A note on the problem of choosing a model of the Universe,III

From the analysis of relativistic and quantum-mechanical processes at the creation of the expansive evolution phase of the Universe it follows that the Universe can expand only by the limit velocity of signal propagationc.     

A note on the problem of choosing a model of the Universe,II

The energy balance in the solar maximum corona discussed by Narain and Kumar (1986) is objectionable. Hence, the conclusions drawn by them may not be reliable.     

A note on the problem of choosing a model of the Universe,I

The author considers the possibility of transition of the current universe expansion to contraction. The considerations are based on the fact that a homogeneous Universe is structured into non-homogeneous units, the latter expanding as a whole. An analysis of the effects of these wholes on further development shows that in the future contractions may occur only locally; however, the current spatial expansion of the Universe cannot be replaced by a global contraction.     

A note on the elliptic restricted three-body problem

This work considers periodic solutions, arc-solutions (solutions with consecutive collisions) and double collision orbits of the plane elliptic restricted problem of three bodies for =0 when the eccentricity of the primaries,e _p , varies from 0 to 1. Characteristic curves of these three kinds of solutions are given.     

Reconstruction of the early Universe as a convex optimization problem

We show that the deterministic past history of the Universe can be uniquely reconstructed from knowledge of the present mass density field, the latter being inferred from the three-dimensional distribution of luminous matter, assumed to be tracing the distribution of dark matter up to a known bias. Reconstruction ceases to be unique below those scales – a few Mpc – where multistreaming becomes significant. Above 6 h ⁻¹ Mpc we propose and implement an effective Monge–Ampère–Kantorovich method of unique reconstruction. At such scales the Zel'dovich approximation is well satisfied and reconstruction becomes an instance of optimal mass transportation, a problem which goes back to Monge. After discretization into N point masses one obtains an assignment problem that can be handled by effective algorithms with not more than O ( N ³) time complexity and reasonable CPU time requirements. Testing against N -body cosmological simulations gives over 60 per cent of exactly reconstructed points.
We apply several interrelated tools from optimization theory that were not used in cosmological reconstruction before, such as the Monge–Ampère equation, its relation to the mass transportation problem, the Kantorovich duality and the auction algorithm for optimal assignment. A self-contained discussion of relevant notions and techniques is provided.     

A note on the linear stellar model

For a purely gaseous self-gravitating stellar configuration with linear matter density distribution the total power generated by nuclear reactions is considered. The analytic connection between physical parameters of the macroscopic and microscopic levels of the stellar equilibrium configuration is revealed.     

A note on relative motion in the general three-body problem

It is shown that the equations of the general three-body problem take on a very symmetric form when one considers only their relative positions, rather than position vectors relative to some given coordinate system. From these equations one quickly surmises some well known classical properties of the three-body problem such as the first integrals and the equilateral triangle solutions. Some new Lagrangians with relative coordinates are also obtained. Numerical integration of the new equations of motion is about 10 percent faster than with barycentric or heliocentric coordinates.     

A note on velocity-related series expansions in the two-body problem

The present note describes a few important series expansions in the two-body problem. They are related to the magnitudeV of the velocity vector and they are important for the treatment of atmospheric drag with the method of general perturbations. These series have been obtained with computerized Poisson series Manipulations. The results are given to order seven in the eccentricity, for both the Mean Anomaly and the True Anomaly.     

A simple Newtonian model for the fractal accelerating Universe

We propose a simple mechanism for driving the recently detected non-decelerating expansion of the observable Universe. It is based on the assumption of the predominance of the vacuum energy over the inert matter and a fractal structuring of the latter. The Newton’s universal gravitational force ensures the attraction between celestial bodies at small and medium astronomical distances, but gives rise to the repulsive interaction between mutually very separated cosmic subsystems, like clusters and superclusters, and thus to the observed accelerating expansion and the fractal structuring.     

A note on adiabatic solutions of the one-dimensional current sheet problem

It has recently been shown that adiabatic solutions of the one-dimensional current sheet problem exist provided that magnetically trapped particles are included in the model together with the current-carrying untrapped “beam” particles. We show here that a formulation of the problem in terms of particle velocity and pitch angle is advantageous, and we derive some general properties of the solutions. In particular it is shown that there is, in general, no discontinuity in the value of the particle distribution function ? across the boundary in velocity space between “beam” and trapped particles, but that there will be a discontinuity in the gradients of ?. An example is given in which the beam population is of bi-Maxwellian form at the outer boundary of the current sheet.     

A model of expanding Universe with continuous mass-creation

In this paper we propose a model Universe in which a prolonged creative act maintains the course of the traces of the Universe creation from the beginning of the world up to the present time. Consequently, we allow the continuous increase of masses of all bodies present in the Universe. Equations describing our model are written in terms of concepts which are developed in the previous paper (Selak, 1978) where we suggested that relevand cosmological reality has repercussions on the formulation of basic physical laws in our surroundings.     

A note on a separation of the linearized equations of motion in the elliptic restricted problem

Some additional remarks are made here concerning an exact proof of the applicability of Hill's equations in the linear-stability question in the elliptic restricted problem of three bodies.     

A note on expansions of functions of velocity in the two-body problem

Fourier expansions of functions of velocity in the two-body problem are obtained in terms of both the true anomaly and the mean anomaly.     

A note on the equilibrium points of the restricted problem of three bodies

Using Sylvester's theorem on matrices, an elegant expression is obtained for the solutions of the restricted problem of three bodies in the neighborhood of the equilibrium points.     

Is the Stephani-Krasiński solution a viable model of the Universe?

We present a detailed study of the inhomogeneous Stephani-Krasinski solution with time-dependent curvature index. In general, the cosmological behaviour of the models depends on six arbitrary functions of time. Such models are termed ‘private universes’ and cannot be in accord with observation in the most general case. Two simple models with changing topology are considered as illustrating examples. In one of these models the pressure turns out to be negative and hence a violation of the weak energy condition in the singularity theorems is possible. A brief review of other inhomogeneous cosmologies is included for the sake of clarity. It is shown that the geodesic equation can be reduced to a complicated differential equation, which depends on the three arbitrary functions involved. Therefore, it is difficult to obtain explicit formulas for the various observational relations.     

A note on the relations between true and eccentric anomalies in the two-body problem

Two simple formulas are given to relate the eccentric and true anomalies in the two-body problem. The problem of the maximum difference between these two angles is alo considered.     

An FLRW interacting dark energy model of the Universe

In this paper, we have presented an FLRW universe containing two-fluids (baryonic and dark energy), by assuming the deceleration parameter as a linear function of the Hubble function. This results in a time-dependent deceleration parameter (DP) having a transition from past decelerating to the present accelerating universe. In this model, dark energy (DE) interacts with dust to produce a new law for the density. As per our model, our universe is at present in a phantom phase after passing through a quintessence phase in the past. The physical importance of the two-fluid scenario is described in various aspects. The model is shown to satisfy current observational constraints such as recent Planck results. Various cosmological parameters relating to the history of the universe have been investigated.     

A note on the mechanism of broad band absorptions and emissions in the type IV decimeter continuum

The broad band absorptions and emissions in the type IV decimeter continuum are remarkable for the simultaneity of their occurrence at widely different frequencies and for their very short durations. During a given event there is a continuous succession of different patterns of broad band features. It is suggested that the different aspects of the broad band features are variations on a common underlying process. The process would seem to be the screening of a large part of the outgoing beam of radiation, which supposedly is ducted along a tube or channel of relatively low density. As an agency which causes the screening, one may think of shocks or solitons that impinge transversaly on the channel along which the radiation propagates. The various patterns of broad band absorptions and emissions would then be related to structural features of series or trains of passing shocks and/or solitons.     

The interaction of matter and radiation in the hot model of the Universe,II

Heating of the primaeval plasma prior to the epoch of recombination results in distortions in the Rayleigh-Jeans region of the microwave relic radiation spectrum (1–60 cm, or more exactly =2.5_–7/8 cm). The present observational data allow limits to be set to such energy injection from which follow upper limits to (a) the amount of antimatter in the universe; (b) the parameters of primaeval turbulence; and (c) the adiabatic fluctuation spectrum for small masses (M<10¹¹ M ).If the heating takes place prior to the epocht=10_1012/5 sec (and in particular at the annihilation of electron-positron pairs atT10⁸–10¹⁰ K,t<300 sec), no observable distortions are expected in the relic radiation spectrum. Here =/_crit is the dimensionless average density of matter in the universe.Translated from the Russian by D. F. Smith.