3. NEW STATIONARY MODEL OF THE UNIVERSE
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3. NEW STATIONARY MODEL OF THE UNIVERSE |
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Introduction
The Universe is the study subject of cosmology. Cosmology is the general part of mathematics, physics, astronomy and philosophy, which studies the structure, evolution, and physics laws of the Universe as a whole.
The integral notion about the Universe puts cosmology in a special position in relation to other sciences. Indeed, if any other science can study its subject fully and comprehensively the investigator of the Universe can only examine part of the subject. Since the whole can exhibit such characteristics which are not present in its parts, the difficulties cosmology has been facing at all times can be understood.
The essence of the difficulties has always been as follows: any physical theory could not fully explain the observed properties of the Universe. If the theory was somehow adjusted to describe some properties of the Universe, the consequence that emerged did not agree with other known features or fell outside the common sense.
The situation is also aggravated by the fact that the Minkowski space-time in the General Relativity, which represents the theoretical foundation of modern classic cosmology, is described by ten variables, while the theory itself offers only six independent equations. Therefore, it is no wonder that no one could construct an objective pattern of the world yet based only on the equations of the General Relativity.
As a result of discrepancies in the theory, particular hypotheses needed to be advanced to explain certain properties of the Universe. For this reason, many different models of the Universe have appeared. Unfortunately, no one of them fully satisfies all the requirements of the laws of logic or conforms to the real world.
At present, the official science adheres to the commonly accepted concept that the Universe appeared 12 billion years as a result of the Big Bang of the substance, which had been in tremendously dense and hot state. After that the substance expanded, cooled down, split into the matter and the electromagnetic field and formed galaxies, which are believed to continue moving farther apart until now.
Such a model is based on the non-steady solutions of the Einstein equations obtained by Soviet geophysics and mathematician Fridman at the beginning of the 1920s and the concept of the exploding commencement in the dynamics of the Universe advanced by American physicist Gamov at the end of the 1940s in XX century.
The objective properties of the Universe, which allegedly confirm this model, are the discovery of the redshift in the spectra of galaxies (proportionally to distance up to them) by American astronomer Hubble in 1929 and the Cosmic Microwave Background Radiation at the temperature 2.7 K by American radio astronomers Wilson and Pansias in 1965.
The first discovery was interpreted by scientists as the result of the motion of galaxies away from each other and the second discovery was construed as the remainder (relic) of the electromagnetic radiation which had segregated from the initial substance and then cooled down to the said temperature during the expansion of the Universe.
The above-mentioned properties of the Universe, incidentally, are not the direct evidence of its expansion. For instance, the decrease in the frequency of light can be the result of either the expansion of the Universe or the dissipation of the energy of light when it spread at great distances, while the Cosmic Microwave Background Radiation can be either the remainder of the high-temperature explosion of the super dense substance or the total radiation of all stars of the stationary Universe with the said dissipation of the energy of light.
The question about the model and the laws of the Universe is comparable with a problem of what is prime: an egg or a hen. So if we define cosmology as the science about the Universe, we are immediately facing the problem of what is initial: the model of the Universe from which the law of physics of the Universe follow, or the laws of physics of the Universe, on the basis of which the model of the Universe is constructed?
Apparently, the problem does not need a direct answer. However, a third question, which is as if a quasi-superstructure over the dilemma about the primacy of the model or the laws of the Universe, requires resolving. The point is about the proportion and interrelation of such philosophical categories as the "whole" and the "part" and also the philosophical law of quantitative changes passing into qualitative changes. Here again, strictly parallel movement is needed.
To study the whole by its part, it is important to have continuous integration of notions on the subject of the investigation from different points of view at every stage of its investigation and continuous coordination of outcomes of the theory under development with the objective reality. Non-observance of the principle of conformity, occurrence of internal contradictions, singularities and paradoxes while applying the given theory for the description of the whole indicates to the falsity of the way taken by the investigators. It is the very situation, which has developed in cosmology nowadays, its official theoretic ground being based on the idea of Big Bang.
1. The speed of light is the tensor
Any observer can not simultaneously be in several systems of readout. This fact guesses viewing all the natural phenomena only in one inertial system of readout. Thus there is a problem what is the speed of light of rather propellant objects.
Correctly to answer this problem, we shall consider two inertial systems of readout 
, 
and bound with them two rulers, as it is shown in a fig. 1.
Fig. 1. Systems of readout
Let at that moment, when the beginnings of rulers 
and 
coincide with each other, the bulb in a point 
, bound with a fixed ruler, will light up. In time 
light will reach a point 
on this ruler. For the same time the relative frame ruler will move and on the contrary point 
there will be a point 
. Thus distance, which light has passed along a relative frame ruler on quantity 
will be less than distance, which it has passed on a fixed ruler. Hence, observer who is taking place in a point 
(that is in fixed system of readout) on the gauges of space and time should make a deduction, that the front of a light wave catches up a point along a propellent ruler with velocity 
. At a motion in the opposite direction will be received 
.
All above-stated does not contradict a postulate of a special theory of relativity, as the speed of light is constant only in inertial systems of readout, and 
- is a speed of light in one inertial system of readout measured on gauges of space and time of other inertial system of readout. Let's term it as a local velocity of light.
Fig. 2. A tensor of speed of light
Thus, from this point of view the local velocity of light represents a tensor of the second rank (naturally, in three-dimensional space) which all builders by the ends contour a ball of radius 
displaced in relation to propellent object forward on quantity of velocity 
of its motion (fig. 2). This ball is a geometrical fashion of a tensor of a local velocity of light [28].
2. The law of gravitation
As it is known, Einstein has offered two views of the equations of the General Theory of Relativity which differ from each other on an addend with the cosmological term 
:
 , |
(1) |
 , |
(2) |
For a unique select of the equations it is necessary to take into account some performance of the Universe. Such performance is global flatness of the Universe which mathematical expression is equality
 . |
(3) |
As for the actual Universe filled with substance with deflection density, 
, with the account (3) the fact of omission of equality (1) becomes obvious. Thus, the flat in global gauges Universe can be featured only with the equation (2). And, the diversions from flat space-time under activity of material masses can be presented precisely (precisely!) only in a composition of the total which corresponds to the assignment of a tensor gravitational field 
on a background of the flat material world in arbitrary coordinates with the metric 
[7, 14, 43]:
 , |
(4) |
The other, not less important property of the Universe is its homogeneity and isotropy in great gauges. Mathematically this property can be reflected as equality to zero of a covariant derivative(derivative) of tensor density 
and corollaries of this equality (in Lorentz coordinates):
 , |
(5) |
where the point with comma designates a covariant derivative, and the comma is usual derivative.
After that the equations (2) with the help of transformation (4) and requirement (5) are given in the field equations of the General Theory of Relativity
 , |
(6) |
where 
is an energy-momentum tensor of a substance together with a substance of a gravitational field which is oozed from the left-hand part of the Einstein equations. Under the same requirements in [7, 28] the identity of Lagrangians for a deduction (2) and (6) is proved also.
Taking into account homogeneity and isotropy of the Universe (that is symmetry of a problem), for a spherical-symmetrical material body of mass 
the equations (6) give the exterior solution as Yukawa potential
 . |
(7) |
The constant 
is termed as radius of gravitational interactions and is determined under the formula
 . |
(8) |
For two of material bodies with masses 
and 
the following law of gravitation is gained
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(9) |
From the analysis of the obtained law follows that in the actual Universe all the material bodies (planets, stars, galaxies) interact with each other more feebler than it follows from the law of Newton gravitation.
3. Identity of inertial and gravitational masses
It is necessary to note that in linear approach the actual law of gravitation (9) becomes:
 , |
(10) |
which shows, that all material bodies in the Universe interact with each other practically only in limits of radius of gravitational interactions equal approximately 1026 m (or 20 billions of light years).
On the other hand, if to compare an actual law of gravitation and law of gravitation of Newton, it appears that the area under a curve of force of the actual law on an interval from 0 up to 
is precisely equal the areas under a curve of the law of gravitation of Newton on an interval from 0 up to 
. Hence, law of gravitation (9) valid for the actual Universe, from the energy point of view by the law of Newton gravitation can be replaced restricting radius of activity of forces by quantity 
. The given approach allows to decide a series of remarkable problems promptly and obviously.
In view of above-stated we shall analyse, how the area of interaction of a material point of mass 
with the Universe will vary at its dispersal up to velocity 
and in what all this will give. It is to show that the new area of interaction of a point with medium also will represent a ball of radius , but moved forward on a course of its motion on quantity 
(as in expression for it is necessary to substitute 
). It is possible also to show that the relation is valid
 , |
(11) |
Thus, the area of interaction of a propellent mass point displaces forward on a course of a motion proportionally velocities of its motion. In a limit, that is when the velocity of a motion is equal to speed of light the propellent point should be on a surface of its area of interactions. But it just and probably only for light.
At dispersal the point 
loses gravitational connection with a part of space 
behind of itself and will enter gravitational connection with a part of space 
ahead of itself (fig. 3). The sizes of the areas both are identical and depend only on velocity , but the situation of a point 
concerning them is unsymmetrical. Hence, the aggregate operation on overcoming forces of a gravitation of area 
and forces of a gravitation of area 
is not equal to zero.
Fig. 3. Change of area of interactions at dispersal of a point
The author managed to find receptions of definition of this operation. If to take into account a probable initial velocity 
a material point, for low speeds the operation has appeared to equal quantity
 . |
(12) |
Thus, we have received, known from mechanics the theorem, of change of a kinetic energy of a body. If the obtained expression to differentiate on velocity and on time, the second Newton's law will be received. All this is valid in a relativistic case.
Characteristic feature of the obtained results is that both in the theorem of change of a kinetic energy, and in the second Newton's law not inertial, but gravitational mass enters so long as only such mass considered from the very beginning. So the identity of inertial and gravitational masses spirit of the Mach principle is proved and the mechanism of interaction of material bodies with the Universe is uncovered.
4. Gravitational viscosity and geodetic curvature of the Universe
After dispersal (cancellation of local force) of material body along coordinate 
its free motion is featured by the equation
 ,  , |
(13) |
where 
is the Hubble constant, which has absolutely other physical sense, as it is accepted in a conventional cosmology.
By presence of the second (dissipative) addend the new law of a free motion differs from the first Newton's law. As a whole one of the most prime statements of this law can be such: if the local forces do not act on a body, the standing of its interaction area from the Universe (on the level 
) in due course does not vary, and it aims asymptotically to the center of this area.
The new property of the Universe is termed as gravitational viscosity. As the stationary value of Hubble has the order 10-18 s-1, the gravitational viscosity practically has no an effect for local processes (for example, in gauges of Solar system). In a distance equal to half of medial distance between galaxies the forces of the gravitational viscosity become comparable with the centrifugal forces and answer for shaping of the medial-gauge structure of the Universe, that is for shaping of galaxies.
The concept of the gravitational viscosity of the Universe adjoins by a tight fashion to the concepts of affinities (parallel transport of vector) in a non-Euclidean geometry of multivariate spaces. For a motion of the nonconservative systems - that is in the general view - there is a relation for the curvature of space
 . |
(14) |
The medial addend with Christoffel's figures of the first kind (affine compendency) 
indicates a degree of normal curvature of space (we shall term it as geometrical) in which the parallel transport of vector and the letter on change of the length of the vector, that is on the existence of a dissipation of energy. It determines so-called geodetic curvature of space
 . |
(15) |
For the actual Universe the geodetic curvature is equal
 , |
(16) |
where 
is constant for the Universe coefficient equal approximately 10-10 m/s2.
In the whole the analysis of all the results shows that the motion concerning the Universe has a character of a terrain clearance motion, but on activity of the local physical laws it cannot be noted (except for inertia and red bias in spectrums of radiation of other galaxies).
5. The law of distribution of light and the Hubble diagram
The analysis of interaction of light with the Universe has shown that gravitational potential (
) acts on it, giving power loss and, as a corollary, change frequency 
in relation to initial 
under the law.
 . |
(17) |
The given law completely permits photometer paradox, explains a nature of red bias in spectrums of radiation of other galaxies without engaging a Doppler effect and gives a new formula of definition of distances up to galaxies
 , |
(18) |
where 
is parameter of red bias of light frequency.
In view of the new law of distribution of light dependence "visual stellar magnitude 
- red bias 
" (the Hubble's diagram) gains a view:
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(19) |
In a gamut of apparent values of stellar magnitudes the given dependence practically is linear and completely coincides experimental datas.
The law (17) completely explains a nature, numerical performances and character of allocation of background microwave radiation. Actually, it is not a relic of the Big Bang, and aggregate radiation of all radiants of electromagnetic radiation (stars, galaxies etc.) of the Universe. If to integrate the whole radiation impinging on a single site on space from zero to infinitum the temperature of this radiation will be determined by the formula
 , |
(20) |
where 
is medial mass and complete radiation flow of a medial star (or galaxy); 
is the Stefan-Boltzmann constant.
The evaluations show, that temperature of integrated radiation is equal to several degrees above terrain clearance zero (more precisely to calculate it is impossible), as it is observed actually. And its spectrum corresponds to a radiation spectrum of an absolute black body.
6. Large-scale structure of the Universe
The actual law of gravitation has a series of pleasant features. So, the evaluation of a binding energy of a material body of mass 
from the Universe gives quantity
 , |
(22) |
which is equal precision to an internal energy of a body taken with an inverse. In contrast to it, the law of Newton gravitation gives a minus perpetuity. That is why with application of a Newton's laws to the infinite Universe the gravitational paradox also has appeared. In the actual Universe with the actual law of gravitation such paradox does not exist, and the mass appears a measure of connection of the given material body with the whole Universe.
The actual law of gravitation gives one more important corollary: with mass shown in interactions with a material body depends on a relation of radius of a body 
to radius of gravitational interactions 
 . |
(23) |
At 
the mass of a body is proportional to its volume, and at 
(or that is the same when 
) to surface area of a body. It gives in a deduction about ability of a substance to create screen effect. It is capable to explain virial paradox and existence of gravitational-makes of areas of the Universe.
The interesting physical sense has also radius of gravitational interactions (8). It appears that it corresponds in precision to radius of a black hole on which surface the speed of light is equal to the first solar escape velocity. Thus, it is possible to tell that we live at in the center of a black hole, but it is not our privilege, and the property of the Universe to form around of any point gravitational-makes area. By the way acceleration due to gravity on a surface of such black hole is equal only 10-10 m/s2.
On the other hand, if to unit two identical material objects in one, not changing density the mass of the obtained object shown in interactions will be less than total masses of builders. It also should be expected, as the formally given law is similar to the law of nuclear interactions in the field theory of nuclear forces.
In classical physics there is a special theorem proving that inside a spherical-symmetrical material shell the gravitational field misses or, more precisely, that resultant of force, all the gravitational forces is equal to zero. Using of the actual law of gravitation it has appeared that the closer point is to a shell the stronger it is attracted to it. Differently, any spontaneous obturating of a material medium of the Universe as a shell conducts to the further shaping of such shell. That is why the Universe has cellular structure in major gauges where the aggregations of galaxies are in thin walls of these meshes and superaggregation and on crosses of meshes.
It is necessary to note, that in 1971 Karlsson has found out for the first time a cyclic change of a spectral radiant density of quasars proportional argument 
, where 
is red bias of their spectrums. Such allocation of quasars correlates with allocation of galaxies forming in the Universe homogeneous thin-walled aggregations as meshes.
In view of the formula (18) cyclic changes of a spectral radiant density of quasars are conversed to cyclic dependence of allocation of quasars on distances indicating homogeneity of the Universe not only in space, but also in time, that is on its stationarity for the last a minimum of 40 billions years (so much time the electromagnetic waves went to us from the farthest quasars).
Thus, the author has designed the new stationary model of the Universe which approximately on 30 parameters is compounded with the properties of the actual Universe and has the same right on existence as well as model of Big Bang.
