Gravitational instability of vacuum and the cosmological problem
It is shown that, with the account of the gravitational interaction, the physical vacuum can spontaneously partially "dissociate" into particles and antiparticles without violation of any conservation laws. Possible cosmological significance of this effect is discussed. A "vacuum cosm...
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irk-123456789-1118732017-01-16T03:02:42Z Gravitational instability of vacuum and the cosmological problem Fomin, P.I. Квантово-полевые и групповые подходы теоретической физики. Семинар памяти Петра Ивановича Фомина It is shown that, with the account of the gravitational interaction, the physical vacuum can spontaneously partially "dissociate" into particles and antiparticles without violation of any conservation laws. Possible cosmological significance of this effect is discussed. A "vacuum cosmological model" is formulated, in which vacuum is taken as the initial state of the Metagalaxy. A generalization of the classical cosmological Einstein equations is made which allows one to take into account phenomenologically the e®ect of gravitational instability of vacuum. This work was reported at the seminar of the Department of the Theory of Gravity on January 26, 1973. (The seminar is lead by K. A. Piragas). Показано, що при врахуваннi гравiтацiйної взаємодiї, физiзичний вакуум спроможний без порушення будь-яких законiв збереження спонтанним способом частково "дисоцiювати" начастинки та античастинки. Обговорюється можливе космологiчне значення цього ефекта. Формулюється "вакуумна космологiчна модель", в якiй вакуум приймається за початковий стан Метагалактики. Зроблено узагальнення класичних космологiчних рiвнянь Ейнштейна, якi дозволяють феноменологiчно врахувати ефект гравiтацiйної нестiйкостi вакуума. Работа доповiдалась на семинарi вiддiлу теорiї гравiтацiї 26.01.1973 p. (Керiвник семiнару К.А. Пiрагас). Показано, что при учете гравитационного взаимодействия, физический вакуум способен без нарушения каких-либо законов сохранения спонтанным образом частично "диссоциировать" на частицы и античастицы. Обсуждается возможное космологическое значение этого эффекта. Формулируется "вакуумная космологическая модель", в которой вакуум принимается за начальное состояние Метагалактики. Сделано обобщение классических космологических уравнений Эйнштейна, позволяющие феноменологически учесть эффект гравитационной неустойчивости вакуума. Работа доложена на семинаре отдела теории гравитации 26.01.1973 г. (Руководитель семинара К.А. Пирагас). 2013 Article Gravitational instability of vacuum and the cosmological problem / P.I. Fomin // Вопросы атомной науки и техники. — 2013. — № 3. — С. 6-9. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS: 95.35.+d, 98.80.Es http://dspace.nbuv.gov.ua/handle/123456789/111873 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
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English |
| topic |
Квантово-полевые и групповые подходы теоретической физики. Семинар памяти Петра Ивановича Фомина Квантово-полевые и групповые подходы теоретической физики. Семинар памяти Петра Ивановича Фомина |
| spellingShingle |
Квантово-полевые и групповые подходы теоретической физики. Семинар памяти Петра Ивановича Фомина Квантово-полевые и групповые подходы теоретической физики. Семинар памяти Петра Ивановича Фомина Fomin, P.I. Gravitational instability of vacuum and the cosmological problem Вопросы атомной науки и техники |
| description |
It is shown that, with the account of the gravitational interaction, the physical vacuum can spontaneously partially "dissociate" into particles and antiparticles without violation of any conservation laws. Possible cosmological significance of this effect is discussed. A "vacuum cosmological model" is formulated, in which vacuum is taken as the initial state of the Metagalaxy. A generalization of the classical cosmological Einstein equations is made which allows one to take into account phenomenologically the e®ect of gravitational instability of vacuum.
This work was reported at the seminar of the Department of the Theory of Gravity on January 26, 1973.
(The seminar is lead by K. A. Piragas). |
| format |
Article |
| author |
Fomin, P.I. |
| author_facet |
Fomin, P.I. |
| author_sort |
Fomin, P.I. |
| title |
Gravitational instability of vacuum and the cosmological problem |
| title_short |
Gravitational instability of vacuum and the cosmological problem |
| title_full |
Gravitational instability of vacuum and the cosmological problem |
| title_fullStr |
Gravitational instability of vacuum and the cosmological problem |
| title_full_unstemmed |
Gravitational instability of vacuum and the cosmological problem |
| title_sort |
gravitational instability of vacuum and the cosmological problem |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2013 |
| topic_facet |
Квантово-полевые и групповые подходы теоретической физики. Семинар памяти Петра Ивановича Фомина |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/111873 |
| citation_txt |
Gravitational instability of vacuum and the cosmological problem / P.I. Fomin // Вопросы атомной науки и техники. — 2013. — № 3. — С. 6-9. — Бібліогр.: 6 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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AT fominpi gravitationalinstabilityofvacuumandthecosmologicalproblem |
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2025-07-08T02:49:59Z |
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2025-07-08T02:49:59Z |
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1837045382961430528 |
| fulltext |
GRAVITATIONAL INSTABILITY OF VACUUM AND THE
COSMOLOGICAL PROBLEM
P.I. Fomin
Bogolyubov Institute for Theoretical Physics, 03680, Kiev, Ukraine
Preprint ITP-73-137P∗
It is shown that, with the account of the gravitational interaction, the physical vacuum can spontaneously partially
”dissociate” into particles and antiparticles without violation of any conservation laws. Possible cosmological signif-
icance of this effect is discussed. A ”vacuum cosmological model” is formulated, in which vacuum is taken as the
initial state of the Metagalaxy. A generalization of the classical cosmological Einstein equations is made which allows
one to take into account phenomenologically the effect of gravitational instability of vacuum.
This work was reported at the seminar of the Department of the Theory of Gravity on January 26, 1973.
(The seminar is lead by K. A. Piragas).
PACS: 95.35.+d, 98.80.Es
1. The purpose of the present paper is to pay at-
tention to the effect of the gravitational instability of
vacuum and to consider its possible cosmological sig-
nificance. The essence of this effect is that, with the
account of the gravitational interaction, the vacuum
in finite spatial volumes can spontaneously partially
“dissociate” into particles and antiparticles (we call
it “bimatter”) without violation of the law of conser-
vation of energy: the created bimatter falls into its
own gravitational potential well and, in the case of
sufficiently large proper mass M of bimatter (which
is the mass without the account of the gravitational
binding energy), this well can be sufficiently deep so
that the gravitational binding energy U(M) totally
compensates for the energy Mc2 :
Mc2 + U(M) = 0 . (1)
Such strong fields should be considered in frames of
the general theory of relativity (GR); in this case, GR
leads to the notion of a closed space [1, 2] (see below),
but the essence of the effect can be qualitatively un-
derstood already on the level of the Newtonian de-
scription of gravity. In frames of the Newtonian the-
ory,
U(M) = −ηGM2a−1 , η ∼ 1 , (2)
where G is the gravitational constant, a is the spatial
size (radius) of the system, and η is a dimension-
less positive coefficient depending on the details of
the mass distribution (η = 3/5 in the case of a uni-
form ball). Substituting (2) into (1), we arrive at the
equation
Mc2
(
1− ηGM
c2a
)
= 0 , (3)
which admits two solutions, namely, M = 0 and
M =
c2a
ηG
. (4)
The first solution corresponds to the vacuum state
of quantum fields; the second one corresponds to
the configuration under consideration (we shall call
it “null system”) arising as a result of partial dis-
sociation of vacuum into particles and antiparticles.
Both states have equal (zero) total values of strictly
conserved quantities — energy, charge, baryon and
lepton numbers (the difference is only in their spatial
density distributions) — and, therefore, transitions
between them are possible. In this case, dissociation
of vacuum is a thermodynamically favorable process.
Indeed, the vacuum, as a state without excitations,
should be assigned zero entropy, whereas a null sys-
tem is characterized by high entropy: because of de-
cays of unstable particles and pair annihilations, it is
quickly heated to temperatures corresponding to its
density (T ∼ ρ1/4), even if it had zero temperature
at the time of its creation.
In the transition |vacuum〉 → |null system〉, the
average mass density ρ increases from ρvac = 0 to
some maximum value ρ0 which can be roughly es-
timated by assuming that the creation of the null
system corresponds to a situation in which the com-
ponents of every created hadron pair turn out to be
∗This preprint indisputably establishes priority of P.I. Fomin in problem of quantum birth of the Universe. The English
version of the preprint printed by the Decision of the Scientific Counsel of the Institute for Theoretical Physics of the Ukrainian
Academy of Sciences.
6 ISSN 1562-6016. PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2013, N3(85).
Series: Nuclear Physics Investigations (60), p.6-9.
separated by distances
r ≥ r0 ∼ 10−13 cm , (5)
starting from which one already can speak of the ex-
istence of real particles. Since hadron masses are of
the order m ∼ 1 GeV/c2, this corresponds to the
following condition on the average mass density:
ρ ≤ ρ0 ∼ m
r3
0
∼ 1015 g · cm−3 . (6)
Expressing M in (4) through ρ,
M = ξa3ρ , ξ ∼ 4 , (7)
we find
a =
c√
ηξGρ
, M =
c3
√
η3ξG3ρ
. (8)
From the physical reasoning, it is clear that most
probable is creation of a null system with minimal
possible values of a and M , hence, with maximal ρ.
Accepting condition (6) for ρ, on the basis of (8), we
obtain
amin ∼ 3 · 106 cm , Mmin ∼ 7 · 1034 g ∼ 35M¯ .
(9)
This estimate is, of course, conditional and can be
modified with the modification of the estimate (6) of
the upper bound for density. We note that the for-
mally possible increase, relative to (5), of the “pack-
ing” of hadron pairs does not immediately lead to an
increase of the mass density because one should take
into account that, in this case, the mass deficit due
to strong interactions also rapidly increases.
2. From the viewpoint of GR, the space occupied by
a null system created from the vacuum is curved and
closed. Its closeness is connected with the equality of
the total energy to zero [1, 2]. In Fig. 1, we schemati-
cally show the curvature and topology of space before
and after the creation of a null system. The space
of the null system S0 sort of “branches-off” from the
vacuum space Sv. This process should be regarded
as a peculiar tunneling transition from one quasi-
stationary state of quantum fields to another one.
Sv
a
Sv Sv
S0
Fig.1
Here, we will not discuss the equations describing
quantum transitions of this kind and the magni-
tude (undoubtedly, very small) of the corresponding
probabilities. We shall pay attention to the impor-
tant question of the future evolution of the created
null system. Since, according to estimate (8), a null
system is a macroscopic multi-particle state, for an
approximate description of its evolution, one can
apply the classical semi-phenomenological approach
considering it as a result of averaging of the quantum
equations. The evolution of the metric of the space
of S0 should be described in this case by the classical
Einstein equations, somewhat generalized, however,
to take into account the gravitational instability of
the vacuum. We are talking now about the instabil-
ity of the vacuum filling the curved space of the null
system S0. This instability is of two kinds. First,
new closed spaces S′0 etc. can branch-off from S0 as
well as from Sv. These processes, however, do not
affect the evolution of the space S0 itself, and we will
not take them into account. Second, the dissociation
of the vacuum of S0 can lead simply to an increase
of the number of particles and antiparticles in the
space S0 and to the corresponding increase in the
mass M of bimatter and entropy of the null system.
This process is energetically allowed since, according
to (4), an increase in M can be compensated by an
increase in the system radius a (the role of which is
played by the curvature radius in GR); moreover, it is
thermodynamically favorable and, therefore, should
necessarily occur. The question about its intensity
cannot be solved theoretically at present and should
be considered on a phenomenological level.
How should one generalize the Einstein equations
to take into account phenomenologically the disso-
ciation of vacuum? Vacuum can be characterized
by energy-momentum tensor of the form [2, 3, 4]
T vac
µν = −λgµν . We assume that the invariant vac-
uum energy density λ depends on the curvature of
space (hence, on space and time coordinates), and,
just for a trial, we take the simplest dependence
λ = kκ−1R(x) , (10)
where κ = 8πGc−4, R is the scalar curvature, and k is
a dimensionless constant having the meaning of the
“coefficient of elasticity of vacuum.” This assump-
tion agrees with the idea due to A. D. Sakharov [5]
that vacuum resists curving of space, demonstrating
the property of “elasticity,” and can in principle be
verified in frames of quantum field theory in a Rie-
mannian space. With the account of (10), the Ein-
stein equations take the form
Rµν −
(
1
2
− k
)
gµνR = κTµν . (11)
The divergence of the tensor of mass of bimatter Tµν
is now different from zero, T ν
µ; ν 6= 0, which reflects,
in frames of the made assumptions, the contribution
from the dissociation of vacuum. It is not difficult to
show that equations (11), under certain conditions
on the parameter k, indeed lead to an increase of the
mass of bimatter M and to an increase of the vol-
ume of the space of S0. These equations, at the same
time, do not contradict the known gravitational ef-
fects since, outside the masses, they reduce to the
usual equations Rµν = 0.
3. The effect of gravitational instability of vac-
uum gives a foundation for a new approach to the
7
cosmological problem. Assuming that it is this ef-
fect that determines the creation and evolution of the
Metagalaxy, we arrive at a “vacuum” cosmological
model the main provisions of which can be formu-
lated as follows:
1. The initial state of the Metagalaxy is vacuum;
2. The Metagalaxy is a “null system,” i.e., it is
characterized by zero total values of the strictly
conserved quantities: energy, charge, baryon
and lepton numbers; the consequence of this,
according to GR, is the spatial closeness of the
Metagalaxy;
3. The Metagalaxy is created from vacuum at
some moment of time t = 0 as a result of the
quantum transition |vacuum〉 → |null system〉
of the type described above, and has size and
proper mass of order (9) at the moment of cre-
ation;
4. After that, its mass and entropy increase as
a result of continuous dissociation of vacuum;
this growth causes expansion of the space of
the Metagalaxy;
5. The evolution of the Metagalaxy is approxi-
mately described by the Einstein equations of
type (11).
Equations (11), in particular, imply that dissoci-
ation of vacuum proceeds with maximal intensity at
places with maximal mass density — this opens up
the possibility of explaining the mysterious activity
of galactic nuclei [6]. In this case, one can indicate
(this will be published elsewhere) a sufficiently effec-
tive mechanism of separation of the bimatter created
in the nuclei into matter and antimatter and, there-
fore, to rebut the known arguments [2] against the
charge death of the Universe.
A more detailed development of the discussed is-
sues will be published elsewhere.
Institute for Theoretical Physics of the Ukrainian
Academy of Sciences
Kiev-130
References
1. L. D. Landau and E. M. Lifshitz. Field Theory.
Moscow: ”Nauka” 1967.
2. Ya. B. Zel’dovich and I. D. Novikov. Relativistic
Astrophysics, Moscow: ” Nauka” 1967.
3. J. Schwinger // Phys. Rev. 1949, v.75, p.651.
4. É. B. Gliner // Zh. Eksper. Teor. Fiz. 1965, v.49,
p.542.
5. A. D. Sakharov. // Dokl. Akad. Nauk SSSR.
1967, v.177, p.70.
6. Problems of Modern Cosmogony/ Ed. by
V. A. Ambartsumyan, Moscow: ”Nauka” 1972.
Fig.2. Title-page of the
Preprint ITP-73-137P
The manuscript was received at the Publishing
Department on September 7, 1973.
c© Institute for Theoretical Physics, 1973.
8
ГРАВИТАЦИОННАЯ НЕУСТОЙЧИВОСТЬ ВАКУУМА И КОСМОЛОГИЧЕСКАЯ
ПРОБЛЕМА
П.И. Фомин
Показано, что при учете гравитационного взаимодействия, физический вакуум способен без нару-
шения каких-либо законов сохранения спонтанным образом частично "диссоциировать"на частицы
и античастицы. Обсуждается возможное космологическое значение этого эффекта. Формулируется
"вакуумная космологическая модель", в которой вакуум принимается за начальное состояние Мета-
галактики. Сделано обобщение классических космологических уравнений Эйнштейна, позволяющие
феноменологически учесть эффект гравитационной неустойчивости вакуума.
Работа доложена на семинаре отдела теории гравитации 26.01.1973г.
(Руководитель семинара К.А.Пирагас).
ГРАВIТАЦIЙНА НЕСТIЙКIСТЬ ВАКУУМУ I КОСМОЛОГIЧНА ПРОБЛЕМА
П.I. Фомiн
Показано, що при врахуваннi гравiтацiйної взаємодiї, физiзичний вакуум спроможний без порушен-
ня будь-яких законiв збереження спонтанним способом частково "дисоцiювати"на частинки та анти-
частинки. Обговорюється можливе космологiчне значення цього ефекта. Формулюється "вакуумна
космологiчна модель", в якiй вакуум приймається за початковий стан Метагалактики. Зроблено уза-
гальнення класичних космологiчних рiвнянь Ейнштейна, якi дозволяють феноменологiчно врахувати
ефект гравiтацiйної нестiйкостi вакуума.
Работа доповiдалась на семинарi вiддiлу теорiї гравiтацiї 26.01.1973p.
(Керiвник семiнару К.А.Пiрагас).
9
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