Some problems in the theory of early universe evolution
We continue consideration of physical characteristics of early Universe. Here our attention is concentrated on the three topics: thermodynamics, relic helium, energy of physical vacuum. Продовжуємо розгляд фізичних характеристик раннього Всесвіту. Зосереджуємо нашу увагу тут на трьох питаннях: термо...
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| Опубліковано в: : | Вопросы атомной науки и техники |
|---|---|
| Дата: | 2007 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2007
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Some problems in the theory of early universe evolution / S.S. Sannikov-Proskuryakov // Вопросы атомной науки и техники. — 2007. — № 3. — С. 206-209. — Бібліогр.: 6 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860068909600735232 |
|---|---|
| author | Sannikov-Proskuryakov, S.S. |
| author_facet | Sannikov-Proskuryakov, S.S. |
| citation_txt | Some problems in the theory of early universe evolution / S.S. Sannikov-Proskuryakov // Вопросы атомной науки и техники. — 2007. — № 3. — С. 206-209. — Бібліогр.: 6 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | We continue consideration of physical characteristics of early Universe. Here our attention is concentrated on the three topics: thermodynamics, relic helium, energy of physical vacuum.
Продовжуємо розгляд фізичних характеристик раннього Всесвіту. Зосереджуємо нашу увагу тут на трьох питаннях: термодинаміка, реліктовий гелій, енергія фізичного вакууму.
Продолжаем рассмотрение физических характеристик ранней Вселенной. Сосредотачиваем наше внимание здесь на трех вопросах: термодинамика, реликтовый гелий, энергия физического вакуума
|
| first_indexed | 2025-12-07T17:09:34Z |
| format | Article |
| fulltext |
SOME PROBLEMS IN THE THEORY
OF EARLY UNIVERSE EVOLUTION
S.S. Sannikov-Proskuryakov
A.I. Akhiezer Institute of Theoretical Physics
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine;
e-mail: sanpros@kipt.kharkov.ua
We continue consideration of physical characteristics of early Universe. Here our attention is concentrated on
the three topics: thermodynamics, relic helium, energy of physical vacuum.
PACS: 98.80.Cq, 98.80.Bp, 05.70.–a, 65.40.Gr , 05.70.Jk
1. THERMODYNAMICS
Zero cycle. First of all it is needed to emphasize that
the notion of temperature may be introduced for ensem-
bles of Hamiltonian (or Lagrangian) dynamical systems
only. For bi-Hamiltonian system (ether) such a notion
(as well as energy) does not exist. However after the
Big Bang (in the first cycle) when Lagrangian fields and
particles arisen physical temperature appears. In zero
cycle ensemble of quanta is characterized by funda-
mental parameter T which enters in Gibbs distribution
function [1-3], where
f
f
fTe /ε− ϕϕε =
f
f
fourth compo-
nent of 4-momentum of quantum (in connection
with this formula we might call T as a non-physical
“temperature” of quasi Lagrangian subsystem of bi-
Hamiltonian system ). In the normal state
mean size of quantum is determined by the relation
(we use the system where fundamental con-
stants ) is connected with maximal size of
ensemble
f
)f,( f
f
f
f
1== h
f T/1=λ
c fλ
2
f
)0(
maxR
)0( /1f =
3/1)0( )fN
/1=
2/3G
λ
f
TG
3
fT
( G is gravitational con-
stant) by means of formula ,
where is the number of quanta in
ensemble. At the collapse of ensemble the size and
size of quantum decrease so that the relation
takes place (T stays constant like at
the “isothermal” compression). It is important to em-
phasize that Universe in zero cycle is collapsed because
separate quanta (each individual field ) is con-
structed in that point at which is attached: this is the
main property of bi-Hamiltonian system (in general
theory of dynamical systems such manifolds are called
attractors). In zero cycle entropy of Universe is zero:
(there are no interactions besides the gravita-
tional one, therefore each quantum may be in one
state only). And if Universe in this cycle to characterize
by physical temperature, so it must be equal zero
(“cold” cycle).
3/1))0(
max )/(
f
R
(xf
0(
fN
)
fλ R=
f
N
/(R=λ
0=S
f
f
First cycle. At compression of our ensemble size of
each quantum will be, after all, equaled
where is fundamental parameter (analogous of T )
by which condensed state of our system is character-
ized. Hereby the size of ensemble in whole (Universe)
is
f ff T/1=λ
fT f
f
ff TTGR /10(
min
f→
) =
f
(T is negative magnitude). In
this moment total quantum transition (irreversible con-
fluence) is beginning. It is so called Big Bang.
Hereby the energy
f
ff TT − f ≅T is secreted. It spends
in main for the Universe space expansion. It is impor-
tant to emphasize that the Universe expands because the
process of pushing out of inner points of each
spaceuscule
xx,
( ))(), xf
Π
() xfx
(f x takes place. Inside the
spaceuscule some discontinuum (isomorphic to the Can-
tor’s perfect manifold ) stays only (in general theory
of dynamical systems such manifolds are called repel-
ers). It is important to emphasize also that pushing out
of spaceuscule points has pulsating character deter-
mined by excitation spectrum of degenerate parameters
of condensed state e (that is very strong
degenerate one due to the switching on of interactions
described by parameters . Interesting to note: in [4]
vibrations of electromagnetic field Whittecker identifies
with vibrations of space-idea underlined his ether the-
ory). Einstein paid his attention on the paradox in cos-
mology: (at small mass matter
)(xχ )(iχ
χ
))0( << 0(MM
c
η
V <<=
>>
) wave
equations are getting relativistic theory (GR). However
in Universe theory is non relativistic matter. Relative
velocities in and connecting with them
energies of motion are small in the suggested theory
there are two kinds of motion: radial (total super relativ-
istic) motion with velocity V and relative with
. Total Universe energy (
cϕθ ,
cV << )0(Mη ) is hence
dark energy, so paradox is explained. Thus quantum f
may stands in many different states labeled
and marked by different values of
degeneration parameters . Quantity of such states cor-
responding to one quantum (and also one fundamen-
tal particle) usually calls as specific entropy and de-
notes . We have to calculate this magnitude. In expo-
,...2 fiχ,1 ef, ef iχ
χ
f
S
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2007, N 3 (1), p. 206-209. 206
nent phase is a usual Lagrangian field pulsa-
tions of which have ultrarelativistic character. Density
of such pulsations we denote . At the pure thermody-
namic approach this magnitude depends on temperature
like . Now we determine physical temperature
by the formula T where a is some
function of Universe radius (or time evolution t ). Then
the specific entropy is written
χie
n =γ
χ
γn
aη/
3T
T fT= )(R
)0(
3)(
fN
TR
=
3
S
cρ
)0(
3
f
R
VT=
sR
3/
≤
a4
f
S =γ
(SNS f
0(
fNη
f
T 4==
n
n
=
U =
V
fT
(s =
T 4
f
/4
f
T=
f
=
T
fT
ργ
η
4/1/η
a=
fT
US
b
p
sR η
equS =
=equ
(3 bη
+
R =
R
/ S
S
N= γ
a
e
p
)(Rb
)a
N
p
(b−
K
ηγ =
e+
N
nγ (1)
(obviously number of condensed states coincides
with number of normal states and equals to number
of fundamental particles in the Universe). Hereby for-
mula for entropy of Universe in whole is written
)0 , (2)
where is volume of Universe. If, beginning from
and (the end of the de-Sitter’s stage),
Universe expansion would be adiabatic (Gamov hy-
pothesis), so (because
). However [1-3], from obvious
inequality where and
it follows that
=
R
R =
1) )
ργ
/η
η=const
ρc
4
1
≥a
fT=
)(Ra
, i.e. at the end
of de-Sitter’s stage temperature T , but not
. Writing current radius of Universe in analogous
form where (like ) is some func-
tion of (or ) we get
b
t
3η (3)
(here is the equilibrium specific entropy).
Hence entropy of Universe in whole is
, where is the number of
photons (relic radiation) in Universe. It is essential that
and depend on time evolution t by different man-
ner, and therefore adiabatic condition ( b ) was ful-
filled in past not always. Question about adiabatic re-
gime of Universe expansion has been already discussed
in literature [1-3]. One considers that this regime was
set long after the Big Bang when temperature decreased
lower than (ionization energy of H-atom), i.e.
in atomic era. It is needed for this that the system
“ “ had bound state and interaction (force) be-
tween and e was potential. It is shown in [1-3] that
these conditions took place not always. All depends on
phase state of configuration space of Universe. There
exist three phase states of space: Lebesgue’s continuum,
Bohr’s compact and discontinuum [1-3]. Only in Lebes-
gue’s continuum system “ ” has bound states (en-
(energy binding ) and its angular momentum in it
is not quantized) [1-3]. It turns out that at T
(post de-Sitter’s stage) . Independent estimations
of functions and [1-3] show that in the end of the
de-Sitter’s stage ( ), hadron era ( ) lepton era
( ) and atomic era ( ) had the numerical values
0, 1/3, 2/3, 1 and was equaled to 1/4, 1/2, 3/4, 1.
Consequently in these eras ratio has
values . Entropy
achieving its maximal value in atomic era holds this
value at further expansion of Universe (so only after
atomic era adiabatic regime takes place). Before atomic
era Universe had lower entropy. With this fact lower en-
tropy of Universe space is connected: after the de-Sitter’s
stage configuration space was exist in the Bohr’s compact
phase (see also [1-3]). The signs (relics) of that epoch
conserved near to our time. In this epoch taking about one
year special material structures characterized by lower
entropy were arisen. The most interesting from them are,
we consider, various forms of living matter [1-3].
η
)a−
4000
)0(
fN
<ε
b
10, 69 −
)2/1(s
)2
(
i
s
D
D
×
⊗
)2/ =
)1(
))1(
s
i
D
D
)1
1(
))1(
)0(
s
s
s
D
D
D
⊗
),0(
K4000>
)(3 ab−η
S
4He
)2(sSU⊗ i
⊗
))2/1(
))2/1
).1()
)0()0(
s
s
D
D
⊗
⊗
d
( )
))2()1(
)0()2(
)0()1
ss
s
s
D
D
D
+
⊗
⊗
.2,1,
)2()0( sD⊗
ab ≠
aR b
(1,3−
η
4He
())2
()) iD
⊗
×
1() D+
)1(
)0(
i
sD
⊗
+
)0(
)0(
)0(
i
i
I
D
D
⊗
⊗
)0 sD⊗
a
sR
a
10,
/1(
2/1
(D
(
D+
⊗
)
D
+
=
+
(iD
HR
equ =
)
)2(i
(
s
s
D
D
×
0(i
i
D
D=
)
((
i
i
D
D
D
+
+
0=s
iD
LR
1(iD
(
=
/1(D
(
+
0(iD
(
+
+
4He
(2 iD
/ SS
1012
SU
)2/1(
)2/ ⊗
)0(
))1(s
+
0(
)1(
))1(
s
i
D
D
×
)
10 =η
D⊗
/1(
1(2/1
si D
)(D×
)1(
)0
sD
D+
sD
()1(
)0(
)1
i
sD
+
⊗
1(D⊗
−
)
1
⊗
(
⊗
s
0
0
2. RELIC HELIUM
Usually one considers that creation of cosmic
is a result of nucleon-synthesis or nucleon-fusion [5].
We consider that cosmic appeared as a result of
disintegration of super dense body of Universe at its
expansion. Due to the quantum correlation between spin
and isospin and switching on the strong interaction be-
tween nucleons the bound conglomerates may remain
but not only individual nucleons will be. Nucleon skele-
ton (see [1-3]) is described by the representation
of the group (
and are isotopic and usual spin indices; is the di-
rect product). Two-particle conglomerates are described
by the representation
)2/
s
(
(i
D
D
(× is the Kronecker multiplication). As
, so we have )2
(
i
i
D
D
Due to the Pauli exception principle only two latter
terms are realizable in the Nature; hereby states
correspond to the deuteron . Proceed-
ing from these states we build four nucleons conglom-
erates. They are described by the representation
)⊗
2
(
i
i
D
D
D
)0
is an isosinglet with usual spin It is de-
scribed by the representation
and .
At strong interaction switching on the latters correspond
207
to the bound states of four nucleons ( ). The rest are
states of four nucleons without bound states. Number of
possible states with isospin and usual spin is
. Using this formula we get that the total
number of states consisting of four nucleons is 36.
Number of states for is 10. Ratio 10/36=0.27
gives the percentage of in the Universe. Cosmic
observations give the same number [5].
4He
i s
)12)(12( ++ si
4He
4He
0(0 000 ∫= XTP
∑ −
ms
s
,
2 2()1(
)(XDm
+
s
∫= d0
+
m
∂
∂ D
t 2
2
0(
∑
=
ms
vac
,
ρ ∫ d 3)1
+ m2p
I sin)(θ
)I)( 22 ppYI −=
),( 0 YYY =
),cos( Yp
(XDm
+
∫+± )12( ds
22 mp =
−2
2
)
)pY
+ 2m
[∑ ∫± ppd2 3
0=Y 2p=2)pY −
3. ENERGY OF PHYSICAL VACUUM
Here a contribution of physical vacuum (zero vibra-
tions of the Lagrangian particle fields) into energy of
Universe is calculated. In quantized field theory energy
of physical vacuum is determined by the expression
), 3Xdt , see [6], where T is the
total energy-momentum tensor of all quantized fields
and 0 is the state of physical vacuum. Magnitude
may be expressed as the following sum
µν
0P
+ t Xt
i
s 3),1)1 , (4)
where is the Pauli-Jordan function of positive
frequency, and m are spin and mass of particle. In
the local theory (point-like particles) energy density of
vacuum is given by the sum (see [6])
+± ps 22( , (5)
where signs “+” and “–“are for bosons and fermions
correspondingly. It is obviously infinite magnitude.
However in the bilocal field theory (non-point, smear-
ing particles [1-3]) particles have the space-time struc-
ture described by the function
I
I where
is the Heaviside function and
are the inner space-time coordinates of par-
ticle. In the case of physical vacuum these variables are
free (see [1-3]; for massless particles structure function
is ). For smearing particles the Pauli-Jordan
function is given in [1-3]. Using this func-
tion the expression for energy density of vacuum is
written in the form of sum of integrals
(,2Y θ
), Y
−
22
22
23
(
(sin
YppY
Yp
pp , (6)
(here we took into account that for free particles
; for massless particles we have the sum
]pYcos
(
vacρ
because there are only two
chiral states). We else may choose the system in which
and therefore . In result
the expression for is the sum of terms
2
0
22 YYp
,)()(4)12(
sin
)12(
02204
0
0
0223
mYKmY
Y
s
Yp
Yp
mppds
π
+=
++± ∫
∓
(7)
where is the Macdonald’s function. So for bosons
is a negative magnitude and for fermions it is a
positive one. At the limit of small this gives
(at m when the structure function
is we have ). In another limit
we have . To estimate the
numerical value of we resort to the following
consideration. So far as at the Universe expansion the
ratio where is a free length and is radius of
the Universe) is invariant (see above) so we have to
consider that Y . Obviously the physical vacuum
appeared together with particle appearance after the so
called de-Sitter’s stage when the radius of the Uni-
verse has been . At this
stage had the minimal value equaled to the funda-
mental “length” 1 . At the Lebesgue phase (space for
elementary particles is always the Lebesgue one)
and hence
2K
8)1+
{pY
∞→
λ/R
0Y
skR/
vacρ
2( s∓
cos
0mY
RY0 =
0mY
R
R
13/5
ff T
4
0/Yπ
}
0
R
0=
48∓
2/3 em −
vacρ
32/7 hc
4
0/Yπ
5
0/0 YmY
/12/ / G
2/
R
2T
λ
~
s =
k/
3/
.
4)12(
2
24
4
×
+= ∑
s
ms s
svac
hkR
mcRK
hkR
mcR
R
Rhcks πρ ∓
(8)
At small masses ( ) and
(just after the de-Sitter’s stage) we have
Gevkhcmc 1~2 << sRR ~
./)12(
8)12(8)12(
4
4
4
4
4
cTs
T
Thcks
R
Rhcks
vac
f
s
σ
ππ
+=
+=
+
∓
∓∓
(9)
Here the condition is used (see above),
and T (see above).
From this it follows that for nucleon vacuum
(that is compatible with the den-
sity of nuclear matter). Nowadays
and hence for nu-
cleon vacuum that is, of course, negligible small magni-
tude. More over at we have the strict equality
because there are two neutrinos
with chiralities 1/2 and two states of photon with chirali-
ties 1. Note that charge and spin densities of physical
vacuum are strictly zero because integrals
fsTRRT =
f 10~
~ evac −ρ
0=
0
424 /8
fvac Thckπσ =
345 /10~ cmeVvacρ
1810~/ sRR
=+= vac
B
vac
F
vac ρρρ
eV15
1018
eV
cmR 2710~ ,
3/ cm
m
∫ = 0
sin
0
03
Yp
Yp
pd and ∫ cos3 ppd = 00Y .
208
REFERENCES
1. S.S. Sannikov-Proskuryakov. About cosmological
aspects of relativistic bi-Hamiltonian system //Russian
Physics Journal. 1995, v. 2, p. 106-115.
2. S.S. Sannikov-Proskuryakov. Cosmology and a
Living Cell //Russian Physics Journal. 2004, v. 47,
p. 500-511.
3. S.S. Sannikov-Proskuryakov. About strong inter-
action of fundamental particles //Ukr. Journ. of Phys.
2002, v. 47, p. 615-628.
4. E. Whittecker. History of the theory of electro-
magnetism and ether. M.: “MATHESIS”, 2001, р. 125
(in Russian).
5. S. Weinberg. Gravitation and cosmology. M.:
“Mir”, 1975, p. 696 (in Russian).
6. N.N. Bogolubov, D.V. Shirkov. The introduction
to the theory of quantized fields. M.: “Nauka”, 1973,
р. 38 (in Russian).
НЕКОТОРЫЕ ПРОБЛЕМЫ В ТЕОРИИ ЭВОЛЮЦИИ РАННЕЙ ВСЕЛЕННОЙ
С.С. Санников-Проскуряков
Продолжаем рассмотрение физических характеристик ранней Вселенной. Сосредотачиваем внимание
здесь на трех вопросах: термодинамика, реликтовый гелий, энергия физического вакуума.
ДЕЯКІ ПРОБЛЕМИ У ТЕОРІЇ ЕВОЛЮЦІЇ РАННЬОГО ВСЕСВІТУ
С.С. Санников-Проскуряков
Продовжуємо розгляд фізичних характеристик раннього Всесвіту. Зосереджуємо увагу тут на трьох
питаннях: термодинаміка, реліктовий гелій, енергія фізичного вакууму.
209
|
| id | nasplib_isofts_kiev_ua-123456789-110955 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T17:09:34Z |
| publishDate | 2007 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Sannikov-Proskuryakov, S.S. 2017-01-07T14:22:46Z 2017-01-07T14:22:46Z 2007 Some problems in the theory of early universe evolution / S.S. Sannikov-Proskuryakov // Вопросы атомной науки и техники. — 2007. — № 3. — С. 206-209. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS: 98.80.Cq, 98.80.Bp, 05.70.–a, 65.40.Gr , 05.70.Jk https://nasplib.isofts.kiev.ua/handle/123456789/110955 We continue consideration of physical characteristics of early Universe. Here our attention is concentrated on the three topics: thermodynamics, relic helium, energy of physical vacuum. Продовжуємо розгляд фізичних характеристик раннього Всесвіту. Зосереджуємо нашу увагу тут на трьох питаннях: термодинаміка, реліктовий гелій, енергія фізичного вакууму. Продолжаем рассмотрение физических характеристик ранней Вселенной. Сосредотачиваем наше внимание здесь на трех вопросах: термодинамика, реликтовый гелий, энергия физического вакуума en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники QED processes in strong fields Some problems in the theory of early universe evolution Деякі проблеми у теорії еволюції раннього всесвіту Некоторые проблемы в теории эволюции ранней вселенной Article published earlier |
| spellingShingle | Some problems in the theory of early universe evolution Sannikov-Proskuryakov, S.S. QED processes in strong fields |
| title | Some problems in the theory of early universe evolution |
| title_alt | Деякі проблеми у теорії еволюції раннього всесвіту Некоторые проблемы в теории эволюции ранней вселенной |
| title_full | Some problems in the theory of early universe evolution |
| title_fullStr | Some problems in the theory of early universe evolution |
| title_full_unstemmed | Some problems in the theory of early universe evolution |
| title_short | Some problems in the theory of early universe evolution |
| title_sort | some problems in the theory of early universe evolution |
| topic | QED processes in strong fields |
| topic_facet | QED processes in strong fields |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/110955 |
| work_keys_str_mv | AT sannikovproskuryakovss someproblemsinthetheoryofearlyuniverseevolution AT sannikovproskuryakovss deâkíproblemiuteorííevolûcíírannʹogovsesvítu AT sannikovproskuryakovss nekotoryeproblemyvteoriiévolûciiranneivselennoi |