Generalized large number hypothesis and cosmological constant

By generalizing Dirac's large number hypothesis we infer that the cosmological constant varies witht ^–2, as expected from earlier studies.     

Modified large number hypothesis

In the Brans-Dicke theory, a certain large number hypothesis is equivalent implicitly to an equation of state. The equation of state corresponding to Dirac's large number hypothesis, however, is not reasonable. The Whitrow-Randall relation is regarded as a modification of Dirac's large number hypothesis, but it is not in fact in keeping with Dirac's original intention to relate only a single cosmological parameter to the gravitational constant. In view of those facts, an alternative modification of Dirac's large number hypothesis is proposed.     

Vacuum cosmological solution in a 6D universe

A simple vacuum cosmological solution that is a function ofct, Gm/c ² andeG ^1/2/C² is obtained in the 6D space-time-mass-charge universe which is proposed by Wesson [1] with the introduction of the sixth coordinate of charge in order to obtain a unified theory of gravity and electromagnetism along the line of his original 5D space-time-mass universe [2]. It reduces to a similar solution to that of the radiation era in the 4D FRW universe through the compactifications of the extra dimensions. The trajectory of a test particle in the 6D universe is also studied by using the solution.     

Cosmological principle and primordial spinor fields

An exact solution of Dirac's equation in an open Robertson-Walker universe is constructed such that the corresponding energy-momentum densityT _µv obeys the cosmological principle. However, in anopen universe, this principlemust always be violated by the other physical densities of the cosmological solution (e.g. pseudoscalar, (axial-) current and polarization). If the current densityj _µ = isrequired to obey the cosmological principle, then the universe must beflat.     

Velocity Operators and Time-Energy Relations in Relativistic Quantum Mechanics

According to both Dirac's and Kemmer's relativistic quantum theories, the eigenvalues of the velocity operator are +c and –c. This false result is avoided if certain alternative particle coordinates are adopted. Another advantage is that the new coordinates occur in additional constants of the motion. These are sui generis angular momenta obtained by taking the vector product of the nonstandard coordinates with the linear momentum. An additional virtue of the new velocity operator is that, like in classical mechanics, it is proportional to the linear momentum. Besides, the zeroth component of the new set of coordinates does not commute with the hamiltonian, which results in a genuine indeterminacy relation between time and energy.     

The principle of reciprocity

It is shown that the validity of the principle of reciprocity for arbitrary motion impiies that the rate of a moving clock departs from the (instantaneous) special relativistic value by a term -xx/2c ² wherex is the distance of the clock. Through this effect the cosmological red shift can be understood as arising from the outward acceleration of radiating atoms in galactic gravitational fields. In this way the relation (GM/2cL ²) (1/H) between Newton's constant of gravitationG, the massM and linear dimensionL of a typical galaxy and Hubble's constantH is derived. This relation is verified by present-day observations. Implications of these considerations for quasars are briefly discussed.As a possible test of this theory it is suggested that the spectra of galaxies be searched for the presence of blue-shifted lines which are expected to be fainter by three to four magnitudes in comparison with the red-shifted lines.     

Hydrodynamic vacuum sources of dark matter self-generation in an accelerating universe without a Big Bang

We have obtained a generalization of the hydrodynamic theory of vacuum in the context of general relativity. While retaining the Lagrangian character of general relativity, the new theory provides a natural alternative to the view that the singularity is inevitable in general relativity and the theory of a hot Universe. We show that the macroscopic source-sink motion as a whole of ordinary (dark) matter that emerges during the production of particles out of the vacuum can be a new source of gravitational vacuum polarization (determining the variability of the cosmological term in general relativity). We have removed the well-known problems of the cosmological constant by refining the physical nature of dark energy associated precisely with this hydrodynamically initiated variability of the vacuum energy density. A new exact solution of the modified general relativity equations that contains no free (fitting) parameter additional to those available in general relativity has been obtained. It corresponds to the continuous and metric-affecting production of ultralight dark matter particles (with mass m ₀ = (ħ/c ²) $ \sqrt {12\rho _0 k} $ \sqrt {12\rho _0 k} ≈ 3 × 10⁻⁶⁶ g, k is the gravitational constant) out of the vacuum, with its density ρ₀, constant during the exponential expansion of a spatially flat Universe, being retained. This solution is shown to be stable in the regime of cosmological expansion in the time interval −∞ < t < t _max, when t = 0 corresponds to the present epoch and t _max= 2/3H ₀ cΩ_0m ≈ 38 × 10⁹ yr at Ω_0m = ρ₀/ρ_c ≈ 0.28 (H ₀ is the Hubble constant, ρ_c is the critical density). For t > t _max, the solution becomes exponentially unstable and characterizes the inverse process of dark matter particle absorption by the vacuum in the regime of contraction of the Universe. We consider the admissibility of the fact that scalar massive photon pairs can be these dark matter particles. Good quantitative agreement of this exact solution with the cosmological observations of SnIa, SDSS-BAO, and the decrease in the acceleration of the expansion of the Universe has been obtained.     

The Cosmological constant and the coincidence problem in a new cosmological interpretation of the universal constant “c”

In a recent paper (Vigoureux et al. in Int. J. Theor. Phys. 47:928, 2007) it has been suggested that the velocity of light and the expansion of the universe are two aspects of one single concept connecting space and time in the expanding universe. It has then be shown that solving Friedmann’s equations with that interpretation (and keeping c=constant) can explain number of unnatural features of the standard cosmology (for example: the flatness problem, the problem of the observed uniformity in term of temperature and density of the cosmological background radiation, the small-scale inhomogeneity problem…) and leads to reconsider the Hubble diagram of distance moduli and redshifts as obtained from recent observations of type Ia supernovae without having to need an accelerating universe. In the present work we examine the problem of the cosmological constant. We show that our model can exactly generate Λ (equation of state P _φ =−ρ _φ c ² with Λ∝ R ⁻²) contrarily to the standard model which cannot generate it exactly. We also show how it can solve the so-called cosmic coincidence problem.     

Existence of Noncompact Static Spherically Symmetric Solutions of Einstein SU(2)-Yang–Mills Equations

We consider static spherically symmetric solutions of the Einstein equations with cosmological constant Λ coupled to the SU(2)-Yang–Mills equations that are smooth at the origin r=0. We prove that all such solutions have a radius r _c at which the solution in Schwarzschild coordinates becomes singular. However, for any positive integer N, there exists a small positive Λ _N such that whenever 0<Λ<Λ _N , there exist at least N distinct solutions for which the singularity is only a coordinate singularity and the solution can be extended to r≥r _c . Received: 5 June 2000 / Accepted: 13 March 2001     

Cosmological Post-Newtonian Expansions to Arbitrary Order

We prove the existence of a large class of one parameter families of solutions to the Einstein-Euler equations that depend on the singular parameter e = v_T/c{\epsilon=v_T/c} (0 < e < e₀){(0< \epsilon < \epsilon_0)}, where c is the speed of light, and v _T is a typical speed of the gravitating fluid. These solutions are shown to exist on a common spacetime slab M @ [0,T)×\mathbb T³{M\cong [0,T)\times \mathbb {T}^3}, and converge as e\searrow 0{\epsilon \searrow 0} to a solution of the cosmological Poisson-Euler equations of Newtonian gravity. Moreover, we establish that these solutions can be expanded in the parameter e{\epsilon} to any specified order with expansion coefficients that satisfy e{\epsilon}-independent (nonlocal) symmetric hyperbolic equations.     

The Einstein Constant c in Light of Mach's Principle. Cosmological Applications

In a recent paper, O. Costa de Beauregard shows that Mach's conjecture can be expressed by the equation U=c ² (U denoting the cosmological potential). This result leads us to a geometrical interpretation of Einstein's constant c (the so-called velocity of light) which appears as intimately connected to the expansion of the universe. We also present some cosmological consequences of that interpretation for the horizon problem, for the problem of the homogeneity of the cosmic background radiation, and for the problem of the flatness of the universe.     

“Regge-like” relations for stable (non-evaporating) black holes

Within a purely classical formulation of “strong gravity,” we associated hadron constituents (and even hadrons themselves) with suitable stationary, axisymmetric solutions of certain new Einsteintype equations supposed to describe the strong field inside hadrons. Such equations are nothing but Einstein equations—with cosmological term—suitably scaled down. As a consequence, the cosmological constant Λ and the massesM result in our theory to be scaled up, and transformed into a “hadronic constant” and into “strong masses,” respectively. Due to the unusual range of Λ andM values considered, we met a series of solutions of the Kerr-Newman-de Sitter (KNdS) type with rather interesting properties: aim of the present work is putting forth such results, while “translating” them into the more popular language of ordinary gravity. The requirement that those solutions be stable, i.e., that their temperature (or surface gravity) bevanishingly small, implies the coincidence of at least two of their (in general, three) horizons. Imposing the stability condition of a certain horizon does yield (once chosen the values ofJ, q and Λ) mass and radius of the associated black hole. In the case of ordinary Einstein equations and for stable blackholes of the KNdS type, we get in particular Regge-like relations among massM, angular momentumJ, chargeq and cosmological constant Λ; which did not receive enough attention in the previous literature. For instance, with the standard definitionsQ ² = Gq²/(4πε ₀ c ⁴), a ≡ J/(Mc), m ≡GM/c ², in the case Λ=0 in whichm ²=a²+Q² and ifq is negligible, we findm ²=J. When considering, for simplicity, Λ>0 andJ=0 (andq still negligible), then we obtainm ² = 1/(9Λ). In the most general case, the condition, for instance, of “triple coincidence” among the three horizons yields for |Λa ²|<< 1 the couple of independent relationsm ² = 2/(9Λ) andm ² = 8(a ² + Q². Another interesting point is that—with few exceptions—all such relations (amongM, J, q, Λ) lead to solutions that can be regarded as (stable) cosmological models. Work partially supported by INFN, MURST, and CNR and by CNPq, FAPESP, and CAPES.     

Theory of Gravitational-Inertial Field of Universe. IV. The Universe and the Microcosm

On basis of principle of discreteness of the space and time the following relations are obtained Λ_oM_oc = 2π?, τ_oE_o = 2π? and c² = 2GM_o/Λ_o giving the values of fundamental elements of length Λ_o ≈ (?G/c³)^1/2, mass M_o ≈ (?c/G)^1/2, time τ_o ≈ (?G/c⁵)^1/2 and energy E_o ≈ (?c⁵/G)^1/2. The geon crown of any critical system and the crown of the Universe must have a thickness equal to the fundamental length Λ_o = 2(π?G/c³)^1/2 = 5.74. 10^?33 cm. Each critical system has its specific (most probable) quantum with an average invariant mass which in the case of the Universe is equal to (2π²?H_u/Gc)^1/3 ≈ 300 m_e where H_u is Hubble's constant. There are all reasons to consider the universal virtual quanta of an invariant mass m_u ≈ 300 m_e as carriers of gravitational, electromagnetic and nuclear fields in the Universe.     

Magnetized cosmological models in bimetric theory of gravitation

Bianchi type-III magnetized cosmological model when the field of gravitation is governed by either a perfect fluid or cosmic string is investigated in Rosen’s [1] bimetric theory of gravitation. To complete determinate solution, the condition, viz., A=(BC) ⁿ , where n is a constant, between the metric potentials is used. We have assumed different equations of state for cosmic string [2] for the complete solution of the model. Some physical and geometrical properties of the exhibited model are discussed and studied.     

TIGHT MACH-STYLE CONNECTION BETWEEN THE EINSTEIN MASS-ENERGY AND INERTIA-GRAVITY EQUIVALANCES. REMARKS ON A RECENT EXPERIMENT BY MIKHAILOV

Equivalence of the two famous Einstein equivalences is, U denoting the cosmological potential, expressed à la Mach as U=c ². The electrostatic analog is induction of an extra mass –c ^–2eV (esu) in an electron immersed in the constant Coulomb potential c=Q/R enclosed in a charged sphere. This effect has been evidenced in a recent experiment by Mikhailov.     

Novel solutions of RG equations for α(s) and β(α) in the large-N c limit

A general solution of RG equations in the framework of background perturbation theory is written in the large-N _c limit. A simplified (model) approximation to the general solution is suggested that allows β(α) and α(s) to be written to any loop order. The resulting α _B (Q ²) coincides asymptotically at large |Q ²| with standard (free) α _s , saturates at small Q ²≥0, and has poles at timelike Q ² in agreement with analytic properties of physical amplitudes in the large-N _c limit.

     

Momentum transfer dependence behaviors of ionization and dissociation of oxygen

The decay pathways of the structured ionization region of oxygen at different momentum transfers,i.e.,0,0.23 a.u.(atomic unit),and 0.91 a.u.,are studied by measuring the ion and the scattered electron coincidently.It is found that the dipole-forbidden superexcited states of(2σu)-1(c4Σu-)npσu 3Σg-← X3Σg-decay into different channels according to the principal quantum number n.The broad ridge above 35 eV,which may be due to inner-valence excited states of(2σg)-1nλ or multiply excited states,is observed both at small and large momentum transfers,and its decay channel of O++ O is dominant.     

Gravitational vacuum hypothesis and cosmology with variable particle number

We discuss a heurisitic model of gravitational vacuum as a set of virtual, radiating planckeons, particles with Planck size (L) and mass (/cL). Combined with Dirac's large number hypothesis, this gives the minimum universe scale factor valuea _min10^–13 cm, the strong interaction length (a = L just whena=a _min ). Taking this state as an initial one using standard quantum techniques, we consider particle creation by planckeons. Under some reasonable assumptions we obtain the present number of particles with nucleon mass close to observations,N 10⁸⁰. A criterion for gravitational stability of particles is formulated and some applications of the corresponding mass formula are considered. In particular, Fermi's weak interaction constant is expressed in terms ofa andL and a finite value for the neutrino mass is obtained.     

Critical currents in polycrystalline thin films of high-T c superconductors

Summary It is shown that the behaviour of the temperature dependence of the critical current in polycrystalline thin films of high-T _c superconductors depends crucially on the assumption made concerning the nature of the intergranular material. The usual assumption of a superconductor-insulator-superconductor (=SIS) ?sandwich? between each grain leads to a crossover fromI _c∼(1−T/T _c) toI _c∼(1−T/T _c)^3/2, for temperatures nearT _c (whereI _c is the critical current,T the absolute temperature, andT _c the superconducting transition temperature). Instead, for a superconductor-normal metal-superconductor (=SNS) sandwich the dependenceI _c∼(1−T/T _c)² is found for all temperatures. Consideration is given to the effect of self-magnetic field on the analysis. The comparison between expressions for continuous and granular systems is extended. Due to the relevance of its scientific content, this paper has been given priority by the Journal Direction.     

The individual success of musicians, like that of physicists, follows a stretched exponential distribution

Over the last five years or so, a number of studies have focussed on the distribution of `success' in physics and other sciences; in these studies, `success' is measured by the number of times a paper, or an author, is cited. The distribution of citations of individual papers approximates to a power-law [S. Redner, Eur. Phys. J. B 4, 131 (1998)], while lifetime total citations of the 1120 most-cited physicists follows a stretched exponential [J. Laherrère, D. Sornette, Eur. Phys. J. B 2, 525 (1998)]. Here, I examine the distribution of success in popular music, a field of creativity that has social structures very different from those of physics, and which is generally held to be controlled primarily by fashion. For this study, the lifetime total success of bands was measured by the total number of weeks they were in the weekly `top 75' list of best-selling recordings. Like the lifetime success of physicists reported by Laherrere and Sornette, the success of the 6107 bands that appeared in the UK `top 75' from 1950 until 2000 follows a stretched exponential of the form P(x)dx = c(x ^{c - 1}/x ₀ ^c)exp[- (x/x ₀)^c]dx; for the music data, c = 0.5 and x ₀ = 9.37. Received 23 October 2001 Published online 25 June 2002