Ashtekar-Kodama Gravity as a Classical and Quantum Extension of Loop Quantum Gravity

This paper presents a new theory of gravity, called here Ashtekar-Kodama (AK) gravity, which is based on the Ashtekar-Kodama formulation of loop quantum gravity (LQG), yields in the limit the Einstein equations, and in the quantum regime a full renormalizable quantum gauge field theory. The three fundamental constraints (hamiltonian, gaussian and diffeomorphism) were formulated in 3-dimensional spatial form within LQG in Ashtekar formulation using the notion of the Kodama state with positive cosmological constant Λ. We introduce a 4-dimensional covariant version of the 3-dimensional (spatial) hamiltonian, gaussian and diffeomorphism constraints of LQG. We obtain 32 partial differential equations for the 16 variables Emn (E-tensor, inverse densitized tetrad of the metric) and 16 variables Amn (A-tensor, gravitational wave tensor). We impose the boundary condition: for large distance the E-generated metric g(E) becomes the GR-metric g (normally Schwarzschild-spacetime). The theory based on these Ashtekar-Kodama (AK) equations, and called in the following Ashtekar-Kodama (AK-) gravity has the following properties. • For Λ = 0 the AK equations become Einstein equations, A-tensor is trivial (constant), and the E-generated metric g(E) is identical with the GR-metric g. • When the AK-equations are developed into a Λ-power series, the Λ-term yields a gravitational wave equation, which has only at least quadrupole wave solutions and becomes in the limit of large distance r the (normal electromagnetic) wave equation. • AK-gravity, as opposed to GR, has no singularity at the horizon: the singularity in the metric becomes a (very high) peak. • AK-gravity has a limit scale of the gravitational quantum region 39 μm, which emerges as the limit scale in the objective wave collapse theory of Gherardi-Rimini-Weber. In the quantum region, the AK-gravity becomes a quantum gauge theory (AK quantum gravity) with the Lie group extended SU(2) = ε-tensor-group(four generators) as gauge group and a corresponding covariant derivative. • AK quantum gravity is fully renormalizable, we derive its Lagrangian, which is dimensionally renormalizable, the normalized one-graviton wave function, the graviton propagator, and demonstrate the calculation of cross-section from Feynman diagrams.

The Origin of Quarks in Quantum Gravity

A theory of quantum gravity has recently been developed by the author based on the concept that all forces converge to one at the moment of Creation. This primordial field can only interact with itself, as no other field exists, contrasting with the Standard Model of Particle Physics in which each elementary particle is an excitation in its own quantum field. The primordial field theory of quantum gravity has produced a model of a fermion with a mass gap, ½-integral spin, discrete charge, and magnetic moment. The mass gap is based on an existence theorem that is anchored in Yang-Mills, while Calabi-Yau anchors ½-integral spin, with charge and magnetic moment based on duality. Based on N-windings, this work is here extended to encompass fractional charge, with the result applied to quarks, yielding fermion mass and charge in agreement with experiment and novel size correlations and a unique quantum gravity-based ontological understanding of quarks.

Quantum Gravity Based on Generalized Thermodynamics

This paper proposes a novel approach and simplified model of Quantum Gravity based on the unification framework of Generalized Thermodynamics which suggests cross-related terms and modified equations of General Relativity and Quantum Mechanics. To address the “background problem”, a metric tensor is introduced into stationary Schrödinger equations via curved coordinates yielding quantum spacetime variation term. Then quantum Lagrangian is added to Einstein-Hilbert functional yielding quantum stress-energy tensor. Obtained from one variational principle, two theories are linked by a common quantum spacetime field. The theory offers some interpretations of the quantum vacuum spacetime fluctuations, zero-point-fields, quantum fields shifting towards high spacetime densities, the quantum nature of spacetime, and black hole singularity.

Ontology of Quantum Gravity

A theory of Quantum Gravity based on Primordial Field Theory is applied to a fundamental particle, the neutron. The result is compared to the current quantum description of the neutron bouncing in a gravitational field. Our quantum gravity theory yields results in agreement with the Q-bounce experimental data, but ontologically different from quantum mechanics. The differences are summarized and imply that this experiment on a fundamental particle has the potential to radically alter the ontology of field theory.

Loop Quantum Gravity Harmonic Oscillator

Attempts to unify Gravity Theory and Quantum Field Theory (QFT) under Loop Quantum Gravity Theory (LQG), are diverse;a dividing line between classical and quantum is sought with Schrödinger cat-state experiments. A Primordial Field Theory-based alternative is presented, and a gravity-based harmonic oscillator developed. With quantum theory applied at micro-scales and gravity theory at meso- and macro-scales, this scale-gap contributes to the conceptual problems associated with Loop Quantum Gravity. Primordial field theory, spanning all scales, is used to conceptually stretch key ideas across this gap. An LQG interpretation of the wave function associated with the oscillator is explained.

Counting the Microstates at the Black Hole Horizon and the Immirzi Parameter of Loop Quantum Gravity

Motivated by Bekenstein’s original thought that led him to his famous area-entropy formula for a black hole and by our recent study regarding the black hole dynamics, we identify the appropriate microscopic degrees of freedom in loop quantum gravity that are responsible for the black hole entropy. We achieve consistent results by taking the j = 1/2 edges as dominant and by subjecting these edges to experience quantum fluctuations at the horizon. This also leads to a modification of the value of the Immirzi parameter in the SU(2) framework.

Quantum Gravity, Constant Negative Curvatures, and Black Holes

For purposes of quantization, classical gravity is normally expressed by canonical variables, namely the metric and the momentum . Canonical quantization requires a proper promotion of these classical variables to quantum operators, which, according to Dirac, the favored operators should be those arising from classical variables that formed Cartesian coordinates;sadly, in this case, that is not possible. However, an affine quantization features promoting the metric and the momentric to operators. Instead of these classical variables belonging to a constant zero curvature space (i.e., instead of a flat space), they belong to a space of constant negative curvatures. This feature may even have its appearance in black holes, which could strongly point toward an affine quantization approach to quantize gravity.

The Unification of Classical and Quantum Gravity

The favored classical variables that are promoted to quantum operators are divided into three sets that feature constant positive curvatures, constant zero curvatures, as well as constant negative curvatures. This list covers the spin variables, the canonical variables, and the affine variables, and these three topics will be briefly reviewed. In this discussion, appropriate coherent states are introduced which are the principal items that are critical in the unification of relevant classical and quantum realms. This analysis can also serve to unify classical gravity and quantum gravity without any speculative aspects.

Maximum Momentum,Minimal Length and Quantum Gravity Effects of Compact Star Cores

Based on the generalized uncertainty principle with maximum momentum arid minimal length, we discuss the equation of state of ideal ultra-relativistic Fermi gases at zero temperature. Maximum momentum avoids the problem that the Fermi degenerate pressure blows up since the increase of the Fermi energy is not limited. Applying this equation of state to the Tolman-Oppenheimer Volkoff （TOV） equation, the quantum gravitational effects on the cores of compact stars are discussed. In the center of compact stars, we obtain the singularity-free solution of the metric component, gtt ～-（1 ＋ 0.2185×r^2）. By numerically solving the TOV equation, we find that quantum gravity plays an important role in the region r～10^4α0（△x）min. Current observed masses of neutron stars indicate that the dimensionless parameter α0 cannot exceed 10^19.

A Simple Factor in Canonical Quantization Yields Affine Quantization Even for Quantum Gravity

Canonical quantization (CQ) is built around [Q, P] = iħ1l , while affine quantization (AQ) is built around [Q,D] = iħQ, where D ≡ (PQ +QP) / 2 . The basic CQ operators must fit -∞ < P, Q < ∞ , while the basic AQ operators can fit -∞ < P < ∞ and 0 < Q < ∞ , -∞ < Q < 0 , or even -∞ < Q ≠ 0 < ∞ . AQ can also be the key to quantum gravity, as our simple outline demonstrates.

(4 + 4)-Dimensional Space-Time as a Dual Scenario for Quantum Gravity and Dark Matter

In this work, we make a number of proposals to explain how a world of (4 + 4)-dimensions can be useful for a better understanding of both dark matter and quantum gravity. The key idea is to look for some advantage of considering self-dual invariants in (4 + 4)-dimensions rather than in a separate context of (1 + 3)-dimensions or (3 + 1)-dimensions. In fact, we show that by considering the duality concept in (4 + 4)-dimensions we may provide an alternative meaning of a framework for loop quantum gravity. Moreover, considering the Dirac equation in (4 + 4)-dimensions for a particle without electric charge and mass, we show that when it is projected into the (1 + 3) and (3 + 1)-worlds may describe a system with electric charge and mass. We also discuss the relation between the three physical scenarios;(4 + 4)-world, black-holes and dark matter.

Why Geometry Radiates: Quantum Gravity as Perspective

It is reasonably expected 1) that a theory of quantum gravity will unify the extremes of scale currently described by General Relativity and quantum mechanics, and 2) that black holes are the crucible from which a theory of quantum gravity will emerge. In perspective, we already have a mechanism that links the local, macroscopic frame with the remote, apparently microscopic frame. A simple mathematical principle acts as a limit on D(n), suggesting a “maximum physical reality”, and that effects which are clearly perspectival at D=3 become “more real” (effectively observer-independent) with each D(n) increment. The model suggests alternative interpretations of gravitation and the quantum, entanglement, space, the Standard Model of particles and interactions, black holes, the measurement problem and the information paradox.

Spontaneous Quantum Gravity

This article gives an elementary account of the recently proposed theory of spontaneous quantum gravity. It is argued that a viable quantum theory of gravity should be falsifiable, and hence it should dynamically explain the observed absence of quantum superpositions of space-time geometries in its classical limit.

Quantum Gravity

Quantum gravitational theory, based on the hypothesis of the absolute reference system, reveals the function of the effects of the gravitational field at the microscopic and macroscopic scale. The quantum nature of gravitational potential, and the dynamics and kinetic energy of photons and elementary particles under the influence of the gravitational field are studied, and a quantum interpretation of gravitational redshift is given. There is also a complete agreement of this quantum gravitational theory with the existing experimental data.

A Way to Quantum Gravity

We present a simple way to approach the hard problem of quantization of the gravitational field in four-dimensional space-time, due to non-linearity of the Einstein equations. The difficulty may be overcome when the cosmological constant is non-null. Treating the cosmological contribution as the energy-momentum of vacuum, and representing the metric tensor onto the tetrad of its eigenvectors, the corresponding energy-momentum and, consequently, the Hamiltonian are easily quantized assuming a correspondence rule according to which the eigenvectors are replaced by creation and annihilation operators for the gravitational field. So the geometric Einstein tensor, which is opposite in sign respect to the vacuum energy-momentum (plus the possible known matter one), is also quantized. Physical examples provided by Schwarzschild-De Sitter, Robertson-Walker-De Sitter and Kerr-De Sitter solutions are examined.

Up-to-constants comparison of Liouville first passage percolation and Liouville quantum gravity

Liouville rst passage percolation(LFPP)with the parameterξ>0 is the family of random distance functions{D_(h)^(ϵ)}ϵ>0 on the plane obtained by integrating e^(ξh),along paths,where{h_(ϵ)}ϵ>0 is a smooth molli cation of the planar Gaussian free eld.Recent works have shown that for allξ>0,the LFPP metrics,appropriately re-scaled,admit non-trivial subsequential limiting metrics.In the caseξ<ξcrit≈0.41,it has been shown that the subsequential limit is unique and de nes a metric onγ-Liouville quantum gravity(LQG)γ=γ(ξ)2(0,2).We prove that for allξ>0,each possible subsequential limiting metric is nearly bi-Lipschitz equivalent to the LFPP metric D_(h)^(ϵ)whenϵis small,even ifϵdoes not belong to the appropriate subsequence.Using this result,we obtain bounds for the scaling constants for LFPP which are sharp up to polylogarithmic factors.We also prove that any two subsequential limiting metrics are bi-Lipschitz equivalent.Our results are an input in subsequent works which shows that the subsequential limits of LFPP induce the same topology as the Euclidean metric whenξ=ξ_(crit)and that the subsequential limit of LFPP is unique whenξ≥ξcrit.

A Number Theoretic Analysis of the Enthalpy, Enthalpy Energy Density, Thermodynamic Volume, and the Equation of State of a Modified White Hole, and the Implications to the Quantum Vacuum Spacetime, Matter Creation and the Planck Frequency

In this paper, we analyze the enthalpy, enthalpy energy density, thermodynamic volume, and the equation of state of a modified white hole. We obtain new possible mathematical connections with some sectors of Number Theory, Ramanujan Recurring Numbers, DN Constant and String Theory, that enable us to extract the quantum geometrical properties of these thermodynamic equations and the implication to the quantum vacuum spacetime geometry of our early universe as they act as the constraints to the nature of quantum gravity of the universe.

Upsilon Constants and Their Usefulness in Planck Scale Quantum Cosmology

This paper introduces the two Upsilon constants to the reader. Their usefulness is described with respect to acting as coupling constants between the CMB temperature and the Hubble constant. In addition, this paper summarizes the current state of quantum cosmology with respect to the Flat Space Cosmology (FSC) model. Although the FSC quantum cosmology formulae were published in 2018, they are only rearrangements and substitutions of the other assumptions into the original FSC Hubble temperature formula. In a real sense, this temperature formula was the first quantum cosmology formula developed since Hawking’s black hole temperature formula. A recent development in the last month proves that the FSC Hubble temperature formula can be derived from the Stephan-Boltzmann law. Thus, this Hubble temperature formula effectively unites some quantum developments with the general relativity model inherent in FSC. More progress towards unification in the near-future is expected.

The Quantum Microverse: A Prime Number Framework for Understanding the Universe

This study aims to demonstrate a proof of concept for a novel theory of the universe based on the Fine Structure Constant (α), derived from n-dimensional prime number property sets, specifically α = 137 and α = 139. The FSC Model introduces a new perspective on the fundamental nature of our universe, showing that α = 137.036 can be calculated from these prime property sets. The Fine Structure Constant, a cornerstone in Quantum Electrodynamics (QED) and Quantum Chromodynamics (QCD), implies an underlying structure. This study identifies this mathematical framework and demonstrates how the FSC model theory aligns with our current understanding of physics and cosmology. The results unveil a hierarchy of α values for twin prime pairs U{3/2} through U{199/197}. These values, represented by their fraction parts α♊ (e.g., 0.036), define the relative electromagnetic forces driving quantum energy systems. The lower twin prime pairs, such as U{3/2}, exhibit higher EM forces that decrease as the twin pairs increase, turning dark when they drop below the α♊ for light. The results provide classical definitions for Baryonic Matter/Energy, Dark Matter, Dark Energy, and Antimatter but mostly illustrate how the combined α♊ values for three adjacent twin primes, U{7/5/3/2} mirrors the strong nuclear force of gluons holding quarks together.

Tunneling of massive vector particles under influence of quantum gravity

This study set out to investigate charged vector particles tunneling via horizons of a pair of accelerating rotating charged NUT black holes under the influence of quantum gravity.To this end,we use the modified Proca equation incorporating generalized uncertainty principle.Applying the WKB approximation to the field equation,we obtain a modified tunneling rate and the corresponding corrected Hawking temperature for this black hole.Moreover,we analyze the graphical behavior of the corrected Hawking temperature T'_H with respect to the event horizon for the given black hole.By considering quantum gravitational effects on Hawking temperatures,we discuss the stability analysis of this black hole.For a pair of black holes,the temperature T'_H increases with the increase in rotation parameters a andω,correction parameterβ,black hole acceleration a,and arbitrary parameter k,and decreases with the increase in electric e and magnetic charges g.