolb, Pi, and Raby is initially zero. The result gives support to a formulation of VEV conditions used right after a Planck instant of time. As it is, we will from first principles examine what adding acceleration does as to the HUP previously derived. In doing so we will be tying it in our discussion with the earlier work done on the HUP. The HUP results, so modified are appropriate for the Pre-Planckian results and may explain why the slow roll formulation as given by Padmanabhan holds where there is the phenomenon of for Pre-Planckian space-time. This leads to a very paradoxical result that in Pre-Planckian physics the traditional slow roll formulas are satisfied even if . But it also puts in extremely tight restrictions upon the formulation of the degree of freedom problem, as given in Equation (26) in this document.

Reconsidering “Does the Sum Rule Hold at the Big Bang?” with Pre Planckian HUP, and Division Algebras

In 2012, the author submitted an article to the Prespacetime Journal based upon the premise of inquiry as to the alleged vanishing of disjoint open sets contributing to quantum vector measures no longer working, i.e. the solution in 2012 was that the author stated that quantum measures in 4 dimensions would not work, mandating, if measure theory were used, imbedding in higher dimensions was necessary for a singularity. The idea was to use the methodology of String Theory as to come up with a way out of the impasse if higher dimensions do not exist. We revisit this question, taking into account a derived HUP, for metric tensors if we look at Pre-Planckian space-time introducing a pre-quantum mechanical HUP which may be a way to ascertain a solution not mandating higher dimensions, as well as introducing cautions as to what will disrupt the offered solution. Note that first, measurable spaces allow disjoint sets. Also, that smooth relations alone do not define separability or admit sets Planck’s length, if it exists, is a natural way to get about the “bad effects” of a cosmic singularity at the beginning of space-time evolution, but if a development is to be believed, namely by Stoica in the article, about removing the cosmic singularity as a breakdown point in relativity, there is nothing which forbids space-time from collapsing to a point. Without the use of a Pre Planckian HUP, for metric tensors, the quantum measures in four dimensions break down. We try to ascertain if a Pre Planckian HUP is sufficient to avoid this pathology and also look at if division algebras which can link Octonionic geometry and E8, to Quark spinors, in the standard model and add sufficient definition to the standard model are necessary and sufficient conditions for a metric tensor HUP which may remove this breakdown of the sum rule in the onset of the “Big Bang”.

Examination of Schrodinger Equation in Pre-Planckian Space-Time Early Universe

We look at the Vuilli (1999) write up of a generalized Schrodinger equation with its Ricci scalar inclusion, in curved space-time. This has a simplified version in Pre-Planckian regime, which leads to comparing a resultant admissible wave function with Bohmian reformulations of quantum physics. As was done earlier, we compare this result with a formulation of a modified “Poisson” equation from Poissons and Will from 2014, and then use inflaton physics. The resulting inflaton is then compared to the wave functional in the first part of this document.

Gedanken Experiment for Looking at δg<sub>tt</sub> for Initial Expansion of the Universe and Influence on HUP via Dynamical Systems, with Positive Pre-Planckian Acceleration

We examine through the lens of dynamical systems a “one dimensional” time mapping of emergent VEV from Pre-Planckian space time conditions. As it is, we will from first principles examine what adding acceleration does as to the HUP previously derived. In doing so, we will be trying it in our discussion with the earlier work done on the HUP. not equal to zero, constant, but large would frequently imply which would have three dissimilar real valued roots. And the situation with not equal to zero yields more tractable result for which will have implications for the HUP inequality in Pre-Planckian space-time, and buttresses an analysis of a 1 dimensional “time” mapping for emergent VEV (vacuum expectation values).

Gedanken Experiment Examining How Kinetic Energy Would Dominate Potential Energy, in Pre-Planckian Space-Time Physics, and Allow Us to Avoid the BICEP 2 Mistake

We use Padmabhan’s “Invitation to Astrophysics” formalism of a scalar field evolution of the early universe, from first principles, to show something which seems counter intuitive. How could, just before inflation, kinetic energy be larger than potential energy in pre-Planckian physics, and what physics mechanism is responsible for the Planckian physics result that Potential energy is far larger than kinetic energy. This document answers that question, as well as provides a mechanism for the dominance of kinetic energy in pre-Planckian space-time, as well as its reversal in the Planckian era of cosmology. The kinetic energy is proportional to , with initial degrees of freedom, and T the initial temperature just before the onset of inflation. Our key assumption is the smallness of curvature, as given in the first equation, which permits adoption of the Potential energy and Kinetic energy formalism used, in the Planckian and pre-Planckian space-time physics. Interpretation of this result, if done correctly, will be able to allow a correct distinguishing of relic gravitational waves, as to avoid the BICEP 2 pickup of galactic dust as a false relic Gravitational wave signal, as well as serve as an investigative template as to if quantum gravity is embedded in a deterministic dissipative system, as cited in the conclusion.