The proposition of being
local and limited area in our
expanding universe of G.
Gamow’s Fireball
(ON THE LOCALITY OF THE
SOURCE OF CMB)
S. S. Poghosyan
Yerevan, Armenia
armon-1954@mail.ru
I.
II.
The defects of standard cosmological system
(SCM), which specify the occurring of the
recombination’s process in the local and limited
area (in the volume) of the universe, and not in
the whole volume of the universe.
the proposition of being changeable the CMB
photons’ quantity (N y ), as well as the decision
of the subordinate mass’s quantity of the
recombination
III. the proposition of being isolated, autonomous
system of G. super clusters, which allow us to
suppose, that those were in a compact state and
in that state has occurred the recombination.
Revealing the defects of Friedman-Lemetr’s model,
instead of finding the solution of those problems via
the revising and reforming the original foundations
of the theory, the experts chose the easy way,
because the problems of Friedman-Lemetr’s model
become outstanding when we explore the primary
stages of the evolution of the universe, then the
experts assumed, that we cannot extrapolate
Friedman-Lemetr’s model with those primary stages,
and the above stages of expanding, if it describes
correct, in that case it is necessary to find separate
theory, which will describe the initiative and the
primary stages of the universe… it was invented the
inflationary scenario, which in opinion of that
scenario’s authors, <<overcomes> the defects of
Friedman’s model.
***
1.
I.
The conceptual problems of SCM, which
specify and confirm, that the process of the
hydrogen recombination has occurred in the
local and limited area of our expanding
universe and not in the whole volume of the
universe.
The horizon problem is one of the SCM
conceptual problems. During the whole
expanding it reveals the existence of the areas
which have not neither causal nor
consequential connection with each other within
the universe.
Arise a question, how it can be maintained
identical physical conditions in such areas which are
not connected and interacted with each other and
about which dedicate the CMB background’s
homogeneity.
It seems that the inflationary scenario solves that
problem. According which although all those areas have
not physical condition with each other, but because
have emerged from the same point, in that case they
maintain the <<memories>> about the common position,
physical conditions.
Many noticed, that this is not solution of the problem,
but camouflage. So it is being overlooked the main and
primary part of the issue: whether is not our universe a
united and physical system?, How can’t the components
of the physical system are connected physically with each
other, and are free from causal and consequential
connection.
And then, how explain the strict reducing of those
areas’ quantity which are not connected with each other
with causal and consequential connection in the process
90
4( 5)
of the universe’s expanding from 10 till the 10
. This
circumstance has not and cannot have
scientific
explanation, because it is known, it is impossible physical
system, full body in the nature, the components of which
are not connected with each other physically. Such
conglomerate cannot develop in a direction, obey to
some patterns, cannot survive as an integrity.
The horizon’s paradox in F-Lemetr’s model originates
from the
mU = PU • VU = const assumption, which
theoretically was so benefit that consulted the mass’s
(energy) preservation law and the cosmological principle
ensuring the model’s dynamics (expending or
compression). This dynamic model suddenly got its
confirmation in Hubble’s revelation: galaxies leave form
each other with 𝑣 = 𝐻𝑟 law. This was viewed as an
experimental proof of that model, which was promotion
for ubiquitous accepting of that model.
But SCM paradoxes including the horizon’s problem
stayed unsolved.
a)
Firstly, there is not any experimental
proof, that the mass of our universe stay
unchangeable during the expansion
b)
Secondly,
if
the
mass
stay
unchangeable, then it is also necessary to
consult the others laws of the protection, for
example: the protection law of the rotational
2
torque:
JU =
GmU
= const
C
,
which
contradicts to the izotopration principles of the
universe.
c)
And thirdly, the horizon’s problem
dedicates, that the model does not correspond
to the reality, because infringes the main
principle of the physics: the principle of
causality.
2.
The second important conceptual
problem is the flatness problem, which
substance…
These are theoretical problems and originate from
the primary assumption of F-Lemetr’s model, if as
mU = pv = const , supervise of which, that the
radius of the universe is growing much faster, than
the
tU time. So the mode of the universe’s
expanding is irregular changeable.
From these paradoxes the experts has done a
correct conclusion, that we cannot use Friedman’s
theory to describe the very early stages of the
expansion of universe.
So it turns out, that the very late stages of the
expansion of that theory describe correct, and the
stages of the early period no.
The point is, that the defects of that Cosmo model
become outstanding and bright are being used
towards to the early periods of the universe, but this
is not mean, that it is generally correct. That theory
also describe wrong the stages of the late period,
including the stage of the recombination too,
because the above mentioned problems of that
theory, how the experts have described, are really
conceptual. So the foundation of that theory must be
reviewed, that model need to be changed
conceptually, but not to be attached of the
inflationary model.
So it is clear, that the SCM is a theory with patches
but not a complete and united physical theory.
According
to
Gamow,
during
the
recombination the mass of the universe is equal:
mU = 10 g 56 , and the radius is puny for 10 3 times:
RU = 10 cm 25 from today Hubble’s radius. Why is
the radius of the universe being accepted such, so it
corresponds to the physical conditions which are
necessary for the recombination. One of those
conditions
subordinate
requires,
that
plasma
of
the radius
the
of the
Fireball
and
recombination is direct comparative to the length
of the CMB photon’s wave and is inversely
comparative to T temperature: RU ~ ry ~
1
.
T
During the recombination is
ry = 10 cm
4 ( 5)
3
little 10 times from today index, and T is even so
big. So, if we view the universe as a Fireball, then
the
RU radius is little 10 3 times: 𝑅𝑈 = 1025 с𝑚 .
And, it seems, everything is right, because are
making the index of the physical conditions which
are necessary for the recombination: the density
𝑚𝑈 =1056 𝑔
𝜌𝑟𝑒𝑐 = (𝑅
25
3
𝑈 =10 с𝑚)
3
= 10−20
𝑔
с𝑚3
Friedman’s model : 𝜌𝑈 ≈ 1065
, so it is
and appropriate
г
с𝑚3
=
1056 𝑔
10−9 с𝑚3
in that
time.
It is impossible to overcome this inconsistence even via
the inflationary scenario.
This fact also testifies, that the above mentioned
regularity of the <<Fireball>> is not belong to the
universe. Much more, it is clear, that the radius of the
universe (or righter Hubble’s radius) is being related to 𝑟𝛾
and 𝑇𝑈 differently: in the complexion of 𝑅𝑈 ~𝑟𝛾2 ~
1
𝑇2
, if
RU is being increasing n times, then the 𝑟𝛾 is being
Т𝑟𝑒𝑐 = 10 𝐾 temperature. Gamow’s dedicate is
the
true. In 1965 it was discovered the CMB radiation
and so the model of the hot universe or Big
Explosion definitive won.
But the issues stayed.
increasing √n times, and the 𝑇𝑈 is being dwindling √n
1) Firstly, in the case of 𝑚𝑈 = 𝜌𝑈 ∙ 𝑣𝑈 = 𝑐𝑜𝑛𝑠𝑡 the
𝑅𝑈 = 1025 с𝑚 radius is little 103 times from the
gravitational radius of the universe: 𝑅𝑔(𝑈) =
2𝐺𝑚𝑈
𝑐2
times.
II.
≪ 𝑅𝑟𝑒𝑐(𝑈) = 1025 с𝑚, so in the satge of
the recombination our universe has been Black
Hall.
2) Secondly, the horizon’s problem is being
maintained in the stage of the recombination,
too. So, in the volume of 𝑣𝑈(𝑟𝑒𝑐) = 1075 с𝑚3
there are areas which are not connected with
each other with causal and consequential
connection, which are independent and are not
interact with each other, but surprisingly in all
those autonomous areas almost in the same
time occur the process of the recombination.
3) in the stage of recombination the radius of our
universe is big 102 times from the horizon’s
radius:
𝑅𝑈(𝑟𝑒𝑐) = 1025 с𝑚 ≫ 𝑅ℎ = 𝑐𝑡𝑟𝑒𝑐 = 𝑐 ∙
1013 с = 1023 с, which is also unnatural.
The mass/energy immutability of the <<Fireball>> is
one of the important physical stipulations of the
recombination’s theory, as well as the immutability of the
photon’s quantity (relativistic particles) during the
adiabatic expansion.
As the SCM attributes the recombination’s process to
the whole universe, then all the experts argue, that the
CMB photon’s quantity in our universe, the 𝑁𝛾 is
unchangeable. If we proof the vice versa, then it will be
revealed that theory’s vulnerability.
According to the recombination’s theory, in the stage
of the recombination is 𝜌𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 = 𝜌𝐶𝑀𝐵 , and it means,
that in that stage the plenary energy of the whole
photons is equal to the energy of the material’s rest (all
the protons): 𝑁𝑝 ∙ 𝑚𝑝 ∙ 𝑐 2 = 𝑁𝛾 ∙ 𝑇𝑘, moreover it is also
known
***
It emanates from the analysises of Friedman’s
1
model’s problems, that the 𝑅 ~𝑟𝛾 ~ regularity of
𝑇
the adiabatic expanding fire ball is not belong to the
universe.
So, for example, doing extrapolation to the
beginning of the universe’s expansion, in the case of
𝑧 = 1031 corresponding with the above mentioned
law, it must be 𝑇𝑈 = 1032 𝐾, but it is known, that for
the Planck’s temperature it corresponds the 𝜌𝑝𝑙 =
1093(4) Planck’s density, whilst correspond to
The proposition of being changeable of the
CMB photon’s quantity, as well as the decision
of the quantity of the recombination’s
subordinate mass.
specific entropy:
𝑁𝛾
𝑁𝑝
= 1010 , which is also a
protected greatness.
It was clear, that the Fireball’s energy subordinate to
the recombination is equal to 𝐸𝑟𝑒𝑐 = 𝑁𝑝 ∙ 𝑚𝑝 ∙ 𝑐 2 = 𝑁𝛾 ∙
𝑇𝑘.
a) Firstly, the Fireball’s mass/energy is determined
by the proton’s mass/energy. Knowing the today
proton’s quantity in our universe: 𝑁𝑝 = 𝑛𝑝 ∙
𝑣𝐻 = 10−7 ∙ 1084 с𝑚3 = 1077 , we can slough
the 𝑁𝑝 quantity unchangeable, and the Fireball’s
mass in the stage of recombination will be
𝑚𝑟𝑒𝑐 = 1077 ∙ 𝑚𝑝 = 1053 𝑔 , which yields 103
times to the 𝑚𝑈 = 1056 𝑔 = 𝑐𝑜𝑛𝑠𝑡 greatness.
So what? in the stage of recombination the
mass/energy
of
the
universe/fireball
is
determined with TM mass, which did exceed
3
So (emanating from the dimension’s principle) we got
10 times to the mass of the common material.
a new equation, 𝜎𝑇 4 =
In that case the recombination process would
the universe-fireball:
be impossible.
b) Secondly, if the fireball’s mass/energy is
determined by the all protons’ and photons’
mass/energy, then in that case it is violated
Friedman-Lemetr’s main assumption 𝑚𝑈 =
𝜌𝑣 = 𝑐𝑜𝑛𝑠𝑡, and the universe’s mass has been
reduced 103 times during the recombination.
Lets continue our idea. We are interested in the
𝑚
, which can be used towards
𝑡3
𝜎𝑇𝑈4
=
𝑚𝑈
3
𝑡𝑈
, from where 𝑚𝑈 =
𝜎𝑇𝑈4 𝑡𝑈3 . In this latter put the recombination stage’s
𝑇𝑟𝑒𝑐 = 3 ∙ 103 𝐾 and 𝑡𝑟𝑒𝑐 = 1013 𝑐 indicators, and we
will get the universe-fireball’s mass: 𝑚𝑈 ≈ 1048 𝑔 . So
the 𝑚𝑈 is changeable. From the 𝑚𝑈 = 𝜎𝑇𝑈4 𝑡𝑈3 equation
we can decide the fireball’s energy: 𝑚𝑈 ∙ 𝑐 2 = 𝜎𝑇𝑈4 ∙ 𝑡𝑈3 ∙
4
3
𝑐 2 , Е𝑟𝑒𝑐 = 𝜎𝑇𝑟𝑒𝑐
∙ 𝑡𝑟𝑒𝑐
∙ 𝑐 2 , this equalize to the Е𝑟𝑒𝑐 =
𝑁𝛾 ∙ 𝑇𝑟𝑒𝑐 𝑘 equation and we will get 𝑁𝛾(𝐶𝑀𝐵) =
1
𝜎𝑇 3 𝑐 2
3 𝑘
𝐻𝑟𝑒𝑐
,
plasma’s (fireball) mass, energy and the CMB photons’
where 𝐻𝑟𝑒𝑐 =
quantity subordinated to the recombination. Stefan-
known index of recombination stage 𝑇𝑟𝑒𝑐 = 3 ∙ 103 𝐾
Boltsman’s radiation law is broadly used in the
astrophysics and cosmology. The astronomers via the
𝐿
4𝜋𝑅 2
= 𝜎𝑇 4 equation, if it is known to the astrophysical
object, e. g. the star’s absolute illumination: L radius and
his R radius, can decide the star’s 𝑇𝑒𝑓 effective
temperature. And the cosmologists decide the CMB
energy's density via the 𝜀𝐶𝑀𝐵 = 𝜎𝑇 4 =
𝐿
4𝜋𝑅 2
or his 𝜎𝑇 4 equivalent phrase have
4𝜎𝑇 4
𝑐
𝑚
𝑡3
equation.
dimension
and are used in the science with several meanings:
1)density of the waves’ energy of the flux(waves’
intensity), 2) sound’s intensity, 3) Pointing vector, 4)
surface density of the radiation flux.
and 𝐻𝑟𝑒𝑐 =
𝑡𝑟𝑒𝑐
1
𝑡𝑟𝑒𝑐
. In this equation also it is put two
= 10−13 𝑐 −1 , from which it will be
making in that stage CMB photons' quantity 𝑁𝛾(𝐶𝑀𝐵) =
1082 , and from 𝑁𝑝 =
𝑁𝛾
1010
we will get 𝑁𝑝 = 1072 .
So the 𝑁𝛾(𝐶𝑀𝐵) relict photons’ quantity during the
expansion of our universe is also changeable. And it
follow form these all, that the recombination has
occurred not in the whole volume of the universe, but
in his a local area, moreover not one time, but 105
times.
The proposition of being isolated,
autonomous of G. superclusters, which
allow to assume, that those were in the
compact state and right in that state has
occurred recombination
commonly accepted fact that the Metagalaxy is
homogeneous on large scales is determined by the very
even and homogeneous distribution of superclusters of
galaxies in the Metagalaxy.
The article presents a new hypothesis that the theory
of Gamow’s “Fireball’’ does not refer to our universe
or the Metagalaxy, it refers to the main structural
unit (component) of the Metagalaxy - superclusters
of galaxies.
b) Let us compare the above mentioned with the
following obvious and commonly accepted fact
(established through observations and accepted by
everyone)−on spatial scales smaller than 100 Mpc., the
Metagalaxy is strictly inhomogeneous: there are
vacuums and vice versa high concentration of matter
here and there. The latter are mainly superclusters of
galaxies while the first ones are voids formed between
them. As gravitational grouping and clusterization is
typical of only dark matter and baryonic matter, they
are mainly concentrated in superclusters of galaxies in
the Metagalaxy. As it was discovered in the last two
decades ago, dark matter is distributed in galaxies,
clusters of galaxies and superclusters in a sphericalsymetric way, according to the laws of M ( R )  R
III.
To my mind, each supercluster of galaxies is a
separate, autonomic component of the large-scale
structure of our Metagalaxy (MG). Any supercluster
of galaxies emerges and develops as one, united
physical system. Consequently, if superclusters are
expanding today, they used to be compressed, in a
compact state, with high density and temperature in
the past. And really, if standard cosmological model
(SCM) views the expanding universe as compressed
and extremely dense in the past, why could not
superclusters of galaxies (which, as specialists believe,
are subject to the Hubble expansion), too, were
regarded as extremely compressed, extremely dense
and hot in the past?
This hypothesis of mine contradicts to the SCM
but fully corresponds to the concept of Gamow’s
“Fireball” (to the requirements of the recombination
of hydrogen in the adiabatically expanding volume).
What are my bases for claiming that superclusters of
galaxies are autonomic, separate physical systems
with
their
unique
physical
parameters
(characteristics), composition, special laws of change
and development:
a) On scales larger than 100 Mpc the Metagalaxy is
homogeneous and is inhomogeneous on smaller scales
[1,2]. It is confirmed by astronomical observations of
homogeneous distribution of superclusters of galaxies:
there are approximately 100 superclusters of galaxies in
the
volume
of
V  (10 cm)  10 cm
27
3
81
3
[3].
Consequently, their number reached about 𝑁с.г. = 105
in the Hubble volume
V
mg .
 1084 cm3
.
The
background scanning of CMB found out that the first
peak of intensity corresponds to 10 and is connected
with the concentration of baryons on these scales of
space − the more the concentration, the higher the peak
of intensity [4]. It is therefore not accidental that the
first peak corresponds to the spatial scale of
superclusters of galaxies-1026cm. On larger scales, more
than 100 Mpc., the fluctuations of RR are not strong,
which, too, attest that on larger metagalactic scales
superclusters of galaxies are distributed homogeneously
and there are not physical systems larger than
superclusters of galaxies in the Metagalaxy. Thus, the
1
and 𝜌 ∝ 𝑅2 [5]. This means that there is not dark matter
beyond superclusters of galaxies. "Quite a big contrast in
density implies a gravitational coupling of supercluster
(Ursa Major) on the whole... The supercluster Ursa
Major is sufficiently isolated system" [6]. A striking
example of the disconnection is the recently discovered
supercluster of galaxies of Laniakeya [7].
All the mentioned enables us to claim that
though superclusters of galaxies are subject to Hubble
expansion, they are all the same separate, autonomic
and complete physical systems. This means that
superclusters of galaxies used to be more compressed
and compact with high density and temperature.
Let us do a mental experiment: let us compress the
contemporary superclusters so much as to make their
present radius - Rs. g .
 1026 cm
decrease 103 times, i.e.
Friedmann’s cosmological model will be used in relation
to
contemporary
galaxies,
preserving
ms. g .  V  const . It means that the number of
protons in superclusters of galaxies does not change in
course of time −
change
the
N p ( s. g .)  1072  const ,
number
N ( s. g .)  Vs. g .  n  10
81( 2)
of superclusters
follows
S
N
Np
of
relic
does not
photons
−
 const in the volume
(Vs. g .  1079
)
cm3
 1010  const .
, too, from which
So superclusters of galaxies in a compressed state,
when Rs. g .  10
23
cm
, have an average density -
3
 s. g .  10 21
g , and temperature - Ts. g .  3  10 K .
cm3
That is to say all the conditions for Gamow’s
“Fireball” are present: a) There is the adiabatically
expanding volume of the plasma with the
corresponding requirements - m  V  c o n s, t
S
N
Np
 const , Rs. g . ~ r ~
1
T
Gamow’s “Fireball” were precisely these proto
superclusters of galaxies, each of them has undergone
that phase of evolution (but not together and
simultaneously) and not our universe or Metagalaxy, as
SCM states.
Let us compare these two models of “Fireball’’
to find out which of them is superior and which is
closer to reality.
and so on.
b) The condition for the recombination of hydrogen
Ts. g .  3 103 K.
–  s. g .  10 21
g ,
cm3
What prevents us from accepting and acknowledging
that in the past (at 𝑧 = 103 ) in the condition of
RECOMBINATION EPOCH
“Fireball”- Universe
(SCM)
“Fireball” – Proto-superclusters of galaxies
(our model)
( 6)
mUn  1055
 const.
g
ms. g .  10 48
g
25
RUn  10 cm
23
Rs. g .  10cm
Un  10 21
g
 s. g .  1021
g
cm3
3
cm3
TUn  310 K
tUn  1,2  1013
c - time of recombination
(7)
EUn  1076
erg  const.
 Un  1 erg
c
t s. g .  1,2  1013
c
Es. g .  1069
erg
 s. g .  1 erg
cm3
cm 3
LUn  10 63
erg
Ts. g.  3103 K
c5
 L pl 
G
Ls. g .  10 56
erg  L pl 
c
RUn  Rg
Rs . g .  R g
RUn  ctUn
Rs. g .  ct s. g .
( 6)
mUn  1055
g
the whole mass of the universe
emerged at the very beginning of the expansion
(before and after inflation) and remains unchanged
before and after recombination.
c5
 const .
G
The mass of superclusters of galaxies does not change
after the recombination.
This comparison shows the absolute superiority
the suggested model of the “Fireball”, superclusters of
galaxies, and its correspondence to reality.
1.
Firstly, the Friedmann-Gamow model
presupposes that in the period of recombination the
radius of the expanding volume of the plasma, i.e. the
Thus:
radius of the universe is Rrec  10 cm , which means:
25
а) the mass of the universe changed and took the
corresponding
RUn( rec)
gravitational
radius RUn( g ) , i.e. the universe turned into a
black hole, i.e. recombination processes are out of
the question, b) RUn( rec )  ctUn( rec ) , which is an
insuperable controversy for the Friedman's basic
model, too.
In the suggested model of us, the radius of
the expanding volume of the plasma, i.e. the radius of
the compact proto supercluster of galaxies is
23
Rs. g.( rec)  10cm
,
which
gravitational
is
greater
than
radius
Rs. g.( rec)  10  Rs. g.( g )  10
23
cm
20
cm
the
-
and at the same
time - Rs. g .( rec)  ct s. g .( rec) .
2.
Secondly,
recombination
SCM
Lrec 
implies
76
erg
13
EUn 10

trec 10
that
during
 1063
erg , which is
c
much greater than the marginal luminosity existing in
nature, so I mean the Plank value of luminosity-
c5
L pl 
 3  1059  const .
G
Lrec  1056
erg  L pl 
c
In
our
model
c5
and consequently, it is
G
more realistic. By the way, during a comparatevly short
period of the recombination, as it is known, the great
deal of thermal energy (Es.g. = 1069
erg ) is realesed, which
leads to the great explosion of the compact protosuperclusters of galaxies. Apparently the assumption of
the Nobel laureate - Hannes Alfvén is confirmed, that
Big explosions were many times in our universe or in
Metagalaxy.
3.
And at last, thirdly: on the problem of the mass
of the plasma subject to recombination. How to
determine the numerical value of mrec ? Friedmann’s
hypothesis stipulates − m 
V  const . It is a
working idea, but we have no experimental basis to use
this idea in relation to our universe or the Metagalaxy,
meanwhile we have a definite basis to use it in such
astrophysical systems, as superclusters of galaxies. The
Friedmann-Gamow theory of the “Fireball”,
on
condition that m  V  const . , is true in relation to
superclusters of galaxies, as confirmed by the following
well-known law -
Lrec
m
4
 Trec
 3rec .
2
4Rrec
t rec
It follows from this that the mass of the plasma,
subject
to
recombination,
is
equal
to
4
3
mrec  Trec
 trec
 1048
g
,
if
we
put
into
the
equationonly two quantities, characterising physical
processes of the neutral recombination of hydrogen,
accepted by all specialists –
Trec  3 103 K ,
t rec  1013
c
Thus it becomes clear, that the contemporary
cosmological understandings (SCM) about the epoch
of the recombination does not correspond to reality.
Recombination of hydrogen gas could not take place
throughout the whole volume of our universe.
Because of different reasons many researchers have
sought local sources of background microwave
radiation (relic radiation), but such investigations
were carried out mainly in the frames of the
stationary cosmological model. We managed to find
a model of the local source of the relic radiation,
which proceeds from the cosmological model of the
expanding universe and corresponds to it. But our
new concept about the recombination epoch is based
on a new, GchԱ cosmological model of the universe
with a strictly flat space [8]. This theory changes our
understanding about our universe and its
subsystem−the Metagalaxy.
The list of literature
1. Sarkar Prakash, Yadav Jaswant, Pandey Biswajit, Bharadwaj Somnath The scale of
homogeneity of the galaxy distribution in SDSS DR6. — Monthly Notices of the Royal
Astronomical Society, 2009.
2. Gong Zhi-Yuan Testing the Homogeneity of Large-scale Structure with the SDSS Data. —
Chinese Astronomy and Astrophysics, 2010.
3. The Neighbouring Superclusters.
4. Successes of physical sciences, 2007, George F. Smoot - Anisotropy of the relic radiation: the
discovery and scientific significance.
5. A.D.Chernin, Stars and Physics, 2004, Moscow.
6. F. G. Kopylova, A.I. Kopylov – Letters to the Astronomical journal, 2007, tome 33, No 4, page
243-254. F. G. Kopylova, A.I. Kopylov — Analysis of the properties of clusters of galaxies in
the region of the Ursa Major supercluster, Astrophysical Bulletin, 2009, tome 64, No 1, page
1-23.
7. http://www.sciencedaily.com/releases/2014/09/140903133319.htm
8. S.S.Poghosyan, "The Armon structure of Metauniverse", Yerevan, 2010.