Radius Of Universe Research Articles

The Changing Dynamics of a Universe in Transition

It is shown in this paper that the distorted space model of matter can describe a universe transitioning between conception and an open-ended finality. We use the verbiage “distorted” to communicate the concept of “energetic-manifold-warping” and to distinguish “spatial-warping” from “classical matter-warping”, although the concept of “matter” is in fact, in the present “distorted-geometry” context, the “geometric distortion energy” of the spatial manifold itself without a classical “matter stress-energy source”. An energy conserving alternative to black-body radiation-emission structural-modeling is manifest as an energetically unstable Universe (an originally stable but subsequently collapsing state, followed by an explosive expansion, thereby exhibiting an energy-creation process of one day!). The energy transition dynamics are described for a spherical, gravitational, and electromagnetic, geometrically-based mimic of matter existing at quantitative measures of a size challenging observation, that is, at a calculated Universe (gravitational body) [Formula: see text][Formula: see text]m and [Formula: see text][Formula: see text]J. The Universe (electromagnetic body) radius is calculated [Formula: see text][Formula: see text]m. We have modeled the structure with a composite, two-component, geometric-coupling_constant and initial structural conditions representing Friedmann’s critical density, [Formula: see text]_critical energy-density (8.898(–10)[Formula: see text][Formula: see text]J/m3) for the gravitational energy-density and [Formula: see text]_electron (8.7(10)[Formula: see text][Formula: see text]J/m3)[Formula: see text][Formula: see text][Formula: see text]the [Formula: see text]_critical energy-density for the geometric-electromagnetic extremum; the geometric extrema are curvature and energy-density extrema. A collapsing initial-phase-1 state, posited as a Friedmann-defined, distorted-geometry (DG) configuration with two equal-energy species or energy-density states, transitions electromagnetically, via an intermediate “mediator or force carrier” state (a W-boson structure in beta-decay), to a final 3-component state (ala a mimic of the beta decay transition process).

Unified cosmological scale versus Planck scale: As above, so below!

We will demonstrate that the mass (equivalent mass) of the observable universe divided by the universe radius is exactly identical to the Planck mass divided by the Planck length. This only holds true in the Haug universe model that takes into account Lorentz’s relativistic mass, while in the Friedmann model of the universe, the critical mass of the universe divided by the Hubble radius is exactly equal tomp/(2lp). Furthermore, in a recently suggested quantum gravity model, the mass of the universe divided by the radius of the universe is exactly identical tomp/lp; that is, the Planck mass divided by the Planck length. This is much more than just a speculative approximation, for the findings are consistent with a new unified quantum gravity theory that links the cosmological scale directly to the Planck scale.

A Possible Way to Unify Four Types of Interactions: Gravitational, Electromagnetic, Nuclear and Electroweak Interactions by using a Hydrodynamic Analogy

A principle of equivalence and a unique particle are used for a possible unification of four types of interaction. For gravity, the hydrodynamic analog consists of the interaction of two sources, giving attraction for both emission and absorption. For electromagnetics, sources and vortices are used together with the formula Biot-Savart- Laplace. For nuclear forces, the HD equivalent of pi-mesons (Yukawa) is given. As electroweak interaction, the beta decay for neutron and proton via their quark structure is considered. The unique connecting particle used is called HD-graviton, a photon-like particle having the wave length of the Universe radius at a certain age of the Universe.

Calculating the Cosmological Constant, and a Minimal Time Step, for Our Present Universe. In Fidelity to the Topics Spoken as a Presenter in the Zeldovich 4 Conference, September 11, 2020

The following is a rendition of what was presented by the author, September 11, 2020 in the DE section of that conference. The topics, while not original, are in strict fidelity with the topics the author was allowed to present in ICRANET Zeldovich 4, 2020. We present a history of the evolution of the cosmological constant “issue” starting with its introduction by Einstein for a static universe, which did not work out because his static universe solution to the Ricci Scalar problem, and GR was and is UNSTABLE. Another model of the cosmological constant has a radius of the Universe specified which is proportional to one over the square root of the cosmological constant, whereas our idea is to use the matching of two spacetime first integrals, for isolating a nonperturbative cosmological constant solution right at the surface of the start of expansion of the universe, i.e. a phenomenological solution to the cosmological constant involves scaling of a radius of the PRESENT universe. Our presented idea is to instead solve the Cosmological constant at the surface of the initial space-time bubble, using the initially derived time step, delta t, as input for the Cosmological constant. As it is, the Zeldovich 4 Section I was in was for Dark Energy, so in solving the initial value of the Cosmological constant, I am giving backing to one of the models of DE as to why the Universe reaccelerates one billion years ago. We conclude as to a reference to a multiverse generalization of Penrose Cyclic Conformal Cosmology as input into the initial nonsingular space-time bubble.

Minimum Time Transition Between Quantum States in Gravitational Field

Here it is started with the proportionality between Planck’s and related gravitational parameters. Using the ratio between Planck mass and related minimal gravitational radius (half of Planck length) we obtain maximal radial density (kg/m) in gravitational field. On the other hand, minimal radial density one obtains using the ratio between Planck mass and related maximal radius in gravitational field. It is based on new Relativistic Alpha Field Theory (RAFT) that predicts the existence of minimal and maximal gravitational radius in a gravitational field. Thus, no singularity at the minimal gravitational radius and no infinity at the maximal gravitational radius. It is shown that the maximal radial density is constant and is valid for all amounts of masses. Also, minimal radial density is constant and is valid for all amounts of masses. Using Planck parameters, it is calculated the energy conservation constant <i>k </i>= 0.999934. Since this constant is less from unity and grater from zero, the minimal gravitational radius cannot be zero (no singularity in a gravitational field) and maximal gravitational radius cannot be infinitive (no infinity in gravitational field). Here quantization of a gravitational field is based on the multiplication of the minimal gravitational length (twice of minimal radius) by parameter n =1, 2,… The calculation of the minimum time transition between two quantum state for the proton gives 0.413466×10^-62 seconds. The minimal expansion time from minimal to maximal radius of proton is equal to 1.253992×10^-58 sec. This is in accordance with recently observation, revealing nano big bang: the first millisecond of crystal formation. The calculation of the minimum time transition between two quantum state for Universe is 13.948503×10⁹ years. The minimal expansion time from minimal to maximal radius of Universe is equal to 422,151.136168×10⁹ years. Previous calculation is based on the velocity equal to the speed of light. Since the real transition velocity is less than the speed of light, the real transition and expansion times are greater compare to the previous calculation. Following the previous results, one can understand why the quantum approach has only sense for the small mases i.e. particles.

Electrodynamics in Fock–Lorentz linear fractional relativity

In this paper, we have explored the effect of Fock–Lorentz linear fractional relativity on the electrodynamics laws, where the radius of universe [Formula: see text] emerges as a consequence in the new formulation of Fock’s transformation. By employing the Dirac Hamiltonian analysis scheme, we have studied the case of the free particle, as well as the charged particle in presence of an external electromagnetic field in the new deformed phase space “[Formula: see text]-Minkowski.” The Lorentz force is obtained up to the first-order [Formula: see text]. Furthermore, we have discussed the modified form of Leinard–Wiechart potentials.

3a-D-1 宇宙の大半径とタイムトロンのリトルパン実験

3a-D-1 宇宙の大半径とタイムトロンのリトルパン実験

The Trifold Universe

This paper studies a new concept called universal folding. The visible universe is the result of a complex invisible folding series. There are three major folds (Trifold): from the Plank length, to the radius of an electron, and finally, to the radius of universe. Each of the three-major folds follows the same folding formula. Our findings help us understand the grand architecture of the universe. The ideal average human height, city block size, city size, diameter of the continents, the diameter of the Sun, the distance between the Earth and the Sun, the radius of the solar system, the radius of the Milky Way galaxy, the average diameter of the filament of the universe, and the radius of the universe are important resonance lengths in the formula. This paper helps scientists study everything from a new angle and become aware of the architectural design of the universe.

Pathologies of van Stockum dust/Tipler’s time machine

We study the internal solution, and external vacuum solution for radial cutoff, of “van Stockum dust”, an infinitely long rotating pressureless dust column; its density increases with radius. This interesting but poorly explored spacetime turns out to have a number of exotic properties, especially in the external vacuum region. These solutions have been known for decades, but it seems that they have never been investigated in detail. In this paper we analyze them and describe their peculiar properties. There are three regimes of radial cutoff that are of interest: (1) If the dust column is thick enough that closed timelike loops (CTLs or “time machines”) exist inside the column, then the radius of the entire “universe” is finite, and in fact does not extend much beyond the edge of the matter, even though the metric’s radial parameter is unbounded. This interesting finite proper radius seems to have been missed by earlier investigators. Other exotic properties of the external vacuum in this regime: CTLs exist in cylindrical shells, alternating with shells having no circular CTLs; there are infinitely many such shells, getting closer and closer together as one gets farther from the rotation axis. Also, a separate set of infinitely many cylindrical shells exists, having what might be termed “extreme frame-dragging”, within which motion is possible only in one direction; they alternate with “normal” shells allowing motion in either direction. Gravitational attraction and tides increase with distance from the matter column, and diverge at the “edge of the universe”. In addition, though the radius of the universe is finite, its circumference is infinite; and its boundary is a circle, not a cylinder (the z-axis has shrunk to nothing at the edge). (2) For smaller radial cutoff, but still large enough to produce CTLs, the radius of the universe is infinite; but there are still infinitely many cylindrical shells of CTLs alternating with non-CTL shells. However, the innermost shell begins substantially outside the dust, making this solution even stranger—you have to back away from the matter to find a CTL! And, regardless of how far away you are, there are still infinitely many CTL shells beyond you, the closest only a finite distance away. (3) For radial cutoff too close to produce CTLs, the external solution is more benign; nearby it perhaps approximates that of a finite rotating rod. But “planes” of constant z approach each other at large radii, so that any two enclose a shape somewhat like two pie-pans facing each other and glued together at their edges.

From Fock’s transformation to de Sitter space

As with Deformed Special Relativity, we showed recently that the Fock coordinate transformation can be derived from a new deformed Poisson brackets. This approach allowed us to establish the corresponding momentum transformation that keeps invariant the four-dimensional contraction pμxμ. From the resulting deformed algebra, we construct the corresponding first Casimir. After first quantization, we show by using the Klein–Gordon equation that the space-time of the Fock transformation is the de Sitter one. As we will see, the invariant length representing the universe radius in the space-time of Fock’s transformation is exactly the radius of the embedded hypersurface representing the de Sitter space-time.

Programming a Planck Universe Black-Hole CMB and the Cosmological Constant, a Simulation Hypothesis

1 method of Planck scale Simulation Hypothesis modeling has the programmer God using geometrical objects for the base units such that particle to particle interactions result from geometrical imperatives. Described in this article is a method for programming the cosmic microwave background parameters at the Planck scale. A Planck size micro black-hole is defined as the minimum discrete entity and comprises the Planck units. The simulation clock-rate is measured in units of Planck time whereby for each unit of time a 4-axis hypersphere (the universe space) expands by 1 Planck step which constitutes the addition to the sum universe of a micro black-hole. This constant expansion is the origin of the speed of light. The mass-space parameters increment linearly, the electric parameters in a sqrt-progression, thus for electric parameters the early universe transforms most rapidly. The velocity of expansion is constant and is the origin of the speed of light, the Hubble constant becomes a measure of the universe radius and the CMB radiation energy density correlates to the Casimir force. A peak frequency of 160.2GHz correlates to a 14.624 billion year old universe (sans-particles). The cosmological constant, being the age when the simulation reaches the limit, approximates $t$ = 10$^{123} t_p$.

Steady Flow cosmological model

The possibility that the cosmological constant is decaying as the observable universe grows is explored, and we define a cosmological parameter, depending of the vacuum energy and the universe radius, which should be presently ca. 122 orders of magnitude smaller than at the Planck epoch. From it, a new version of the Friedmann equation for a flat universe is obtained, which allows the estimation of the Hubble parameter at any epoch and the reconstruction of the expansion history. The main result is a quasi-linear expansion dynamics in concurrence with a number of previous works. This behavior is compatible with the main features of observational cosmology and avoids the horizon, flatness, cosmological constant, coincidence and age problems without the need of neither inflation nor initial fine-tuning.

VACUUM FLUCTUATION FORCE ON A RIGID CASIMIR CAVITY IN DE SITTER AND SCHWARZSCHILD–DE SITTER SPACE–TIME

We investigate the net force on a rigid Casimir cavity generated by vacuum fluctuations of electromagnetic field in three cases: de Sitter space–time, de Sitter space–time with weak gravitational field and Schwarzschild–de Sitter space–time. In de Sitter space–time the resulting net force follows the square inverse law but unfortunately it is too weak to be measurable due to the large universe radius. By introducing a weak gravitational field into the de Sitter space–time, we find that the net force can now be split into two parts, one is the gravitational force due to the induced effective mass between the two plates and the other one is generated by the metric structure of de Sitter space–time. In order to investigate the vacuum fluctuation force on the rigid cavity under strong gravitational field, we perform a similar analysis in Schwarzschild–de Sitter space–time and results are obtained in three different limits. The most interesting one is when the cavity gets closer to the horizon of a blackhole, square inverse law is recovered and the repulsive force due to negative energy/mass of the cavity now has an observable strength. More importantly the force changes from being repulsive to attractive when the cavity crosses the event horizon, so that the energy/mass of the cavity switches the sign, which suggests the unusual time direction inside the event horizon.

PRECESSION AND CHAOS IN THE CLASSICAL TWO-BODY PROBLEM IN A SPHERICAL UNIVERSE

We generalize the classical two-body problem from flat space to spherical space and realize much of the complexity of the classical three-body problem with only two bodies. We show analytically, by perturbation theory, that small, nearly circular orbits of identical particles in a spherical universe precess at rates proportional to the square root of their initial separations and inversely proportional to the square of the universe's radius. We show computationally, by graphically displaying the outcomes of large open sets of initial conditions, that large orbits can exhibit extreme sensitivity to initial conditions, the signature of chaos. Although the spherical curvature causes nearby geodesics to converge, the compact space enables infinitely many close encounters, which is the mechanism of the chaos.

Dirac's aether in curved spacetime.

Proca's equations for two types of fields in a Dirac's aether with electric conductivity sigma are solved exactly. The Proca electromagnetic fields are assumed with cylindrical symmetry. The background is a static, curved spacetime whose spatial section is homogeneous and has the topology of either the three-sphere S 3 or the projective three-space P 3. Simple relations between the range of Proca field lambda, the Universe radius R, the limit of photon rest mass mgamma and the conductivity sigma are written down.

2 + 1 kinematical expansions: from Galilei to de Sitter algebras

Expansions of Lie algebras are the opposite process of contractions. Starting from a Lie algebra, the expansion process goes to another one, non-isomorphic and less abelian. We propose an expansion method based in the Casimir invariants of the initial and expanded algebras and where the free parameters involved in the expansion are the curvatures of their associated homogeneous spaces. This method is applied for expansions within the family of Lie algebras of 3d spaces and (2+1)d kinematical algebras. We show that these expansions are classed in two types. The first type makes different from zero the curvature of space or space-time (i.e., it introduces a space or universe radius), while the other has a similar interpretation for the curvature of the space of worldlines, which is non-positive and equal to $-1/c^2$ in the kinematical algebras. We get expansions which go from Galilei to either Newton--Hooke or Poincar\'e algebras, and from these ones to de Sitter algebras, as well as some other examples.

A low matter density decaying vacuum cosmology from a complex metric

A low matter density decaying vacuum cosmology is proposed on the assumption that the universe's radius is a complex quantity if it is regarded as having a zero energy - momentum tensor. But we find that when the radius is real, it contains matter. Using the Einstein - Hilbert action principle, the physical scale factor is obtained as equal to with representing the finite radius of the universe at t = 0. The resulting physical picture is roughly a theoretical justification of the old Ozer - Taha model. The new model is devoid of all cosmological problems. In particular, it confirms the bounds on , the present value of the Hubble parameter: and faces no age problem. We argue that the total energy density consists of parts corresponding to relativistic/non-relativistic matter, a positive vacuum energy, a negative energy and a form of matter with equation of state (textures or generally K-matter), and the following predictions are made for the present non-relativistic era: , , , where a parameter corresponding to K-matter is taken to be unity. It is shown that spacetime with a complex metric has signature changing properties. Using quantum cosmological considerations, it is shown that the wavefunction is peaked about the classical contour of evolution and the minimum radius of the non-singular model is predicted as comparable with the Planck length.

A modified Ozer-Taha type cosmological model

A modified version of the Ozer and Taha nonsingular cosmologicla model is presented on the assumption that the universe's radius is complex if it is regarded as empty, but it contains mattar when the radius is real. It also predicts the values: Ω M ≡ ϱ M ϱ C ≈ 4 3 , Ω V ≡ ϱ V ϱ C ≈ 2 3 and Ω − ≡ ϱ_ ϱ C ⪡ 1 in the present nonrelativistic , where ϱ M = matter density, ϱ V = vacuum energy density, ϱ_ = negative energy density and ϱ C = critical density.

Associated radius, energy and pressure of McVittie’s metric in its astrophysical application

The McVittie metric is found to suffer inherent limitations. It is shown that the radius of the metric associated to the sphere has a correct asymptotic behaviour, ala Schwarzschild at the origin and ala Robertson- Walker when the the radial coordinater approaches infinity; but for intermediate values ofr and acceptable mass values of the Schwarzschild singularity, minimum and maximum are present, both disappearing solely for mass values larger than the universe radius. Furthermore, the pressure is infinite at the Schwarzschild radius, while the energy is negative for particular values of negative universe curvature. An alternative interpretation, reverse to the purposes of the McVittie solution, hints at a metric comparable to an internal solution.

A primordial cosmological scenario and the horizon problem

The coupling of the Einstein-Hilbert Lagrangian with a conformal field in an arbitrary even dimension leads, after reduction to four dimensions, to the ordinary gravity coupled non-trivially to two scalar fields. The vacuum solutions display an initial singularity, but with an infinite proper distance between any two points of the space-time. There is an initial contraction phase followed by an expansion phase. This is a kind of ”anti-Big Bang” scenario. The coupling to a radiative fluid preserves this feature; however, the temperature of the radiative fluid is initially zero, increasing afterwards: its maximum value is related to the moment where the horizon crosses the radius of the Universe. The entropy in the three-dimensional space is inversely proportional to the volume of the internal space, and it can be very high today. We perform also a perturbative study of this model during the contraction phase. There is no explosive growth of the scalar perturbations.