Large number hypothesis

Dirac's large number hypothesis (LNH) and the Whitrow-Randall-Sciama relation are related to some cosmological models. The LNH and Whitrow-Randall-Sciama relations are neither equivalent nor consistent in general relativity, but they may both be valid in the Brans-Dicke theory and in another theory considered in this paper.     

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.     

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.     

Cosmological consequences of the particle-antiparticle gravitational repulsion hypothesis: the Newtonian model of the universe

The model of the gravitationally neutral Universe (GNU), i.e., a giant but finite 3D Ball expanding in the infinite static Euclidean space, is considered. The model is based on the antigravitation between particles and antiparticles. The GNU Ball is filled equally by matter and antimatter clusters and freely expands after epochs of partial annihilation and recombination. The abandonment of the cosmological principle and the problem of our Galaxy position in the GNU Ball are discussed.     

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.     

Noether symmetry approach in matter-dominated cosmology with variable G and Λ

In the framework of renormalization-group improved cosmologies, we use the Noether symmetry approach to get exact and general integration of the matter-dominated cosmological equations. This is performed by using an expression of Λ = Λ (G) determined by the method itself. We also work out a comparison between such a model and the concordance ΛCDM model as to the magnitude–redshift relationship, hence showing that no appreciable differences occur.     

Large numbers hypothesis and Whitrow-Randall-Sciama relation in Brans-Dicke theory

It has recently been suggested in Brans-Dicke theory that the so-called Whitrow-Randall-Sciama relation plus the assumption of a constant deceleration parameter implies the large numbers hypothesis. It is shown that this claim is not always true.     

Large numbers hypothesis. I. Classical formalism

A self-consistent formulation of physics at the classical level embodying Dirac’s large numbers hypothesis (LNH) is developed based on units covariance. A scalar “field”ϕ (x) is introduced and some fundamental results are derived from the resultant equations. Some unusual properties ofϕ are noted such as the fact thatϕ cannot be the correspondence limit of a normal quantum scalar field. Presented at the Dirac Symposium, Loyola University, New Orleans, May 1981. NAS-NRC Senior Research Fellow 1981–1982.     

Large numbers hypothesis. II. Electromagnetic radiation

This paper develops the theory of electromagnetic radiation in the units covariant formalism incorporating Dirac's large numbers hypothesis (LNH). A direct field-to-particle technique is used to obtain the photon propagation equation which explicitly involves the photon replication rate. This replication rate is fixed uniquely by requiring that the form of a free-photon distribution function be preserved, as required by the 2.7 K cosmic radiation. One finds that with this particular photon replication rate the units covariant formalism developed in Paper I actually predicts that the ratio of photon number to proton number in the Universe varies ast ^1/4 precisely in accord with LNH. The cosmological red-shift law is also derived and it is shown to differ considerably from the standard form ofνR = const.     

Steering the universe

We discuss the present status of the Cauchy problem for Einstein's classical field theory of gravity.     

Measuring the universe

When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the Pareto distribution. Power laws appear widely in physics, biology, earth and planetary sciences, economics and finance, computer science, demography and the social sciences. For instance, the distributions of the sizes of cities, earthquakes, forest fires, solar flares, moon craters and people's personal fortunes all appear to follow power laws. The origin of power-law behaviour has been a topic of debate in the scientific community for more than a century. Here we review some of the empirical evidence for the existence of power-law forms and the theories proposed to explain them.     

Scalar field fluctuations in the expanding universe and the new inflationary universe scenario

The behaviour of the scalar fied fluctuations in the exponentially expanding universe and their role in the new inflationary universe scenario are investigated.     

Republication of: Large number coincidences and the anthropic principle in cosmology

This is a reprinting of the paper by Brandon Carter, first published in a little-known volume of conference proceedings in 1974, that moved the anthropic principle from the realm of philosophical speculations to the subject of theoretical physics. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by George Ellis.     

Large boson number IBM calculations and their relationship to the Bohr model

Recently, the SO(5) Clebsch-Gordan (CG) coefficients up to the seniority v _max = 40 were computed in floating point arithmetic (T.A. Welsh, unpublished (2008)); and, in exact arithmetic, as square roots of rational numbers (M.A. Caprio et al., to be published in Comput. Phys. Commun.). It is shown in this paper that extending the QQQ model calculations set up in the work by D.J. Rowe and G. Thiamova (Nucl. Phys. A 760, 59 (2005)) to N = v _max = 40 is sufficient to obtain the IBM results converged to its Bohr contraction limit. This will be done by comparing some important matrix elements in both models, by looking at the seniority decomposition of low-lying states and at the behavior of the energy and B(E2) transition strengths ratios with increasing seniority.     

Large numbers hypothesis: Reply to a paper by Beesham

We discuss a recent paper by Beesham, showing that his criticism of an article by Berman is based on a contradiction, though his arguments are interesting.