The Large Numbers hypothesis and the Einstein theory of gravitation

1979 ◽  
Vol 365 (1720) ◽  
pp. 19-30 ◽  
Keyword(s):  
Gravitational Theory ◽  
Conclusive Evidence ◽  
De Sitter ◽  
Dimensionless Numbers ◽  
Einstein Theory ◽  
Observable Universe ◽  
Slowing Down ◽  
Large Numbers ◽  
Theory Of Gravitation ◽  
The Universe

A study of the relations between large dimensionless numbers leads one to believe that G , expressed in atomic units, varies with the epoch. The Einstein theory requires G to be constant. One can reconcile these two requirements by supposing that the Einstein theory applies with a metric that differs from the atomic metric. The theory can be developed with conservation of mass by supposing that the continual increase in the mass of the observable universe arises from a continual slowing down of the velocity of recession of the galaxies. One is led to a model of the Universe that was first proposed jointly by Einstein & de Sitter (the E.S. model). The observations of the microwave radiation fit in with this model. The static Schwarzchild metric has to be modified to fit in with the E.S. model for large r . The modification is worked out, and also the motion of planets with the new metric. It is found that there is a difference between ephemeris time and atomic time, and also that there should be an inward spiralling of the planets, referred to atomic units, superposed on the motion given by ordinary gravitational theory. These are effects that can be checked by observation, but there is no conclusive evidence up to the present.

Atomic and gravitational metrics in cosmology

1981 ◽  
Vol 374 (1759) ◽  
pp. 447-459 ◽  
Keyword(s):  
Relativistic Cosmology ◽  
De Sitter ◽  
Einstein Theory ◽  
Large Numbers ◽  
The Standard Model ◽  
Self Consistent ◽  
The Status ◽  
Theory Of Gravitation ◽  
S Model ◽  
Do So

Using inferences from his Large Numbers hypothesis (L. N. h.) Dirac (1979) derived a cosmological model, described by an ‘atomic’ metric, that is not in agreement with the Einstein theory of gravitation. He then showed that the same model described by a different metric appears to be the Einstein–de Sitter (E. S.) universe, and thus to agree with the Einstein theory. According to the first description, relative to electromagnetic forces, gravitation becomes weaker with advancing epoch. So long as the L. N. h. is retained, we point out how this physical feature persists no matter what metric is used. Therefore Dirac’s E. S. model is observably different from that of standard relativistic cosmology. We make this explicit by writing into the calculations a ‘Coulomb’ constant to match the gravitation constant. We show how the way we do so is internally self-consistent. In the course of the work it emerges that one of the two main inferences from the L. N. h. is automatically ensured by the E. S. model, which may call for some re-examination of the status of the hypothesis. We discuss the different cosmological redshifts predicted by Dirac’s E. S. model and by the standard model.

Cosmological spacetimes

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Cosmological Model ◽  
Large Scale ◽  
Cosmic Time ◽  
De Sitter ◽  
Matter Distribution ◽  
Observable Universe ◽  
Cosmological Principle ◽  
Riemannian Spacetime ◽  
The Universe ◽  
Copernican Principle

This chapter provides a few examples of representations of the universe on a large scale—a first step in constructing a cosmological model. It first discusses the Copernican principle, which is an approximation/hypothesis about the matter distribution in the observable universe. The chapter then turns to the cosmological principle—a hypothesis about the geometry of the Riemannian spacetime representing the universe, which is assumed to be foliated by 3-spaces labeled by a cosmic time t which are homogeneous and isotropic, that is, ‘maximally symmetric’. After a discussion on maximally symmetric space, this chapter considers spacetimes with homogenous and isotropic sections. Finally, this chapter discusses Milne and de Sitter spacetimes.

scholarly journals Dynamics in Interacting Scalar-Torsion Cosmology

Universe ◽  
2021 ◽  
Vol 7 (7) ◽  
pp. 244
Author(s):  
Andronikos Paliathanasis
Keyword(s):  
Special Interest ◽  
System Analysis ◽  
Stable Solution ◽  
Gravitational Theory ◽  
De Sitter ◽  
Dark Sector ◽  
Background Space ◽  
Qualitative Evolution ◽  
De Sitter Universe ◽  
The Universe

In a spatially flat Friedmann–Lemaître–Robertson–Walker background space, we consider a scalar-torsion gravitational model which has similar properties to the dilaton theory. This teleparallel model is invariant under a discrete transformation similar to the Gasperini–Veneziano duality transformation. Moreover, in the gravitational action integral, we introduce the Lagrangian function of a pressureless fluid source which is coupled to the teleparallel dilaton field. This specific gravitational theory with interaction in the dark sector of the universe was investigated by using methods of the dynamical system analysis. We calculate that the theory provides various areas of special interest for the evolution of the cosmological history. Inflationary scaling solutions and the de Sitter universe are recovered. Furthermore, we calculate that there exist an attractor which provides a stable solution where the two fluid components, the scalar field and the pressureless matter, contribute in the cosmological fluid. This solution is of special interest because it can describe the present epoch. Finally, the qualitative evolution of the cosmographic parameters is discussed.

scholarly journals On the gravitodynamics of moving bodies

Open Physics ◽  
2011 ◽  
Vol 9 (5) ◽  
Author(s):  
Anderson Mol
Keyword(s):  
Dark Matter ◽  
Inertial Mass ◽  
Gravitational Theory ◽  
Dynamic State ◽  
Observable Universe ◽  
Energy Field ◽  
A Value ◽  
Original Works ◽  
The Universe ◽  
Moving Bodies

AbstractIn the present work we propose a generalization of Newton’s gravitational theory from the original works of Heaviside and Sciama, that takes into account both approaches, and accomplishes the same result in a simpler way than the standard cosmological approach. The established formulation describes the local gravitational field related to the observables and effectively implements the Mach’s principle in a quantitative form that retakes Dirac’s large number hypothesis. As a consequence of the equivalence principle and the application of this formulation to the observable universe, we obtain, as an immediate result, a value of Ω = 2. We construct a dynamic model for a galaxy without dark matter, which fits well with recent observational data, in terms of a variable effective inertial mass that reflects the present dynamic state of the universe and that replicates from first principles, the phenomenology proposed in MOND. The remarkable aspect of these results is the connection of the effect dubbed dark matter with the dark energy field, which makes it possible for us to interpret it as longitudinal gravitational waves.

Gravitational theory in atomic scale units in Dirac cosmology

1984 ◽  
Vol 96 (1-2) ◽  
pp. 143-162
Author(s):  
W. Davidson
Keyword(s):  
Gravitational Theory ◽  
Atomic Scale ◽  
Mass System ◽  
Typical Member ◽  
Large Numbers ◽  
General Mass ◽  
Spherical Mass ◽  
Freely Moving ◽  
The Universe ◽  
Cosmological Spacetime

SynopsisThe implication of Dirac's large numbers hypothesis (LNH) that there are two cosmological spacetime metrics, gravitational (E) and atomic (A), is used to formulate the gravitational laws for a general mass system in atomic scale units within such a cosmology. The metric is constrained to be asymptotic to the cosmological A metric at large distance. The gravitational laws are illustrated in application to the case of a single spherical mass immersed in the smoothed out expanding universe. The condition is determined for such a metric to apply approximately just outside a typical member of a cosmic distribution of such masses. Conversely, the condition is given when the influence of the universe as a whole can be neglected outside such a mass. In the latter situation, which applies in particular to stars, a Schwarzschild-type metric is derived which incorporates variable G in accordance with the LNH. The dynamics of freely moving particles and photons in such a metric are examined according to the theory and observational tests are formulated.

Mapping between different cosmological eras in scale-covariant formalism

2020 ◽  
Vol 35 (07) ◽  
pp. 2050044
Author(s):  
Marlos O. Ribas ◽  
Fernando P. Devecchi ◽  
Gilberto M. Kremer
Keyword(s):  
Particle Production ◽  
Direct Consequence ◽  
Einstein Equations ◽  
Relativity Theory ◽  
De Sitter ◽  
Covariant Formalism ◽  
Large Numbers ◽  
New Equation ◽  
De Sitter Universe ◽  
The Universe

In this work we consider the scale-covariant formalism proposed by Canuto et al.,[Formula: see text] in order to map different eras of the universe. This technique considers a scale gauge function that can be adjusted by using different arguments like Dirac’s large numbers hypothesis or a restriction on the particle production rate. A Chaplygin constituent shows to be a consistent idea to establish a mapping between an old decelerated–accelerated universe ruled by Einstein equations and an early universe, where a new equation of state appears together with a modified general relativity theory and a de Sitter universe then emerges. These properties are a direct consequence of the use of the scale-covariant formalism. Besides, a new discussion and remarks are presented related to the well-known barotropic constituent case.

scholarly journals A radical departure from the ‘steady-state’ concept in cosmology

1966 ◽  
Vol 290 (1421) ◽  
pp. 162-176 ◽  
Keyword(s):  
Steady State ◽  
Cosmic Rays ◽  
High Energy ◽  
Expansion Rate ◽  
Coupling Constant ◽  
De Sitter ◽  
Observable Universe ◽  
State Expansion ◽  
The Masses ◽  
Creation Of Matter

The results in this paper are based on an entirely different choice of the undetermined coupling constant f which appears in the theory of creation of matter. Previously f was chosen to make the steady-state expansion rate coincident with the observed expansion rate. Now that we take a much larger value for f , the corresponding steady-state expansion rate is much greater than the observed value. We interpret this difference as showing that we live in a wide, possibly temporary, fluctuation from the steady-state situation. The expansion rate in such a fluctuation follows the Einstein-de Sitter relations. The natural scale set by the new steady-state corresponds to the masses of clusters of galaxies, we obtain 10 13 M0 instead of 10 23 M@ for the ‘observable universe’. It is suggested that elliptical galaxies were formed early in the development of a fluctuation. Our discussion of high energy phenomena leads to im m ediate explanations of the energy spectrum of cosmic rays, of the presence of e + in cosmic rays and of the rate of energy production associated with radio sources.

scholarly journals De Sitter and power-law solutions in non-local Gauss–Bonnet gravity

2018 ◽  
Vol 15 (11) ◽  
pp. 1850188 ◽  
Author(s):  
E. Elizalde ◽  
S. D. Odintsov ◽  
E. O. Pozdeeva ◽  
S. Yu. Vernov
Keyword(s):  
Power Law ◽  
Sufficient Conditions ◽  
Model Parameters ◽  
Local Form ◽  
De Sitter ◽  
Dynamical Equations ◽  
Non Local ◽  
Necessary And Sufficient ◽  
The Universe ◽  
Universe Evolution

The cosmological dynamics of a non-locally corrected gravity theory, involving a power of the inverse d’Alembertian, is investigated. Casting the dynamical equations into local form, the fixed points of the models are derived, as well as corresponding de Sitter and power-law solutions. Necessary and sufficient conditions on the model parameters for the existence of de Sitter solutions are obtained. The possible existence of power-law solutions is investigated, and it is proven that models with de Sitter solutions have no power-law solutions. A model is found, which allows to describe the matter-dominated phase of the Universe evolution.

scholarly journals PRIMORDIAL BLACK HOLE FORMATION FROM INFLATON

2000 ◽  
Vol 09 (06) ◽  
pp. 705-710 ◽  
Author(s):  
XIN HE MENG ◽  
BIN WANG ◽  
S. FENG
Keyword(s):  
Black Hole ◽  
Primordial Black Hole ◽  
Primordial Black Holes ◽  
De Sitter ◽  
Hole Formation ◽  
Black Hole Formation ◽  
Expansion Of The Universe ◽  
Slow Rolling ◽  
The Relationship ◽  
The Universe

Measurements of the distances to SNe Ia have produced strong evidence that the expansion of the Universe is really accelarating, implying the existence of a nearly uniform component of dark energy with the simplest explanation as a cosmological constant. In this paper a small changing cosmological term is proposed, which is a function of a slow-rolling scalar field, by which the de Sitter primordial black holes' properties, for both charged and uncharged cases, are carefully examined and the relationship between the black hole formation and the energy transfer of the inflaton is eluciated. The criterion for primordial black hole formation is given.

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