First, we calculate the minimum length for the creation of a 1045 Hz relic Gravitational wave. Next, we look Padamababhan’s inflaton physics, and work done by the author for a modified Heisenberg Uncertainty principl...First, we calculate the minimum length for the creation of a 1045 Hz relic Gravitational wave. Next, we look Padamababhan’s inflaton physics, and work done by the author for a modified Heisenberg Uncertainty principle for constraints on a minimum time step. Sciama’s work in “Black hole explosions” (1982) gives us a linkage between a decay rate for black holes, in terms of a life time, and the mass, M of the black hole, which when combined with a simple exposition from Susskind and Hrabovsky (2013) for the most basic evolution the time change in energy E(t), which is how we form a first order treatment of the square of a minimum time step . We then reference what was done by Ng (2008) as far as infinite quantum statistics, for entropy as a particle count, and from first principle get constraints upon entropy production, as a function of boundaries on minimum time step. We assume massive Gravity, and obtain a peak 1036 Giga Hertz frequency range (1045 Hertz) for relic Gravitational waves, and Gravitons.展开更多
On page 17 of a book on Modified Gravity by Li and Koyama, there is a discussion of how to obtain a Fifth force by an allegedly non-relativistic approximation with a force proportional to minus the spatial derivative ...On page 17 of a book on Modified Gravity by Li and Koyama, there is a discussion of how to obtain a Fifth force by an allegedly non-relativistic approximation with a force proportional to minus the spatial derivative of a scalar field. If the scalar field says for an inflaton, as presented by Padmanabhan only depends upon time, of course, this means that no scalar field contributing to a fifth force our proposal in the neighborhood of Planck time is to turn the time into being equal to r/[constant times c]. This is in the neighborhood of Planck time. Then having done that, consider the initially Plank regime inflaton field as being spatially varying and from there apply a fifth force as a way to help initiate black hole production and possibly Gravitons.展开更多
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...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.展开更多
We are looking at comparison of two action integrals and we identify the Lagrangian multiplier as setting up a constraint equation (on cosmological expansion). This is a direct result of the fourth equation of our man...We are looking at comparison of two action integrals and we identify the Lagrangian multiplier as setting up a constraint equation (on cosmological expansion). This is a direct result of the fourth equation of our manuscript which unconventionally compares the action integral of General relativity with the second derived action integral, which then permits Equation (5), which is a bound on the Cosmological constant. What we have done is to replace the Hamber Quantum gravity reference-based action integral with a result from John Klauder’s “Enhanced Quantization”. In doing so, with Padamabhan’s treatment of the inflaton, we then initiate an explicit bound upon the cosmological constant. The other approximation is to use the inflaton results and conflate them with John Klauder’s Action principle for a way, if we have the idea of a potential well, generalized by Klauder, with a wall of space time in the Pre Planckian-regime to ask what bounds the Cosmological constant prior to inflation, and to get an upper bound on the mass of a graviton. We conclude with a redo of a multiverse version of the Penrose cyclic conformal cosmology. Our objective is to show how a value of the rest mass of the heavy graviton is invariant from cycle to cycle. All this is possible due to Equation (4). And we compare all these with results of Reference [1] in the conclusion, while showing its relevance to early universe production of black holes, and the volume of space producing 100 black holes of value about 10^2 times Planck Mass. Initially evaluated in a space-time of about 10^3 Planck length, in spherical length, we assume a starting entropy of about 1000 initially.展开更多
Stochastic Quantum Space (SQS) theory is a new version of unified field theory based on three fundamental postulations: Gaussian Probability Postulation, Prime Numbers Postulation, Vacuon Postulation. It build a frame...Stochastic Quantum Space (SQS) theory is a new version of unified field theory based on three fundamental postulations: Gaussian Probability Postulation, Prime Numbers Postulation, Vacuon Postulation. It build a framework with theoretical results agree with many experimental data well. For more information, please refer to the PDF.展开更多
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 resu...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.展开更多
We start with a formulation of a modified “Poisson” equation from Poissons and Will as of 2014, and then use the Padmanabhan inter relationship between an inflaton and an early universe potential system. Then from t...We start with a formulation of a modified “Poisson” equation from Poissons and Will as of 2014, and then use the Padmanabhan inter relationship between an inflaton and an early universe potential system. Then from there, we come up with a quadratic equation for a minimum radius, for producing a “massive graviton” value. We then close with observations as to what this implies as to gravitational physics.展开更多
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. ...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.展开更多
Using a root finder procedure to obtain we use an inflaton value due to use of a scale factor if we furthermore use .?From use of the inflaton, we initiate a procedure for a minimum scale factor, which would entail th...Using a root finder procedure to obtain we use an inflaton value due to use of a scale factor if we furthermore use .?From use of the inflaton, we initiate a procedure for a minimum scale factor, which would entail the , for a sufficiently well placed frequency ω. If the Non Linear Electrodynamics procedure of Camara et al. of General relativity was used, plus the modified Heisenberg Uncertainty principle, of Beckwith, and others, i.e . we come due to a sufficiently high frequency a case for which implies a violation of the Penrose singularity theorem, i.e . this is in lieu of ?. If this is not true, i.e. that the initial , then we will likely avoid for reasons brought up in this manuscript.展开更多
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 magneti...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.展开更多
Using the approximation of constant pressure, a thermodynamic identity for GR as given by Padmanabhan is applied to early universe graviton production. We build upon an earlier result in doing this calculation. Previo...Using the approximation of constant pressure, a thermodynamic identity for GR as given by Padmanabhan is applied to early universe graviton production. We build upon an earlier result in doing this calculation. Previously, we reviewed a relationship between the magnitude of an inflaton, the resultant potential, GW frequencies and also Gravitational waves, GW, wavelengths. The Non Linear Electrodynamics (NLED) approximation makes full use of the Camara et al. result about density and magnetic fields to ascertain when the density is positive or negative, meaning that at a given magnetic field strength, if one uses a relationship between density and pressure at the start of inflation one can link the magnetic field to pressure. From there an estimated initial temperature is calculated. This temperature scales down if the initial entropy grows.展开更多
Using Hall and Reginatto’s condition for a Wheeler De Witt Equation for a Friedman-Walker metric coupled to a (Inflaton) scalar field Φ, we delineate the outer boundary of the value of a scale factor a (t) for quant...Using Hall and Reginatto’s condition for a Wheeler De Witt Equation for a Friedman-Walker metric coupled to a (Inflaton) scalar field Φ, we delineate the outer boundary of the value of a scale factor a (t) for quantum effects, in an expanding universe. The inflaton field is from Padmanabhan’s reference, “An Invitation to Astrophysics” which yields a nonstandard Potential U (a, Φ) which will lead to an algebraic expression for a (t) for the value of the outer boundary of quantum effects in the universe. Afterwards, using the scale factor a (t)=ainitial·tα, with alpha given different values, we give an estimation as to a time, t (time) which is roughly the boundary of the range of quantum effects. How this is unusual? We use the Wheeler De Witt Equation, as a coupling to a given inflaton field Φ and find a different way as to delineate a time regime for the range of quantum effects in an expanding universe.展开更多
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 ...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.展开更多
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 to...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.展开更多
We use the ideas of a million black holes, at the boundary of contribution to the shift from Pre-Planckian to Planckian physics, as a summed up contribution from one million primordial black holes. I.e. this is assumi...We use the ideas of a million black holes, at the boundary of contribution to the shift from Pre-Planckian to Planckian physics, as a summed up contribution from one million primordial black holes. I.e. this is assuming a quantum bounce. This is an extension of work done by the author as to explain the nature of a transition from being tiny to when becomes 1 in value. Taking this into account, this article is a way to delineate the physics, inherent in the transition from to which puts a premium upon the growth of the inflaton, due to , with but with changing from , an 10255 increase in magnitude. This increase in magnitude may be the driver of subsequent inflation. When we have a pre quantum, especially if the inequality becomes an equality, and then the transition to marks the start of quantum gravity, whereas our black hole entropy model used to obtain a non zero entropy contribution from 1 million primordial relic black holes, as referenced, comes from Dr. Sen in an October 10 Run Run Shaw lecture in Stonybrook University.展开更多
We begin by examining a general expression of entropy, and its links to a minimum radius of the universe. We derive an expression for the production of at least 1 unit of entropy, which translates to a value of Planck...We begin by examining a general expression of entropy, and its links to a minimum radius of the universe. We derive an expression for the production of at least 1 unit of entropy, which translates to a value of Planck length in radii to 1000 times Planck radii, for the quantum bubble of space-time which depends upon, of all things, the initial Hubble expansion rate value. If the Hubble parameter has the value of 10^19 GeV, we see a minimum radial length of the Universe of about 1 billion times Planck length. If the Hubble parameter is of 10^19 GeV, the minimum radial length of the universe would be about one Planck length, which is surprising to put it mildly. The higher the initial temperate is, up to a point, the more likely the initial entropy is closer to the Causal barrier mentioned in an earlier publication by the author.展开更多
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 Hu...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”.展开更多
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 ...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 .展开更多
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 Planc...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.展开更多
文摘First, we calculate the minimum length for the creation of a 1045 Hz relic Gravitational wave. Next, we look Padamababhan’s inflaton physics, and work done by the author for a modified Heisenberg Uncertainty principle for constraints on a minimum time step. Sciama’s work in “Black hole explosions” (1982) gives us a linkage between a decay rate for black holes, in terms of a life time, and the mass, M of the black hole, which when combined with a simple exposition from Susskind and Hrabovsky (2013) for the most basic evolution the time change in energy E(t), which is how we form a first order treatment of the square of a minimum time step . We then reference what was done by Ng (2008) as far as infinite quantum statistics, for entropy as a particle count, and from first principle get constraints upon entropy production, as a function of boundaries on minimum time step. We assume massive Gravity, and obtain a peak 1036 Giga Hertz frequency range (1045 Hertz) for relic Gravitational waves, and Gravitons.
文摘On page 17 of a book on Modified Gravity by Li and Koyama, there is a discussion of how to obtain a Fifth force by an allegedly non-relativistic approximation with a force proportional to minus the spatial derivative of a scalar field. If the scalar field says for an inflaton, as presented by Padmanabhan only depends upon time, of course, this means that no scalar field contributing to a fifth force our proposal in the neighborhood of Planck time is to turn the time into being equal to r/[constant times c]. This is in the neighborhood of Planck time. Then having done that, consider the initially Plank regime inflaton field as being spatially varying and from there apply a fifth force as a way to help initiate black hole production and possibly Gravitons.
文摘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.
文摘We are looking at comparison of two action integrals and we identify the Lagrangian multiplier as setting up a constraint equation (on cosmological expansion). This is a direct result of the fourth equation of our manuscript which unconventionally compares the action integral of General relativity with the second derived action integral, which then permits Equation (5), which is a bound on the Cosmological constant. What we have done is to replace the Hamber Quantum gravity reference-based action integral with a result from John Klauder’s “Enhanced Quantization”. In doing so, with Padamabhan’s treatment of the inflaton, we then initiate an explicit bound upon the cosmological constant. The other approximation is to use the inflaton results and conflate them with John Klauder’s Action principle for a way, if we have the idea of a potential well, generalized by Klauder, with a wall of space time in the Pre Planckian-regime to ask what bounds the Cosmological constant prior to inflation, and to get an upper bound on the mass of a graviton. We conclude with a redo of a multiverse version of the Penrose cyclic conformal cosmology. Our objective is to show how a value of the rest mass of the heavy graviton is invariant from cycle to cycle. All this is possible due to Equation (4). And we compare all these with results of Reference [1] in the conclusion, while showing its relevance to early universe production of black holes, and the volume of space producing 100 black holes of value about 10^2 times Planck Mass. Initially evaluated in a space-time of about 10^3 Planck length, in spherical length, we assume a starting entropy of about 1000 initially.
文摘Stochastic Quantum Space (SQS) theory is a new version of unified field theory based on three fundamental postulations: Gaussian Probability Postulation, Prime Numbers Postulation, Vacuon Postulation. It build a framework with theoretical results agree with many experimental data well. For more information, please refer to the PDF.
文摘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.
文摘We start with a formulation of a modified “Poisson” equation from Poissons and Will as of 2014, and then use the Padmanabhan inter relationship between an inflaton and an early universe potential system. Then from there, we come up with a quadratic equation for a minimum radius, for producing a “massive graviton” value. We then close with observations as to what this implies as to gravitational physics.
文摘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.
文摘Using a root finder procedure to obtain we use an inflaton value due to use of a scale factor if we furthermore use .?From use of the inflaton, we initiate a procedure for a minimum scale factor, which would entail the , for a sufficiently well placed frequency ω. If the Non Linear Electrodynamics procedure of Camara et al. of General relativity was used, plus the modified Heisenberg Uncertainty principle, of Beckwith, and others, i.e . we come due to a sufficiently high frequency a case for which implies a violation of the Penrose singularity theorem, i.e . this is in lieu of ?. If this is not true, i.e. that the initial , then we will likely avoid for reasons brought up in this manuscript.
文摘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.
文摘Using the approximation of constant pressure, a thermodynamic identity for GR as given by Padmanabhan is applied to early universe graviton production. We build upon an earlier result in doing this calculation. Previously, we reviewed a relationship between the magnitude of an inflaton, the resultant potential, GW frequencies and also Gravitational waves, GW, wavelengths. The Non Linear Electrodynamics (NLED) approximation makes full use of the Camara et al. result about density and magnetic fields to ascertain when the density is positive or negative, meaning that at a given magnetic field strength, if one uses a relationship between density and pressure at the start of inflation one can link the magnetic field to pressure. From there an estimated initial temperature is calculated. This temperature scales down if the initial entropy grows.
文摘Using Hall and Reginatto’s condition for a Wheeler De Witt Equation for a Friedman-Walker metric coupled to a (Inflaton) scalar field Φ, we delineate the outer boundary of the value of a scale factor a (t) for quantum effects, in an expanding universe. The inflaton field is from Padmanabhan’s reference, “An Invitation to Astrophysics” which yields a nonstandard Potential U (a, Φ) which will lead to an algebraic expression for a (t) for the value of the outer boundary of quantum effects in the universe. Afterwards, using the scale factor a (t)=ainitial·tα, with alpha given different values, we give an estimation as to a time, t (time) which is roughly the boundary of the range of quantum effects. How this is unusual? We use the Wheeler De Witt Equation, as a coupling to a given inflaton field Φ and find a different way as to delineate a time regime for the range of quantum effects in an expanding universe.
文摘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.
文摘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.
文摘We use the ideas of a million black holes, at the boundary of contribution to the shift from Pre-Planckian to Planckian physics, as a summed up contribution from one million primordial black holes. I.e. this is assuming a quantum bounce. This is an extension of work done by the author as to explain the nature of a transition from being tiny to when becomes 1 in value. Taking this into account, this article is a way to delineate the physics, inherent in the transition from to which puts a premium upon the growth of the inflaton, due to , with but with changing from , an 10255 increase in magnitude. This increase in magnitude may be the driver of subsequent inflation. When we have a pre quantum, especially if the inequality becomes an equality, and then the transition to marks the start of quantum gravity, whereas our black hole entropy model used to obtain a non zero entropy contribution from 1 million primordial relic black holes, as referenced, comes from Dr. Sen in an October 10 Run Run Shaw lecture in Stonybrook University.
文摘We begin by examining a general expression of entropy, and its links to a minimum radius of the universe. We derive an expression for the production of at least 1 unit of entropy, which translates to a value of Planck length in radii to 1000 times Planck radii, for the quantum bubble of space-time which depends upon, of all things, the initial Hubble expansion rate value. If the Hubble parameter has the value of 10^19 GeV, we see a minimum radial length of the Universe of about 1 billion times Planck length. If the Hubble parameter is of 10^19 GeV, the minimum radial length of the universe would be about one Planck length, which is surprising to put it mildly. The higher the initial temperate is, up to a point, the more likely the initial entropy is closer to the Causal barrier mentioned in an earlier publication by the author.
文摘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”.
文摘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 .
文摘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.
