scholarly journals The Gravity of the Classical Klein-Gordon Field

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 322 ◽  
Author(s):  
Piero Chiarelli
Keyword(s):  
Cosmological Constant ◽  
Mass Density ◽  
Zero Point ◽  
Gravity Equation ◽  
Space Time ◽  
Vacuum Energy Density ◽  
Tensor Density ◽  
Hydrodynamic Motion ◽  
Klein Gordon ◽  
Cosmological Effect

The work shows that the evolution of the field of the free Klein–Gordon equation (KGE), in the hydrodynamic representation, can be represented by the motion of a mass density ∝ | ψ | 2 subject to the Bohm-type quantum potential, whose equation can be derived by a minimum action principle. Once the quantum hydrodynamic motion equations have been covariantly extended to the curved space-time, the gravity equation (GE), determining the geometry of the space-time, is obtained by minimizing the overall action comprehending the gravitational field. The derived Einstein-like gravity for the KGE field shows an energy-impulse tensor density (EITD) that is a function of the field with the spontaneous emergence of the “cosmological” pressure tensor density (CPTD) that in the classical limit leads to the cosmological constant (CC). The energy-impulse tensor of the theory shows analogies with the modified Brans–Dick gravity with an effective gravity constant G divided by the field squared. Even if the classical cosmological constant is set to zero, the model shows the emergence of a theory-derived quantum CPTD that, in principle, allows to have a stable quantum vacuum (out of the collapsed branched polymer phase) without postulating a non-zero classical CC. In the classical macroscopic limit, the gravity equation of the KGE field leads to the Einstein equation. Moreover, if the boson field of the photon is considered, the EITD correctly leads to its electromagnetic energy-impulse tensor density. The work shows that the cosmological constant can be considered as a second order correction to the Newtonian gravity. The outputs of the theory show that the expectation value of the CPTD is independent by the zero-point vacuum energy density and that it takes contribution only from the space where the mass is localized (and the space-time is curvilinear) while tending to zero as the space-time approaches to the flat vacuum, leading to an overall cosmological effect on the motion of the galaxies that may possibly be compatible with the astronomical observations.

scholarly journals A TOY MODEL OF THE FIVE-DIMENSIONAL UNIVERSE WITH THE COSMOLOGICAL CONSTANT

2004 ◽  
Vol 19 (29) ◽  
pp. 5051-5084
Author(s):  
WOJCIECH TARKOWSKI
Keyword(s):  
Cosmological Constant ◽  
Zero Point ◽  
Einstein Equations ◽  
Vacuum Energy Density ◽  
Coupling Constant ◽  
Virtual Particles ◽  
A Value ◽  
Proposed Model ◽  
Intrinsic Angular Momentum ◽  
Energy Cutoff

A value of the cosmological constant in a toy model of the five-dimensional universe is calculated in such a manner that it remains in agreement with both astronomical observations and the quantum field theory concerning the zero-point fluctuations of the vacuum. The (negative) cosmological constant is equal to the inverse of the Planck length squared, which means that in the toy model the vanishing of the observed value of the cosmological constant is a consequence of the existence of an energy cutoff exactly at the Planck level. In turn, a model for both a virtual and a real particle–antiparticle pair is proposed which describes properly some energetic properties of both the vacuum fluctuations and created particles, as well as it allows one to calculate the discrete "bare" values of an elementary particle's mass, electric charge and intrinsic angular momentum (spin) at the energy cutoff. The relationships between the discussed model and some phenomena such as the Zitterbewegung and the Unruh–Davies effect are briefly analyzed, too. The proposed model also allows one to derive the Lorentz transformation and the Maxwell equations while considering the properties of the vacuum filled with the sea of virtual particles and their antiparticles. Finally, the existence of a finite value of the vacuum-energy density resulting from the toy model leads us to the formulation of dimensionless Einstein equations which may be derived from the Lagrangian with a dimensionless (naively renormalized) coupling constant.

Dark energy and dark matter as due to zero point energy

2012 ◽  
Vol 79 (3) ◽  
pp. 327-334 ◽  
Author(s):  
BO LEHNERT
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Energy Density ◽  
Vacuum Energy ◽  
Mass Density ◽  
Zero Point ◽  
Vacuum Energy Density ◽  
Zero Point Energy ◽  
Observable Universe ◽  
Point Energy

AbstractAn attempt is made to explain dark energy and dark matter of the expanding universe in terms of the zero point vacuum energy. This analysis is mainly limited to later stages of an observable nearly flat universe. It is based on a revised formulation of the spectral distribution of the zero point energy, for an ensemble in a defined statistical equilibrium having finite total energy density. The steady and dynamic states are studied for a spherical cloud of zero point energy photons. The ‘antigravitational’ force due to its pressure gradient then represents dark energy, and its gravitational force due to the energy density represents dark matter. Four fundamental results come out of the theory. First, the lack of emitted radiation becomes reconcilable with the concepts of dark energy and dark matter. Second, the crucial coincidence problem of equal orders of magnitude of mass density and vacuum energy density cannot be explained by the cosmological constant, but is resolved by the present variable concepts, which originate from the same photon gas balance. Third, the present approach becomes reconcilable with cosmical dimensions and with the radius of the observable universe. Fourth, the deduced acceleration of the expansion agrees with the observed one. In addition, mass polarity of a generalized gravitation law for matter and antimatter is proposed as a source of dark flow.

scholarly journals A Theoretical Calculation of the Cosmological Constant Based on a Mechanical Model of Vacuum

2021 ◽  
Author(s):  
Xiao-Song Wang
Keyword(s):  
Cosmological Constant ◽  
Mass Density ◽  
Zero Point ◽  
Momentum Tensor ◽  
Einstein’S Equations ◽  
Field Equations ◽  
Cosmological Constant Problem ◽  
Metric Tensor ◽  
Point Energy ◽  
Einstein's Equations

We suppose that vacuum is filled with a kind of continuously distributed matter, which may be called the $\Omega(1)$ substratum, or the electromagnetic aether. Lord Kelvin believes that the electromagnetic aether must also generate gravity. We also suppose that vacuum is filled with another kind of continuously distributed substance, which may be called the $\Omega(2)$ substratum. Based on a theorem of V. Fock on the mass tensor of a fluid, the contravariant energy-momentum tensors of the $\Omega(1)$ and $\Omega(2)$ substratums are established. Quasi-static solutions of the gravitational field equations in vacuum are obtained. Based on an assumption, relationships between the contravariant energy-momentum tensor of the $\Omega(1)$ and $\Omega(2)$ substratums and the contravariant metric tensor are obtained. Thus, the cosmological constant is calculated theoretically. The $\Omega(1)$ and $\Omega(2)$ substratums may be a possible candidate of the dark energy. The zero-point energy of electromagnetic fields will not appear as a source term in the Einstein's equations. The cosmological constant problem is one of the puzzles in physics. Some people believed that all kinds of energies should appear as source terms in the Einstein's equations. It may be this belief that leads to the cosmological constant problem. The mass density of the $\Omega(1)$ and $\Omega(2)$ substratums is equivalent to that $31.33195$ protons contained in a box with a volume of $1.0 {m}^{3}$.

scholarly journals CPTM Discrete Symmetry, Quantum Wormholes and Cosmological Constant Problem

Universe ◽  
2020 ◽  
Vol 6 (8) ◽  
pp. 121
Author(s):  
Sergey Bondarenko
Keyword(s):  
Cosmological Constant ◽  
Discrete Symmetry ◽  
Space Time ◽  
Einstein Equations ◽  
Vacuum Energy Density ◽  
Extended Space ◽  
Classical Geometry ◽  
Proposed Model ◽  
Charge Parity ◽  
Non Local

We discuss the consequences of the charge, parity, time, and mass (CPTM) extended reversal symmetry for the problems of the vacuum energy density and value of the cosmological constant. The results obtained are based on the framework with the separation of extended space-time of the interest on the different regions connected by this symmetry with the action of the theory valid for the full space-time and symmetrical with respect to the extended CPTM transformations. The cosmological constant is arising in the model due the gravitational interactions between the different parts of the space-time trough the quantum non-local vertices. It is proposed that the constant’s value depends on the form and geometry of the vertices that glue the separated parts of the extended solution of Einstein equations determining, in turn, its classical geometry. The similarity of the proposed model to the bimetric theories of gravitation is also discussed.

scholarly journals Unified Field Theory for Electromagnetic and Gravity Fields with the Introduction of Quantized Space–Time and Zero-Point Energy

2020 ◽  
Author(s):  
Shinichi Ishiguri
Keyword(s):  
Analytical Solution ◽  
Gravity Wave ◽  
Zero Point ◽  
Gravity Equation ◽  
Space Time ◽  
Zero Point Energy ◽  
Point Energy ◽  
Gravity Fields ◽  
The Universe ◽  
Basic Configuration

In our previous papers [1,3], using only the concepts of the zero-point energy and quantized space–times, all the fields including gravity were explained. However, the previous papers had the following limitations: First, the concept of the quantized space-time must be experimentally confirmed. Second, we should clarify the meaning of the quantized Einstein’s gravity equation, which is derived in [1]. Moreover, in another paper [2], we succeeded in describing the neutrinos’ self-energy and their oscillations. However, this paper assumes the rest energy of 3-leptons in advance, which is why we needed to uncover the reason why leptons have 3-generations. As mentioned, using the concepts of the zero-point energy and quantized space–times, we derived the quantized Einstein’s gravity equation in our previous paper [1]. The paper provides an analytical solution of this equalized Einstein’s equation, which implies the conservation of angular momentum in terms of quantized space–times. Employing this solution and without the standard big bang model, a unique form of acceleration equation for the acceleration-expansion universe is derived. Moreover, the temperature of the cosmic microwave background (CMB) emission is also obtained. Further, this solution results in an analytical (not numerical) derivation of the gravity wave. Moreover, based on the configuration of quantized space–times in terms of both electric and magnetic fields, we analytically attempted to calculate every equation in terms of electromagnetic and gravity fields, using the solution of the quantized Einstein’s gravity equation. As a result of this theory, first the calculated acceleration and temperature of CMB emission agree with the measurements. Furthermore, the analytical solution of the quantized Einstein’s gravity equation resulted in all the laws of electromagnetic and gravity fields in addition to the analytically derived gravity wave, which agrees well with the recent measurements. Moreover, the calculations of the energies in the basic configuration of the quantized space–times resulted in all 3-leptons’ rest energies. Considering this basic configuration is uniformly distributed everywhere in the universe, we can conclude that τ-particles or static magnetic field energy derived from the basic configuration of the quantized space–times is the identity of dark energy, which also distributes uniformly in the universe.

scholarly journals Acceleration of cosmic expansion through huge cosmological constant progressively reduced by submicroscopic information transfer

2018 ◽  
Vol 33 (23) ◽  
pp. 1850137 ◽  
Author(s):  
E. Rebhan
Keyword(s):  
Dark Energy ◽  
Cosmological Constant ◽  
Information Transfer ◽  
Mass Density ◽  
Laws Of Nature ◽  
Initial Density ◽  
Categorical Imperative ◽  
Space Time ◽  
Expansion Velocity ◽  
Physical Laws

In a previous paper (Ref. 1), the presence of dark energy in our universe was explained as the fingerprint of a comprehensive, much older and expanding multiverse with positive spatial curvature, whose space–time is spanned by this energy, and which was created out of nothing. This concept is expanded by the addition of a model for explaining the decay of the mass density [Formula: see text] of dark energy from its origin until now by a factor of approximately [Formula: see text]. Elementary particles contain information about which laws of nature they obey, but not what exactly these are. Most likely, the laws are not followed by obedience to a categorical imperative. Rather, it is assumed, that from the very beginning the information about them is coded in submicroscopic patches of the space–time. The initial density [Formula: see text] is supposed to belong to the unimpaired cosmological constant obtained from elementary particle theory. Due to its huge value, it causes an extremely fast spatial expansion by which continuously new space–time elements are created. To them, the information about the physical laws must be transmitted from the already present space–time. This process needs time which with ever-increasing expansion velocity is getting scarcer and scarcer. It is concluded that this impedes the expansion through a friction-like process which can be described by a term proportional to the expansion velocity. This term is subtracted from the expansion acceleration. It is shown that the solutions thus obtained are also solutions of the cosmological standard equations employing a scalar field [Formula: see text]. In consequence, the present model can be considered as a reinterpretation of results which can be obtained with acknowledged methods.

Quantum fields and gravity: Expanding space-times

2020 ◽  
Vol 35 (02n03) ◽  
pp. 2040039
Author(s):  
Claudio Parmeggiani
Keyword(s):  
Energy Density ◽  
Vacuum Energy ◽  
Fock Space ◽  
Zero Point ◽  
Big Bang ◽  
Space Time ◽  
Vacuum Energy Density ◽  
Dimensional Manifold ◽  
Quantum Fields ◽  
Point Energy

We discuss a proposal for a somewhat new formulation of quantum field theory (set in a four-dimensional manifold, the space-time) that includes an analysis of its implications for the evolution of Einstein-Friedmann cosmological models. The proposed theory displays two peculiar features: (i) a local Hilbert-Fock space is associated with each space-time point: we are dealing with a vector bundle whose fibers are Hilbert spaces; the operator-valued sections of the bundle are the quantum fields; (ii) the vacuum energy density is finite, being regularized in a space-time curvature dependent way, independently at each point. In fact everything is finite: self-masses, self-charges, quantum fluctuations: they depend on the space-time curvature and diverge only for a flat metric. In an Einstein-Friedmann model the vacuum (zero-point) energy density is consequently time-dependent and in general not negligible. Then it is shown that, for some choices of the parameters of the theory, the big-bang singularity is resolved and replaced by a bounce driven by the vacuum energy density, which becomes (very) large and negative near the bounce (negative by the contribution of the Fermi fields). But for large times (now, say) the Bose fields’ positive vacuum energy eventually overcomes the negative one and we are finally left with the present vacuum energy: positive and reasonably small.

scholarly journals A Theoretical Calculation of the Cosmological Constant Based on the Theory of Vacuum Mechanics

2019 ◽  
Author(s):  
Xiao-Song Wang
Keyword(s):  
Cosmological Constant ◽  
Energy Momentum Tensor ◽  
Mass Density ◽  
Zero Point ◽  
Momentum Tensor ◽  
Einstein’S Equations ◽  
Field Equations ◽  
Metric Tensor ◽  
Point Energy ◽  
Einstein's Equations

Lord Kelvin believes that the electromagnetic aether must also generate gravity. Based on a theorem of V. Fock on the mass tensor of an elastic continuum, the contravariant energy-momentum tensor of the $\Omega(1)$ substratum is established. Quasi-static solutions of the gravitational field equations in vacuum are obtained. Based on an assumption, relationships between the contravariant energy-momentum tensor of the $\Omega(1)$ substratum and the contravariant metric tensor are obtained. Thus, the cosmological constant is derived theoretically. The $\Omega(1)$ substratum, or we say the electromagnetic aether, may be a possible candidate of the dark energy. The zero-point energy of electromagnetic fields will not appear as a source term in the generalized Einstein's equations. Some people believed that all kinds of energies should appear as source terms in the Einstein's equations. It may be this belief that leads to the so called cosmological constant problem. The mass density of the electromagnetic aether is equivalent to that $31.33195$ protons contained in a box with a volume of $1.0{m}^{3}$.

scholarly journals Casimir energy corrections by light-cone fluctuations

2014 ◽  
Vol 29 (05) ◽  
pp. 1450024 ◽  
Author(s):  
E. Arias ◽  
J. G. Dueñas ◽  
N. F. Svaiter ◽  
C. H. G. Bessa ◽  
G. Menezes
Keyword(s):  
Light Cone ◽  
Zero Point ◽  
Casimir Energy ◽  
Vacuum Energy Density ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Parallel Plates ◽  
Point Energy ◽  
Klein Gordon ◽  
Free Case

We study the effects of light-cone fluctuations on the renormalized zero-point energy associated with a free massless scalar field in the presence of boundaries. In order to simulate light-cone fluctuations, we introduce a space–time dependent random coefficient in the Klein–Gordon operator. We assume that the field is defined in a domain with one confined direction. For simplicity, we choose the symmetric case of two parallel plates separated by a distance a. The correction to the renormalized vacuum energy density between the plates goes as 1/a8 instead of the usual 1/a4 dependence for the free case. In turn, we also show that light-cone fluctuations break down the vacuum pressure homogeneity between the plates.

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