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The brief modern review of the Universe rotation problem is given. Also it was argued the vacuum concept of the Universe rotation, found the galactic coordinates of the Universe rotation axis, based theoretically the concept of the decaleration parameter anisotropy.

One of the most important global characteristics of the Universe is its rotation. In fact, in article [

There are many other approaches to constrain the global rotation.

Based on the idea that a global rotation induces a total net spin of galaxies, the global rotation can be limited [

Beside, authors quoted number of previous articles devoted to clarifying this problem and conclude that study of global rotation is of interest in many different aspects of cosmology, and constraint of the rotation speed of the Universe is important.

To develop a model that preserves the homogeneity and isotropy of the mean CMB, they studied the rotation of the Universe as a perturbation in the RobertsonWalker framework with a cosmological constant. Unlike the Bianchi models, such an approach allows to have non-zero rotation but trivial shear. Since the global rotation does not have any influences on the first-order SachsWolfe effect (SW effect), we need to calculate the metric up to second-order perturbations and find the secondorder SW effect. Then, they constrained the angular speed of the rotation using recent data on CMBA. As the result their model is inhomogeneous with an axial symmetry in general. Moreover, the global rotation in this model is not only radial-dependent, but also time-dependent.

In fact, the angular velocity describes by expression

, where

in SI unit. The subscripts “0” and “e” at radius and conformal time are denoting the hypersurfaces at origin and last photons scattering in SW effect respectively. In doing this the angular velocity of matter can be negative while the rotation speed of the Universe is always positive and is less than at the last scattering surface.

The first experimental evidence of the Universe rotation was done by Birch [

Contrary to this in article [

Nevertheless, the observational proofing of Universe rotation phenomenon is still important up to the present days. Really, in [

Moreover, in [

It is very important to mark that in article [

Another variant of confirmation the Universe rotation axis existence have been done in article [

The novel aspects of the Universe rotation problem were considered in [

The article organizes as follows. In second section we argued the vacuum conception of the Universe rotation. In third section we calculate the galactic coordinates of the Universe rotational axis. Forth section devoted to the theoretical basing picked axis in the Universe existence. In conclusion we briefly summarize the results of article.

But now question arises—if the Universe rotates what is the physical reason of this phenomenon? Such question is very important because in all of previous article the cosmological rotation has been introduced “by hands”. One of the first articles was done by Ellis and Olive [

Note that article [

So, considering a galaxy as the rigid body we’ll examine its rotation under acting of vacuum antigravitational force with respect to the center-of-mass point.

In [

At basing (2.1) it was took into account the vacuum equation of state and fact that according to the Friedmann cosmological model the gravitation produces by generalized mass density, where is the substrate pressure. Let is the angle between vectors and. Then under the condition we find the element of gravitational repelling force

and its total expression

, (2.3)

where integral must be taken over the volume of galaxy and is the vacuum potential.

Introducing the vacuum moments of the galaxy along axes, , and cross-section areas

, corresponding them, it’s possible write down the vacuum perturb force and the vacuum potential as follows

accordingly.

Later on we choose the elliptical galaxy as the model of examining type of galaxies. This lead not only to simplify the process of the analytical solving our problem, but allowed to compare results with the real astronomical database. Consider an elliptical galaxy that have two equal main moments. Than the potential will not depends on angle. Hence, it may be equals to zero, i.e..

For the chosen shape of galaxy its equations of rotational motion are

where coefficient. The system (2.6) is easy transforms to the differential equation of the first order

The solution of this equation describes by standard quadrature, with variable , and [

Basing on this result it is easy to calculate the angular velocity of the elliptical galaxy around axis. In fact, as for this case, than its module equals

This expression describes the angular velocity that galaxy acquires due to the vacuum antigravitation.

Consider, for example, the giant elliptical galaxy NGC 4486 (М 87), that locates from us at distance R_{0} = 15 MPc, while its proper sizes equals. With account of above cited vacuum density we estimate the magnitude of Expression (18) now. Putting

and assuming that, we find

. Substitution the needed values into this expression give the following estimation.

At the same time analyses of (2.9) shows that its maximal magnitude will be under the condition. Then expression for the vacuum angular velocity simplifies and takes on the form

This expression is possible to interpret as the minimal angular velocity in the Universe that vacuum can create at arbitrary object its numerical value is about 10^{−}^{19} sec^{−}^{1}. Hence, the vacuum itself create the identical initial angular velocity at all of cosmic objects. Thus it is possible to say that cosmic vacuum not only creates the microscopic baryonic substance, but pre-determines its global characteristics.

As the condition indicates the passing to the entire Universe it results about its total rotation. As it seems Expression (2.10) is invariant and don’t depend nether the frame of reference nor choosing the geometrical sizes of the Universe at given cosmological epoch. Hence, at the earliest stages of Universe evolution, for example at baryonic asymmetry stage, when vacuum density was about its angular velocity was essentially larger and was equal. For the very early Universe vacuum density was about in order and its angular velocity was drastically larger.

Mark, at such angular velocity the border of Universe moved with linear velocity not larger the speed of light. In fact, as the sizes of Universe at born time were Planckian type, i.e., than linear velocity of the Universe border will be This velocity is smaller that speed of light truly, that is must be in realty.

What about the observable angular velocity of the Universe at the present epoch? In papers [6,7] there were given following estimations of its angular velocity. In article [

From these estimations it result that Universe angular velocity must be in the following range. Our previous estimate of the Universe rotation, as it seems, is in good correlation with the specified interval.

At the same time the peculiarity of quoted articles is the Universe rotation searching in the framework of relativistic cosmology and its determination by a baryonic substrate. In contrary, in our case the Universe rotation determines by Newtonian’s mechanics and is the consequence of vacuum presence. That is why the ratio of Universe angular velocity to the Hubble parameter is about unit, i.e.. From this follows the correctness of Gamov’s remark [

Talking about the Universe rotation it is not ignore the difficulty connected with the determination of the Universe rotational axis and its orientation in the space. Such question was considered by number authors, but from observational point of view preferentially. We’ll examine it from the theoretical positions basing on the coordinate transformation that expressed by Euler angles and galactic coordinates.

Remind that galactic coordinates system this is the system with origin placed on the Sun and extended through the center of Galaxy. Its plane coincides with the plane of Galaxy dick. In doing this, its latitude is measured from galaxies plane to an object and takes magnitudes from −90˚ up to +90˚. Galactic longitude is measured at the Galaxy plane from the baseline connected the Sun and galactic center up to the baseline connected the Sun and object. Counting directs to the same way that the right ascension in the second equatorial coordinates. Therefore the galactic longitude puts in limits from 0 ˚ up to 360˚.

The position of object in galactic coordinates describes by matrix expression

where is the matrix of galactic coordinates while—its basis vectors.

The radius-vector of a celestial object that is expressed by equatorial coordinates may be decomposed by basis vectors of other coordinates of galactic coordinates, in particular. As equatorial coordinates is connected with the Euler coordinates taken under the condition by the equalities and, we have the following relationship

To find the explicit form of transformation between two coordinate systems it is necessary to calculate the rotation matrix from first basis unit vectors to second one. For example, as it follows from above the matrix of galactic coordinates is

Also remind that ort is directed to the point of spring equinox; ort—to the point of right ascension that equals; ort—to the North celestial pole.

Finally, we have to calculate the matrix

. Basing on the magnitudes of angles for right ascension and declination, defined for the B1950 epoch^{1}, it possible to show that [

For next calculations find the concrete magnitudes of Euler angles whose general expression was found in Section 2.

From its results we get

where is the timelife of our Universe. Setting , angular velocity and having in mind that , , , we get following estimations

As and the explicit form of the galactic coordinates matrix will be

From this we get the system of three equations for two variables and

From two last of them we find,. Compare these magnitudes with results of article [20,21], where the galactic coordinates of the Universe rotation axis were determined as. It’s easy to see that the axis passes through the Sun and point O with angular coordinates will coincide with the axis passes through the Sun and point with angular coordinates. That is why it possible concludes that Universe rotation axis has this coordinates namely^{2}.

The divergence between observational angular coordinates and our theoretically predicted coordinates explains by accounting the vacuum density only at the calculation of Euler coordinates. Hence, except vacuum density it is necessary take into account densities of dark matter and baryonic matter that are the integral components of any galaxies structure. Nevertheless, our approach demonstrates the possible way of theoretical deducing the space orientation of the Universe rotational axis.

Its fruitfulness seems through the prism of Universe evolution, already. In fact, as the magnitude of vacuum density is different at different epochs of its evolution, the space orientation of the rotational axis changes, also. For instance, at the baryonic asymmetry epoch when vacuum density, angular velocity, timelife, than Euler angle. So, the angular coordinates of the rotational axis where.

Now we mention the fundamental article [

.

Evidently, these results are possible to summaries as follows, our Universe is anisotropic in realty and possesses by any principal space axis. That is why the cosmological deceleration parameter will be anisotropic, also and must be depend on the principal space direction in definite way. These statements require theoretical basing the direction dependence of the cosmological deceleration parameter phenomenon.

Our searching we start from the well-known results. For the uniform isotropic metric of the space-flat Universe the Einstein’s equations for the scale factor are [

Put that scale factor expresses as, where is the distance in uniform space, while—small addition (perturb term) for describing the possible space anisotropy. Putting it into the Newtonian Equation (4.1) we get two equations—basic one

and perturb one

Later on these equations will be considered independently each other.

Performing the above mentioned Tolman transformation [

It leads to the Hubble expansion law

and to the corresponding acceleration

Now consider the Equation (4.5). Suppose that in this equation, where is the baryonic substance density. The baryonic substance pressure let equals zero, for simplicity.

Last requirement means considering the presence of two-component substance—cosmic vacuum and baryonic dust—in the Universe, that are not interact each other in the basic approximation.

By introducing the designation, from (4.5) it follows

This oscillatory-type equation possesses by two roots

They lead to the presence of two perturb (with respect to (4.7)) velocities

and two corresponding accelerations

From physical viewpoint expressions (4.10)-(4.12) mean that presence of baryonic dust matter creates two space-opposite fluxes that are propagate on the background of expanding and accelerating “Hubble vacuum flux” along the Universe rotation axis. That is why it possible writes down the expressions for total distance, velocity and acceleration of any probe particle (galaxy)

Thus the cosmological deceleration parameter q with the accuracy no higher than is

Basing on the definitions of and we introduce the new coefficient. As in unit of the critical density and vacuum density , coefficient, henceforth.

From (4.14) it is possible find the relative acceleration difference between two baryonic fluxes with respect to the “Hubble vacuum flux”,

Assuming that for modern epoch we approximately get. Hence, the first term in right side of (4.15) tends to 1.2, while the second term tends to zero. So,

Basing on our assumption, that was argued earlier, we may put that it will satisfy if the ratio

. This leads to the estimation

that is in good correlation (case of the upper magnitude index) with the value

in [

So, we briefly reviewed the modern status of the Universe rotation problem. In numbers of examined articles, this problem was considered from different viewpoints and done the following common result—our Universe rotate, most probably. On the this statement grounding it was considered the vacuum concept of the Universe rotation, found the galactic coordinates of the Universe axis rotation and based the concept of the deceleration parameter anisotropy along this axis.

It also was shown that all of our theoretical results have the real observational confirmation.

I would like to express my gratitude to Professor G. F. Smoot III for discussion the Universe rotation problem during his visit the VI Astana world economical forum, 22-24 May 2013, Kazakhstan.