Newtonian Cosmological Model Research Articles

Stabilizing effect of the spacetime expansion on the Euler-Poisson equations in Newtonian cosmology

Abstract The validity of the cosmic no-hair theorem for polytropic perfect fluids has been established by Brauer, Rendall, and Reula [Classical and Quantum Gravity, 11(9), 1994: 2283] within the context of Newtonian cosmology, specifically under conditions of exponential expansion. This paper extends the investigation to assess the nonlinear stability of homogeneous Newtonian cosmological models under general accelerated expansion for perfect fluids. With appropriate assumptions regarding the expansion rate and decay properties of the homogeneous solution, our results demonstrate that the Euler-Poisson system admits a globally classical solution for initial data that are small perturbations to the homogeneous solution. Additionally, we establish that the solution asymptotically approaches the homogeneous solution as time tends to infinity. The theoretical framework is then applied to various types of perfect fluids, including isothermal gases, Chaplygin gases, and polytropic gases.

GRAVITATIONAL INTERACTION FROM THE STANDPOINT OF FIELD-THEORETICAL AND GEOMETRIC PARADIGMS

Considered are energy dependences of the dimensionless constants of the electromagnetic, strong and weak interactions. Elementary particle classification depending on their spin is presented as well as dualistic paradigms based on are physical categories of space-time, matter particles and field-carriers of interactions. Gravitational radiation and static gravitational fields are considered both in the framework of the Lagrangian formalism and GR as well as MacCrea-Milne’s Newtonian cosmological model. Both perturbative and nonperbative approaches to gravity quantization are listed. Advantages and disadvantages of gravity description in the framework of field-theoretical and geometric paradigms have been indicated.

Asymptotic behaviour of the Boltzmann equation as a cosmological model

As a Newtonian cosmological model the Vlasov-Poisson-Boltzmann system is considered, and a slightly modified Boltzmann equation, which describes the stability of an expanding universe, is derived. Asymptotic behaviour of solutions turns out to depend on the expansion of the universe, and in this paper we consider the soft potential case and will obtain asymptotic behaviour.

COSMOLOGICAL CONSTANT AND NONCOMMUTATIVITY: A NEWTONIAN POINT OF VIEW

We study a Newtonian cosmological model in the context of a noncommutative space. It is shown that the trajectories of a test particle undergo modifications such that it no longer satisfies the cosmological principle. For the case of a positive cosmological constant, spiral trajectories are obtained and corrections to the Hubble constant appear. It is also shown that, in the limit of a strong noncommutative parameter, the model is closely related to a particle in a Gödel-type metric.

Inferences from the dark sky: Olbers’ paradox revisited

The classical formulation of ‘Olbers’ paradox’ consists in looking for anexplanation of the fact that the sky at night is dark. We use the experimentaldatum of the nocturnal darkness in order to put constraints on a Newtoniancosmological model. We infer then that the stellar system in such a model shouldhave had an origin at a finite time in the past.

Newtonian Cosmology and Mach's Principle: local vs. global integrability

I discuss the transformation theory of Newtonian mechanics and gravity developed by Cartan and Heckmann and show via coordinate transformations that Heckmann's Newtonian cosmological model has a center, so that the cosmological principle cannot hold globally in that model. This viewpoint disagrees with a recent claim, and is based on a particle mechanics method never before used in this model. It is possible to confuse relativity principles with a position of relativism. Mach's principle has much to do with the latter and little to do with the former. Both general relativity and nonlinear dynamics inform us that most coordinate systems are defined locally by differential equations that are globally nonintegrable: global extensions of local coordinates usually do not exist. By emphasizing local integrability vs. global nonintegrability of equations of motion, and correspondingly local inertial frames, I short circuit Mach's philosophic objections to Newtonian dynamics. The short-circuit follows from a physico-mathematical discussion of inertial frames based on local integrability.

The cosmic no-hair theorem and the non-linear stability of homogeneous Newtonian cosmological models

The validity of the cosmic no-hair theorem is investigated in the context of Newtonian cosmology with a perfect fluid matter model and a positive cosmological constant. It is shown that if the initial data, for an expanding cosmological model of this type, is subjected to a small perturbation then the corresponding solution exists globally in the future and the perturbation decays in a way which can be described precisely. It is emphasized that no linearization of the equations or special symmetry assumptions are needed. The result can also be interpreted as a proof of the non-linear stability of the homogeneous models. In order to prove the theorem we write the general solution as the sum of a homogeneous background and a perturbation. As a by-product of the analysis it is found that there is an invariant sense in which an inhomogeneous model can be regarded as a perturbation of a unique homogeneous model. A method is given for associating uniquely to each Newtonian cosmological model with compact spatial sections a spatially homogeneous model which incorporates its large-scale dynamics. This procedure appears very naturally in the Newton--Cartan theory which we take as the starting point for Newtonian cosmology.

Growth of density inhomogeneities in Newtonian cosmological models with variable Lambda.

We analyze the growth of density perturbations in Newtonian cosmological models with continuous matter creation and obtain the time evolution equation for the mass density contrast. The special case where matter is created by the decay of a cosmological term (\ensuremath{\Lambda}) varying as \ensuremath{\Lambda}=3\ensuremath{\beta}${\mathit{H}}^{2}$ is examined. Constraints on the value of \ensuremath{\beta} from the observed high isotropy of the cosmic microwave background radiation are also obtained.

A static stable universe

view Abstract Citations (9) References (12) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS A Static Stable Universe Crawford, David F. Abstract A static and stable solution to a Newtonian cosmological model is described where the centripetal acceleration of high-temperature particles moving in a three-sphere embedded in a 4D Euclidian space balances the gravitational acceleration. This model is used to show a possible deficiency in the equations of general relativity in that the Newtonian model contains a term corresponding to centripetal accelerations that is not present in Friedmann's equations. Together with a gravitational interaction that can explain the Hubble redshift it provides a viable cosmological model. Publication: The Astrophysical Journal Pub Date: June 1993 DOI: 10.1086/172765 Bibcode: 1993ApJ...410..488C Keywords: Cosmology; Stability; Universe; Astronomical Models; Computational Astrophysics; Gravitational Effects; Relativistic Theory; Astrophysics; COSMOLOGY: THEORY; RELATIVITY full text sources ADS |

An existence theorem for perturbed Newtonian cosmological models

Given a Newtonian Friedmann-like cosmological model ℳO, there exist, locally in time, spatially periodic solutions close to ℳO. Such solutions represent inhomogeneous models that are homogenous and isotropic on a large scale. The Euler–Poisson system is shown to be linearization stable at ℳO.

Newtonian no-hair theorems

A detailed analysis is made of the status of the no-hair conjectures of general relativistic inflationary universe in Newtonian cosmological models. The authors show that the no-hair theorem cannot be proved in Newtonian gravity with a positive cosmological constant. Rigorous results can be derived to show that the mean volume approaches the behaviour of the Newtonian de Sitter universe at large times but no information is available about its shape. This manifestation of the 'gravitational paradox is displayed both in the fluid and N-body formulations of Newtonian cosmology.

Cosmological models in globally geodesic coordinates. II. Near-field approximation

A near-field approximation dealing with the cosmological field near a typical freely falling observer is developed within the framework established in the preceding paper [J. Math. Phys. 28, xxxx(1987)]. It is found that for the matter-dominated era the standard cosmological model of general relativity contains the Newtonian cosmological model, proposed by Zel’dovich, as its near-field approximation in the observer’s globally geodesic coordinate system.

Cartan structures on Galilean manifolds: The chronoprojective geometry

A new geometry is constructed over Galilean manifolds expressing the compatibility requirement between the conformal equivalence notion of two Galilean structures and the projective equivalence notion of two affine connections. It is shown that it is the very geometry of the Newtonian cosmology (chronoprojective flatness is equivalent to isotropy of Newtonian cosmological models); moreover, it also explains various ‘‘accidental’’ symmetries in classical mechanics.

Ellipsoidal Velocity Distributions and a Kinetic Theory of Newtonian Cosmological Models

view Abstract Citations (1) References (3) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Ellipsoidal Velocity Distributions and a Kinetic Theory of Newtonian Cosmological Models Trümper, Manfred Abstract A method is given for obtaining all solutions (F, ) of the self-consistency problem for gravitating, collisionless gases (stellar systems) whose residual velocity distribution is of the type F = `k(w Cw) with a positive, symmetric, time-dependent matrix C. For any given C one can find a solution of Liouville's and Poisson's equations by solving a fifth-order system of ordinary differential equations. All these solutions are of the cosmological type; i.e., they have constant mean mass density and a mean ve!ocity field which is linear in the Cartesian coordinates. On the other hand, for any homogeneous (generally anisotropic) cosmological model in Newton's theory one can find a self-consistent velocity distribution by solving a system of six linear ordinary differential equations. Publication: The Astrophysical Journal Pub Date: March 1971 DOI: 10.1086/150833 Bibcode: 1971ApJ...164..223T full text sources ADS |