AstroNuclPhysics ® Nuclear Physics - Astrophysics - Cosmology - Philosophy | Gravity, black holes and physics |
Chapter 5
GRAVITATION
AND THE GLOBAL STRUCTURE OF THE UNIVERSE :
RELATIVISTIC COSMOLOGY
5.1. Basic
starting points and principles of cosmology
5.2. Einstein's
and deSitter's universe. Cosmological
constant.
5.3. Fridman's
dynamic models of the universe
5.4. Standard
cosmological model. Big
Bang.
5.5. Microphysics and cosmology. Inflationary universe.
5.6. The
future of the universe
5.7. Anthropic
principle and existence of multiple universes
5.8. Cosmology
and physics
5.5. Microphysics and cosmology. Inflationary universe.
If we try to reflect the
earliest past of the universe, then the standard
cosmological model (discussed in the previous §5.4) leads
us to an initial state where the structure, development and
future of the universe were decided by interactions of
"elementary" particles in hot and dense
"germ" plasma , in which the mutual distances
between the particles were very small, these particles were
extremely "inflated" on each other. Here, cosmological
research "shakes hands" with physical research in a
seemingly opposite part of science - in the microworld
of elementary particles . The mystery of the origin universe
is helped to be revealed not only by astronomical observations of
the farthest reaches of the universe, but also by experiments on large accelerators., where collisions of particles
accelerated to high energies give rise to extreme states of
matter (matter and excited fields), similar to conditions in the
very early universe.
^{ }Until recently, physics could not
say anything more definite about the time period t < ~ 10 ^{-4} s, when the density of matter in space
significantly exceeded the nuclear density r » 10^{14} g / cm^{3} , because the properties of
matter at such extreme densities (ie the interaction of
elementary particles in superhigh energies) were not known.
Recently, however, the physics of
elementary particles , especially the theory of electroweak
interactions, grandunification theory and supergravity, thanks to
which it is possible (at least roughly) to understand even
earlier phases - almost to the "Planckian" period t _{p} » 10 ^{-43} s, when the mass density reached
~ 10 ^{94} g / cm ^{3} . This is made possible by a
significant feature of these calibration theories - the so-called
asymptotic freedom , allowing the description of
the interactions of elementary particles at very high energies
approaching the Planck energy E _{p} » 10 ^{19} GeV, which is already dominated
by quantum-gravitational effects. Applications of modern quantum theories of
elementary particles shows that with a gradual change in the
temperature of a super-dense substance, a number of significant phase
transitions occur in it , during which the properties of the
"elementary" particles of which the substance is
composed change very strongly [154], [273].
^{ }It can be assumed that these
phase transitions, which take place during the cooling of the
expanding universe in the earliest stages after the Big Bang,
significantly affected the dynamics of evolution. The study of the of cosmological consequences
of phase transitions
in calibration theories grandunification,
which began
in 1981 with the work af A.Guth [112], leadg to the hypothesis of the so-called inflationary expansion of the universe
, according to which the universe was expanding exponentially
with increasing speed in the earliest stages of its evolution.
One of the basic
concepts of current unitary calibration theories (see §B.6 " Unification
of fundamental interactions. Supergravity. Superstrings. ") is the idea of spontaneous disruption of symmetry between different types of
interactions due to the formation of constant scalar fields j - so-called Higgs
fields -
throughout space. These theories assume that before symmetry
breaking (at very high energies), all vector mesons mediating
interactions have zero rest masses and there are no fundamental
differences between the different types of interactions. After
the formation of Higgs scalar fields of these vector bosons give
effective rest mass, respectively interactions become short-range and the symmetry between different types
of interactions is disrupted. In
Weinberg-Salam theory, the uniform electroweak interactions are
mediated by the exchange of immaterial * 1) vector bosons before
the symmetry is broken, while after the Higgs scalar field, the
vector bosons W and Z gain resting mass, making the corresponding
weak interactions short-range; the photons of the electromagnetic
field remain immaterial. Similarly, in grandunification theories
(GUT), all vector particles are immaterial before symmetry
breaking, and there is no fundamental difference between weak,
strong, and electromagnetic interactions (eg, leptons can
transform into quarks and vice versa). After the formation of the Higgs field
(there are several types of scalar fields in GUT), the vector
mesons X and Y acquire a large rest mass of ~ 10 ^{15} GeV, thus separating strong interactions
from electroweak ones; interconversion of quarks and leptons is
almost the harvest of the wording and the proton becomes
practically stable. Another scalar field then breaks the symmetry
between weak and electromagnetic interactions. Conversely, it can
be expected that a sufficiently high energy of interacting
particles (i.e. at an extremely high temperature of the
substance) scalar field j leading to symmetry breaking
must disappear and symmetry between different types of
interactions is restored.
* ^{1} ) By the abbreviated
name "non- mass particle"
we mean "particles with zero rest mass".
^{ }It is assumed that there was perfect
symmetry at the beginning of the universe. Then a slight quantum
disturbance caused vibrations in the unitary field and a
transition to a lower energy state - a spontaneous disruption
of symmetry . An early disruption of symmetry caused the
interactions to separate from each other, their quantum -
particles - to become different. This reduction in symmetry has
created all the matter and structures in the universe. It can be
said that everything symmetrical that we see around us are
"fragments" of the original symmetry at the beginning
of time.
The phase transitions in a super-dense substance, accompanied (and caused by) changes in the symmetry of the interactions, can be :
Inflationary
expansion of the universe
The theory
of the phase transition during the gradual cooling of a
superdense due to the expansion of the universe just after the
Big Bang was first used by A. Guth [112], who assumed that the
universe was initially in a symmetrical
state with j = 0, in
which, however, the energy of the vacuum (empty space-time itself) e = V ( j
= 0) was very high -
it was a kind of "false vacuum" (Fig.5.7a). In the
terminology of §5.2 it can be said that there was a large value of the cosmological constant L - see note *^{2}
below ). During
expansion (which could initially, as long as the energy density
of the particles exceeded the energy of the vacuum V (0), proceed
according to the law a (t) ~ t ^{1/2 }of the standard model) and by cooling
the universe, the energy density of relativistic particles
(proportional to T ^{4} ) soon became negligibly small
compared to the vacuum energy V (0). However, there has not yet been an immediate (continuous) phase transition to
the state of broken symmetry j
= j_{o} , i.e. from a "false"
to "real" vacuum with L @ 0.
Fig.5.7. Some cosmologically important waveforms of the effective
potential V ( j ) of the scalar field j causing
symmetry breaking in calibration unitary theories.
a ) Effective potential leading to a smooth phase transition of
the 2nd type from the symmetrical state j = 0 of the
"false vacuum" to the state j = j _{o} with disturbed symmetry.
b ) In the
case that the effective potential V( j ) has two
local minima (one corresponds to a stable state j = j _{o} and the other to a metastable state j » 0),
a phase transition of the 1st species occurs.
c) If
the effective potential V ( j ) in
tehe region of small j decreases sufficiently slow, the inflationary expansion of the universe
will continue even during the
phase transition - see the text.
If the effective potential V ( j ) has the shape according to Fig. 5.7b, the symmetrical phase of the false vacuum is stabilized by a small energy barrier, which must be overcome by the tunnel effect before transitioning to the asymmetric state of the real vacuum with j = j _{o} ; then a certain metastable state could first be reached under strong " subcooling", in which the universe was kept for some time still in a symmetrical state of a false vacuum with a large value of L . In this situation, the energy density in the expanding universe is close to the value of V (0) given by the false vacuum and is practically independent of time. According to Einstein-Fridman equations, specifically equation (5.23a), in this state the universe will expand according to the exponential law
a(t) ~ e ^{H. t} , | (5.54) |
where Hubble's "constant" H is
H = Ö [(8/3) p GV (0)] > ~ 10 ^{35} s ^{-1} . | (5.55) |
Equivalently, the
dynamics of cosmological evolution has for some time been
following the de Sitter model (§5.2) under the
"rule" of the large cosmological constant L *). The cosmological
constant , first introduced by Einstein and then
described as the " biggest mistake of his life,
" has been " rehabilitated " in
the form of an inflationary vacuum that can explain the earliest
phases of the universe. ..
*) From a mathematical point of view, the Lagrangian of the
scalar field together with the cosmological metric (5.22) leads
to the bounded equations for gravity and the field j : ^{..}j + 3.^{.}j.^{.}a/a
+ dV(j)/dj = 0, (^{ .}a/a)^{2} + 1/a^{2} = (8pG/3)[V(j) + ^{1}/_{2} ^{.}j^{2}],
where V ( j ) is the
effective potential. Higgs scalar field j used in the
unitary gauge theories Lagrangian contributes to the simplest
case said L _{j} = ^{1} / _{2} ( j _{, i} ) ^{2} - ^{1} / _{2} m ^{2} j ^{2} - ^{L} / _{4} j ^{4} , where m is the mass and l
> 0 is the (self) field
binding constant j . Energy-momentum tensor of the scalar
field will be non-zero only diagonal component equal to T_{o}^{o} = - e, T^{a}_{b} = p.d^{a}_{b}, where
e = ^{1}/_{2} ^{.}j^{2} + ^{1}/_{2}_{ }m^{2}j^{2}, p = ^{1}/_{2} ^{.}j^{2} - ^{1}/_{2}_{ }m^{2}j^{2}. If the
field j changes slowly enough so that ^{.}j ^{2} << m ^{2} j ^{2} , the effective equation of state will be
p = - e , which will lead to the
"deSitter" stage accompanied by exponential
expansion (compare with
§5.2, part of the "deSitter model").
Another argument: The Higgs
scalar field j introduces a constant into the Lagrangian.
As shown in §2.5 (section " Variational
derivation of Einstein's equations "), the constant term in the Lagrang
function leads to the cosmological term L .g _{ik} in Einstein
equations of gravitational
field. Thus, it can be said that the Higgs scalar field
"generates" the cosmological constant L ,
which then, according to deSitter's solution (§2.5), causes gravitational
repulsion , which can be
dominant and lead to inflationary expansion.
When the temperature
decreases at its exponential drop so much that the metastable
state becomes unstable, a phase
transition
occurs from the symmetric state j @ 0
to the state j = j _{o} with disturbed symmetry, the
vacuum state disintegrates and all the energy of the false
vacuum is quickly converted to high-energy
particles :
the universe is again heated to a high temperature T ~ V (0) ^{1/4} and its further evolution is no
longer the standard model of the hot space in the first mode dominant radiation , where a (t) ~ t ^{1/2} , then after with appropriate
cooling in the mode of the dominant
substance with
expansion a(t) ~ t ^{2/3} .
^{ }The universe "blew
itself" enormously "inflated", after which there was a phase
transformation in which the field matter condensed into
particles. If the evolution of the earliest universe really
proceeded according to the inflation hypothesis, it can be
figuratively said that the whole universe - even ourselves - is
composed of matter created by the
end of the inflation phase ...
Fig.5.8. Time course of space expansion according to the inflation model in comparison with the standard cosmological model. |
The evolution of the
universe according to the inflation model is shown in Fig. 5.8 in
comparison with the standard model. The temporary very short
stage of exponential expansion *) , usually called " inflationary " (actually
" super-inflationary "!) , has very serious consequences for
the formation of the global structure of the universe and
provides an opportunity to solve a number of cosmological
problems that were standard. the model of the hot universe until
recently helpless.
*) The beginning of the inflation stage is
estimated at about 10^{-36} seconds from the origin of
the universe. At that time, a strong interaction should be
separated from the other interactions, the matter of the
universe, the universe was going through a phase transition. The
duration of the inflation stage is estimated at about 10 ^{-34
}seconds; during this extremely short time, the dimensions
of the universe have "inflated" 10 ^{26} -times.
^{ }Above all, the inflationary
expansion of the universe makes it possible to elegantly solve
the above-mentioned problem of
horizon
(causality) encountered in explaining global homogeneity and
isotropy of the universe. According to the inflation model, every
two points or particles in the universe - even those that are now
very far apart - were in the past at a very
small
(exponentially small) distance , and could therefore be causally connected . The local
homogeneity and isotropy, establishedby quantum effects, then
expands the exponential expansion into a large area, from which the now observable universe was by further expansion. Thus, with a sufficient length
of the inflation stage, the entire observable part of the
universe was created by the expansion of a single small causally continuous area of the pre-inflation epoch.
^{ }The mystery
of flatness is also solved by the inflation scenario of the
very early universe quite naturally and simply, because with
inflation expansion the radius of the spatial curvature of the
universe a (t) increases exponentially, making the universe
increasingly planar. Rapid inflation has smoothed
out
everything and made the universe flat. Temperature T » V (0) ^{1/4} , to which after the phase
transition warmed the universe, while not dependent
on the length of the stage of exponential expansion. Quantitative
estimates *) indicate that the explanation for the observed
flatness space sufficient that the duration of the inflation
expansion D t meet the relation D t > ~ 70.H ^{-1} , i.e. that during inflation the dimensions of the universe increase at least e^{70}-times » 10^{28}-times. In reality, however, the
time of inflation was probably much longer, so that even if the
initial curvature was however large, after inflation expansion
and warming, the universe became almost completely planar with a
mass density very close to the critical density ( r / r _{crit} @ 1).
*) These estimates are based
on the requirement that the total entropy S of the universe
(which is approximately equal to S » a ^{3} .T ^{3 }_{f} for a closed photon universe , where T _{f} is the
" temperature " of radiation) increases from the original
value of S _{o} » during
inflation expansion a_{o }^{3} .T _{p }^{3} in the Planck period on the present
entropy S » a ^{3} .T _{f }^{3} @ 10 ^{87}
observable parts of the universe of size a » 10 ^{28} cm
containing relic radiation of temperature T _{f} @ 2.7
° K.
Fridman expansion in the
standard model is slowing: d^{2}a/dt^{2}= d^{2}(a_{o}.t^{1/2})/dt^{2} = - ^{1}/_{2} a_{o}.t^{-2/3} < 0. In the inflation stage,
however, expansion acceleration d ^{2} (a _{o} .e ^{Ht} ) / dt ^{2} = a _{o} .H ^{2} .e ^{Ht }positive
. The physical cause
is that at a large negative pressure p = - e = - r .c ^{2} ,
corresponding to a state of false vacuum, the gravitational force
becomes repulsive , as can be seen from equations
(5.23); in §5.2 it was shown how gravity in the de Sitter model
causes mutual repulsion of particles. These
"antigravity" forces lead to an overall expansion of
the universe according to Hubble's law, even if the initial state
was quiescent *). The inflation model thus to some extent answers
the question, why is the universe expanding
?
*) A completely surprising
conclusion of the inflationary concept of the early universe is
the finding that antigravity could have played a more important role
than gravity in shaping the global structure of the universe ! Repulsive
gravity is in stark
contrast to what is now observedby attractive
gravity between material
bodies and particles. However, we must realize that in the
earliest phases of the universe there were no
material-matter particles ,
but only physical fields, which by their internal structure (described by the field potentials and the Lagrangial
or Hamiltonian created from them ) also allow antigravity effects ...
------
-------------------------------------------------- ---
Current note: It is possible to speculate on whether the
transition from a "false vacuum" in the initial stages
of space evolution really took place to a "true vacuum"
with zero energy density, or whether even our current vacuum does
not have a negative energy density - cf. with passage from dark
energy at the end of the
following §5.6 " Accelerated expansion of the
universe? Dark energy? ".
--------------------------------------------------
---------
However, Guth's original model of the inflation universe had some shortcomings related to the well-known fact that during phase transitions due to (quantum) disturbances, numerous "domains" ("bubbles") of a new stable phase within the original environment of the metastable phase arise and gradually expand. In each such "bubble", created by the tunnel passage of the Higgs field j through the potential barrier on the curve V ( j ) according to Fig. 5.7b, an asymmetric state s j = j _{o} is established very quickly and the inflation expansion stops. The walls of these domains in which it is concentrated considerably field energies collide with each other in rapid expansion, which, due to the large size of the domains, would lead to strong inhomogeneity and anisotropy of the universe, contrary to astronomical observations.
Neoinflationary
models
Have therefore designed a further two model
variants inflationary universe [129], [2], [171] - so neoinflationary models , consisting in finding a
suitable course of the effective
potential V ( j ) in the grandunification calibration
theories, which we need to explain the later properties of the
universe. If the curve of the effective potential V ( j ) in the region between the small
potential barrier and the value j _{o }is very
slow (Fig. 5.7c), the process of symmetry breaking due to scalar
field growth may initially be relatively slow, so that
inflationary expansion of space continues (unlike of the original
Guth model) for some time inside the "bubble " after the
phase transition, as long as the energy density maintains an
approximately constant value close to V (0). Only in the vinicity of the equilibrium value j = j _{o}
, where the potential V ( j ) has a large gradient, the stage of slow growth j (accompanied
by exponential expansion) is replaced by an
avalanche transition of the field to the equilibrium value j = j _{o}
with oscillation around the minimum effective
potential: rapidly changing field j produces Higgs bosons decaying
into relativistic particles - the potential energy of the vacuum
state V (0) is converted into the energy of fast particles,
whereby the given area of the universe is "heated" to a
high temperature (T ~ V (0) ^{1/4} ) and its expansion will be
continue according to the standard model. As a result of prolonged inflation phase, the universe was
able to expand significantly more than in the originally model; it is estimated
that this expansion is about e^{2000} -times, which corresponds to the
dimensions of the universe ~ 10^{800} cm. The entire visible part of
the universe would then be deep inside a single
"bubble", so that we could not observe any
inhomogeneities arising at the interface of individual
domains.
^{ }Further research has shown that the
inflation universe scenario can also be successfully implemented
within supergravity theories (calculations were performed
specifically for N = 1 supergravity [103]), although sufficiently
large inflation expansion is achieved only in a relatively narrow
group of theories (in which the course of effective potential
around j = 0 is very gradual). However,
supergravity inflation would be even closer to the big bang -
right after 10^{-43} s, when the process of
spontaneous disruption of supersymmetry and separation of
gravitational interactions took place (see also §B.6 " Unification
of fundamental interactions. Supergravity. Superstrings. ") .
Constant inflation? False
vacuum instability.
The idea of ??inflation at the beginning of the universe can have
different variants. According to the inflation model, there was
initially a "false vacuum" with repulsive gravity,
which expanded exponentially: the more space with the vacuum was
created, the more energy there was, the greater the repulsive
gravity and the sharper the vacuum expanded - faster and faster.
However, the false vacuum was unstable, according to quantum laws, its
small parts randomly transformed into a "true" vacuum,
as if steam bubbles formed in a boiling liquid. These transitions
from the false vacuum manifested themselves in the formation of
very heated matter in the bubble universes - hot "big
bangs" and the subsequent expansion and cooling of the
individual bubble universes started. According to this variant of
the inflation model, our universe is just one of many other universes , forever separated by an
ever-increasing volume of false vacuum (cf. below with a similar
consequence of the so-called chaotic
inflation model
).
Primordial germinal inhomogeneities
and the large-scale structure of the universe
We have outlined above how the inflation scenario of the early
expansion of the universe can solve some basic cosmological
problems of the standard model - the problem of horizon, global
homogeneity and isotropy and flatness. Another advantage of the
inflation model is that it makes it possible to explain the
emergence of germinal
inhomogeneities for the formation of galaxy clusters. Due to the quantum fluctuation of the field j throughout
stage of inflation, small initial inhomogenities
of the energy
density arise, the average size of which is still roughly
the same - they have a random Gaussian spectrum. During fluctuations, these fluctuations
expand to all possible scales and eventually lead to the
inhomogeneities dr of the mass density r in space. Here "spectrum" of
these inhomogeneities dr / r is
nearly independent of their spatial sizes - scale-invariant
spectrum which is well
suited to the theory
of galaxies formation from such primordial "germ"
inhomogeneities.
^{ }However, in order for the
"amplitude" of these inhomogeneities to have a
realistic value of dr / r> 10
^{-4} required for galaxy formation, the field j needs to have a very small binding
constant ( l <~ 10^{ }^{-12} ). In GUT this condition is not met -
quantum fluctuations at the phase transition are too strong here,
the amplitude of fluctuations is about four orders of magnitude
higher; instead of galaxies, only giant black holes could form
here. Germ inhomogeneities amplitude value dr / r » 10 ^{-4}, needed to
the formation of the observed galaxies,
can be obtained only in the supergravity realization
of the inflation
model [103], wherthe field j interacts with other fields only by
gravity , and the binding constants l can
be sufficiently small.
^{ }These primordial inhomogeneities
then further developed in the lepton and radiation era in the
form of plasma fluctuations^{ }and oscillations, which after
"freezing" during recombination and radiation
separation left in the mass distribution density
"imprints", which eventually evolved into a large-scale structure of the universe - clusters of galaxies and
galaxies (cf.
discussion in the previous §5.4, passage " Fluctuations and acoustic
oscillations in plasma substance ") .
Baryon
asymmetry of the universe
The observed baryon asymmetry of the universe (discussed in the
previous §5.4) arose according to current theories of elementary
particles during the decay of some "exotic" particles,
which does not preserve CP-invariance . These could be heavy Higgs bosons , X and Y calibration bosons , or hadrons
containing c-quarks and b-quarks. These particles, now
"exotic" for us, may have been in large quantities at
the beginning of the hadron era. In comparison with the standard
model leads to a more efficient inflation model of
"generation" baryon asymmetry because it takes place at
the end of the imbalance as heavily nserious inflationary stage, when
the expansion and cooling of the universe proceeded much faster
than the decay of the mentioned bosons and their antiparticles,
so that the balance could no longer be established. Average
particle energy (temperature) in the space rapidly decreases
below the threshold creation X and Y , other processes distorting
baryon number conservation becomes negligible, and the resulting
excess baryons over antibaryons in Space "freezes".
Relict
particles
In addition to the "classical" cosmological problems,
the model of inflationary expansion of the very early universe
also helps to solve some new problems arising only after the
cosmological application of calibration unitary theories. This is
mainly a problem of relic magnetic monopoles ,
relic gravitins and possibly. other "exotic" particles
and structures formed according to calibration unitary theories
in the earliest stages of the universe during symmetry-disrupted
phase transitions. Some of these particles and structures are
stable or long-lived, so they could persist into later periods of
evolution of the universe (even longer after initial
nucleosynthesis) and lead to very undesirable (and even
catastrophic) cosmological consequences.
The inflation model contributes to solving the problem of relic
exotic particles by reducing the density of all particles
existing before the phase transition to almost zero during
inflation expansion. Superheavy exotic particles, such as
magnetic monopolies, can only form near the interface of
individual domains, so that with a sufficiently strong
inflationary expansion, they practically do not appear in the
observable part of the universe. Although "lighter"
particles, such as gravitin, could re-emerge after the inflation
phase if space is heated too much during the thermalization of
vacuum energy; however, within supergravity, models can be
created in which the heating of the universe is low enough that
gravitin does not form (and at the same time sufficient to
explain, for example, baryon asymmetry).
Primordial
gravitational waves^{ }
During the inflationary expansion of the universe, quantum
fluctuations are extremely "inflated" and the dynamic
inhomogeneities of gravitational potentials should also generate
massive gravitational waves , in the spectrum of
which the amplitude of the waves should increase towards longer
wavelengths. These gravitational waves, as r elict
, could in principle allow us to "look" into the
inflation phase. However, during the long expansion of space,
after 14 billion years, they have weakened so much that they are
beyond any possibility of direct detection in the foreseeable
future. However, at a time when they were still relatively
strong, they could specifically modulate relic
microwave radiation, which in the future, with a significant
increase in sensitivity, angular and temperature resolution of
instruments, perhaps it would be possible to detect(discussed in §5.4, passage " Microwave relic radiation -
messenger of early space news
" and in §2.7, passage " Measurement of polarization of relic
microwave radiation ") .
Chaotic
inflation and quantum cosmology; vacuum inflation model
The
original theories of the inflation universe, based on phase
transitions in unitary fields, require the fulfillment of
specific initial conditions (certain initial values and field
distribution j ) for their successful implementation ,
which are not convincingly justified and would probably not occur
in the real universe. Recently, however,
another very promising possibility has been shown to realize the
inflationary expansion of a very early universe, which is not
based at all on the mechanisms of phase transitions at high
temperatures: it is so-called chaotic inflation of space
[262] [118] [172]
designed by Linde and Vilenkin in 1983.
^{ }This theory is based on the
situation at times t <~ t^{ }_{p}
at densities r > ~ r _{p} , when due
to strong quantum-gravitational
fluctuations of fields and space-time metrics it can be
assumed that at t <~ t _{p} all values of fields j (at which V ( j )
<~ m _{p }^{4} ) were about as likely; the
distribution of field j in space was therefore more or
less chaotic . Therefore, there were also areas of
space in which the field j was coincidentally strong enough
and yet almost homogeneous. If the dimensions Dl of the region, in which the field j is homogeneous, are larger than the size of the de Sitter
horizon model with thick on the energy V( j ),
i.e.
D l > ~ Ö [3hc / 8 p G.V ( j )] = H ^{-1} | (5.56) |
and field j
varies with time
sufficiently slow, then the inner part of this area will exponentially expand by law a(t) ~ a_{o}.e^{H.t} regardless of the situation outside this
area, ie according to the inflation
scenario . As a result of this enormous expansion,
the value of the field j decreases , the negative pressure
eventually disappears and the phase of exponential expansion therefor ends .
Inflanton field ^{ }
The hypothetical field of these listed properties
that causes inflationary expansion is sometimes called the inflaton field . Such an inflaton field can be a scalar
field j with a quadratic
dependence on the size of the potential energy field V ( j ) = ^{1} / _{2} m ^{2} j ^{2} , which have been considered in
note * ^{2} ) above. In the presence of such
an field, inflation starts automatically if the initial energy
density of the field is greater than that resulting from the
above relations (for a Planck size region, the
initial energy of the inflaton field must be greater than three
times the Planck mass) . In the spirit of quantum field
theory, its quantum inflaton is
introduced, more or less formally .
A complete
cosmological theory ?
The concept of chaotic inflation has, in addition to requiring
almost no a priori initial conditions *), another significant
positive feature: it is the only one that offers some opportunity
to solve even the most fundamental cosmological problem - the
problem of initial singularity and the origin of the universe. As complete it can be considered only that
cosmological theory, which includes also the process
of creation of the universe . According to the quantum theory of
gravity, the quantum fluctuations of metrics and physical fields
are very large at small scales D l
<~ l _{p} . It is therefore the possibility that, as result of these fluctuations, is formed regions filled slowly
varying scalar field j . If size a Dl of
this area is larger than the size of the de Sitter horizon model
with the energy density V(j), then the inner part of
this area will expand exponentially
independently of the outer situation, as mentioned
above.
*) In addition to the
universality of quantum fluctuations, it is sufficient to assume
at least one initial field j (sufficiently weakly interacting with
other fields), which may not be a simple scalar field, it can be
a fermion field or even a vacuum fluctuating space-time curvature
field [174].
^{ }While doing so, the probability that quantum
fluctuations (which
are large only at the energy density of the emerging universe r > ~ r
_{p} )^{ }lead to the formation of an
inflation-expanding universe, it is significant only if the
condition Ö [3 h c
/ 8 p G.V ( j
)] = H ^{-1} <~ m _{p }^{-2} , or V ( j )>
~ m _{p }^{4} is met ; the probability of
quantum formation of the universe at V ( j )
<< m _{p }^{4} is significantly lower *). Given
the condition D l <~ m _{p
}^{-1}
, it follows that if the Fridman universe is created by the
described mechanism and direction, it will most likely be
a closed universe, starting its inflation expansion from the
characteristic magnitude of l <~ l _{p} @ 10 ^{-33} cm.
*) Assuming that the quantum
formation of the universe takes place by the mechanism of
tunneling across the barrier, the probability of the formation of
the universe would be P ~ e ^{-k. }^{r }^{p }^{/ }^{r} ,
where k is a constant.
Thus, with a decrease in density below r _{p} , the probability of quantum formation of
the universe decreases rapidly.
According to this
concept, the universe never had to be in a singular state, but
due to quantum-gravitational fluctuations, it spontaneously
formed "out of nothing" - from a vacuum filled with
virtual particles and fields. According to this vacuum-fluctuation model, the "bubble" of space-time
could inflate at tremendous speed, leading to a big bang. Thus,
an outline of a complete cosmological
theory appears
that uniformly explains the origin of the universe, its evolution
and the structure of matter that fills it. All the details of
this theory are still far from being developed, but some
qualitative features of the basic processes of quantum cosmology *) can be understood already now.
*) Quantum cosmology encounters some basic methodological
problems. For example, it
is not clear what the quantum description of the universe as a
whole actually means. The foundations of quantum theory lie the
process of measurement, which presupposes a certain external
device, resp. an external observer taking the measurement.
However, in the case of quantum cosmology, the quantum system is
the whole universe, which includes all things, so that no
external device or observer can exist here. In fact, only the
most basic concepts are taken over (extrapolated) from quantum
physics - spontaneity, randomness, unpredictability,
fluctuations ...
Spontaneous quantum formation of the
universe by inflationary expansion of sufficiently large quantum
fluctuations.
The creation of more
universes? - multiversum
From the point of view of classical cosmology - §5.1-5.4 - here
we have a single "our" universe (considered globally homogeneous and isotropic) and the idea of ??other universes
seems absurd. However, if we incorporate into the mechanisms of
cosmological dynamics of the origin and evolution of the universe
the concept of quantum physics of fluctuating fields and wave
functions of particles, the possibility arises of the emergence
of different domains so significant and autonomous
that they can be considered separate
universes .
^{ }During the exponential
expansion
discussed above (" Inflationary expansion of the universe ")^{ } in some places, quantum phase
transitions could occur independently, and these regions could
then stop their rapid expansion at a different time than other regions. This could
create different domains or "bubbles", which, if
sufficiently expanded, could become independent
"universes". Our Universe would then be just one of
these "bubbles", in addition to which there could be
many others ...
^{ }The idea of spontaneous quantum
formation of the universe (" Chaotic Inflation ") leads
to other interesting possibilities and consequences. Sufficiently
strong quantum fluctuations similar to the one that led to the
creation of "our" universe could have occurred
independently elsewhere (the
above-mentioned " Chaotic Inflation ").
From the primordial vacuum that gave rise to our world, many other universes could emerge , each with its own specific
laws of physics. This would create a number of different
expanding "bubbles" - a number of independent
universes with different global structures of spacetime and
the properties of particles and matter. Such
a presumed set of spontaneously emerging universes from quantum
fluctuations can create a kind of "fractal tree"
of new and new universes (see the passage
on fractals in
§3.3) . According to some unitary theories of the
field (discussed in §B.6 " Unification
of fundamental interactions. Supergravity. Superstrings. ")
there may be additional " extra-dimensions " in space-time that are hidden to us - they are rolled
up (compacted) into tiny sub-microscopic sizes; 3 spatial dimensions and 1 temporal dimension are developed in our
Universe. Along with our Universe (macroscopically
3 + 1-dimensional), other
" parallel " universes may coexist - with our only
loosely "ideologically similar" - with other developed
and compacted dimensions. And perhaps countless other
"universes", in which it is all completely
different..?.. Our Universe could thus be part of the
"sea" of an infinite
number of other parallel universes ; a "grain of
sand" on a gigantic "beach" §5.7 " Anthropic
principle and existence of multiple universes " ) .
^{ }Another, somewhat extravagant, idea of the existence of
many or infinite numbers of universes is based on Everett's
"multi-world" interpretation of the stochastic laws of
quantum mechanics. According to this hypothesis, expressed by H.
Everett in 1957 [79] , with each interaction
leading to a certain quantum mechanical state in a given
universe, not only the final state occurs in our universe, but in
fact all other possible states are realized ,
but in " other universes ".
Figuratively speaking, in other universes, all "wasted
chances" from our universe are realized. Each historical
event takes place differently inall possible variants in
different parallel worlds . So it is not a different
universe in terms of space-time, but a space of states -
it is a probability space in which all possible
worlds and all events exist simultaneously. These are different
branches of the " probability tree ". In this
configuration space, the individual universes are orthogonal to
each other, so that from the classical point of view there is no
possibility of interconnection between them.
^{ }The virtual mathematical transformation of
the set of many universes was used in attempts
to quantum model the evolution of the universe using the concept
of Feynman quantization of path integrals in
infinite-dimensional so-called " superspace
". (mentioned in §B.5, section "
Feynman quantization of orbital integrals ", passage " Orbital quantization of universes in
" superspace " ") . It was only a purely
speculative abstract model, where the real existence of
different universes was not assumed ....
^{ }Some related gnoseological
questions of quantum physics and its interpretation are
discussed in Chapter 1.1 "Atoms and Atomic Nuclei",
passage " Quantum Recognition " monograph " Nuclear
Physics and the physics of ionizing radiation ".
Multiversum^{ }
If such "multiple" universes do exist, then, may be the
result of one big bang (or quantum
fluctuation) from many others
, just as our Sun is just one of many stars formed in a similar
way in the Galaxy. For the Universe, instead of the usual current
name " universe ", the designation " multiverse
- multiversum " would be more appropriate. It would
be a kind of " super-Copernican "
approach: not only is our planet Earth and the solar system one
of many, but our entire universe is only one of many universes on
a cosmic scale, in which various events take place under the
influence of different physical laws. All these universes
together then create a true all-embracing Universe
- the multiverse.
^{ }These other "universes" are
probably far beyond our observable universe (beyond the
cosmological horizon), or they may exist in different time
epochs, or they coexist as "parallel" to our universe
in a different topology, other dimensions, or in another
"branch" of the quantum wave function. There is no evidence
for anything like this, and maybe never will be ... These
hypothetical other "universes" are invisible to us and
probably can have no effect on our universe. No experimental test
available in one universe can reveal the existence of another
universe or its properties. So we have to admit, unfortunately,
that for all the curiosity and allure, the concept of many
universes is not a verifiable or rebuttable scientific theory in
the sense of "Popper's razor", but only a mere
hypothesis of a "metaphysical" character
..!..
A multiverse (multiversum,
megaverzum, metaverzum) with parallel worlds or universes,
multiple and alternative universes, is therefore just a hypothetical
thesis of countless possible universes - including ours,
which perhaps exist somewhere and together create natural
reality.
^{ }Even if such "universes"
existed, they would be beyond our means of space-time knowledge -
they would probably be inaccessible and unobservable
to us in principle . Perhaps some possibility of indirectly
proving the existence of multiple universes could be the
collision of our universe with another universe.
This event would leave traces of an otherwise average homogeneous
and isotropic mass distribution and could be observed ascircular
defect in the distribution of relic radiation (so far beyond the possibilities of current detection
technology) ; however, even if such defects
were observed, they could probably be explained in other
alternative ways ...
Constant inflation ?^{ }
Quantum fluctuations in the vacuum, in which inflationary
expansion takes place, may be "spewing" new and new
universes with various properties everywhere and constantly. This
would lead to a kind of permanent "eternal
inflation", in which the "sprouting"
of new and new universes is constantly taking place. The
environment - the manifold - in which the individual
universes arise and move, is called hyperspace. Thus, according to these
concepts, the entire Universe appears as a bubbling
"foam" of expanding "bubbles" floating in the
empty background of the primordial vacuum - from separate
universes, each governed by its own laws of physics *). Parallel
universes live their "own lives". Anything that is
physically possible can take place in some parallel universe. The
key to the mystery of the uniqueness of our (anthropic) universe
could be statistical regularities in the multiverse.
*) In the initial manifold, quantum
fluctuations create fields with different distributions of
potential minima and maxima in different parts of them, which by
constant exponential inflation gives rise to universes with different
particle masses and different physical laws of
their interactions . According to multidimensional
unitary theories of the field (§B.6
" Unification of fundamental interactions.
Supergravity. Superstrings.
") , the basic
properties of individual universes would be decided by the mode of compacting the extra-dimensions of the initial manifold.
^{ }According to these hypotheses,
our entire visible universe is only a small area in one of such bubbles. Otherwise, very few
"bubbles" have physical and geometric properties
suitable for creating more complex structures - galaxies, stars,
planets and ultimately life (cf. " Anthropic Principle or Cosmic God ") .
^{ }In light of similar concepts, it appears
that the traditional (and would seem obvious) cosmological
requirement for the Universe as a whole to become homogeneous and
isotropic during expansion is not necessary - it is enough for
these properties to exhibit individual
"mini-universes", or at least metagalaxies in which we
live. We will return to this question in § 5.7
"Anthropic Principle and the
Existence of Multiple Universes
".
The origin
of the universe from "nothing"
?
The emergence of the universe from "nothing" may seem
strange and unacceptable, contrary to all our
knowledge - the laws of conservation. However, the definition of
"nothing" is different here from the usual meaning of
the word. In quantum physics, " nothing " =
" vacuum " means a space in which, for short
moments, elementary particles begin and end their existence in vacuum
fluctuations . In a kind of " space-time foam"
in the swarm of vacuum fluctuations, tiny submicroscopic
"universes" are constantly emerging and disappearing. The
vast majority of these emerging "bubble" universes will
immediately collapse and disappear, but according to the laws of
quantum probability, once in a while such a large fluctuation
will occur that it is capable of further development - inflationary expansion (as discussed above in
the passage of " chaotic inflation "). in addition to "our" universe as
they arise and different universes in a
topologically different space ...
Superluminal speed at
the beginning of the universe?^{
}
The fact that when the creation of the universe various regions
expanded and moved away from each other at speeds significantly
higher than the speed of light may appear to contradict
the basic principles of the special theory of relativity (STR -
§1.6 "Four - dimensional spacetime and special theory of relativity "). However, it should be borne in mind that STR
applies to inertial reference frames that do not exist here. The
individual expanding regions cannot be connected by any signal,
so that formally the superluminal velocity cannot be physically
manifested. And finally, the explanation of the permissibility of
superluminal velocities at the very beginning of the universe may
be based on the situation that the initial universe was only an amorphous
manifold , where there was no metric or causality
...
To sum it up, the inflationary expansion scenario of a very early universe solves, so to speak, "one blow" some of the most important problems of contemporary cosmology: Why is the universe so perfectly homogeneous and isotropic on a large scale? Why is the average density of matter in space so close to the critical density? Why did fluctuations with the spectrum suitable for the formation of the observed galaxies occur in the otherwise homogeneous distribution of matter in the universe? Why isn't the universe filled with magnetic monopolies and other "exotic" particles?
The concept of the inflationary universe leads to significant changes in our perceptions of the origin and global structure of the universe. Above all, the universe is probably much larger than previously thought: we live within a metagalaxy that is only a tiny part of the whole created by inflationary (and later Fridman) expansion. Furthermore, phase transitions of the unitary field accompanied by inflationary expansion could have arisen spontaneously in a number of places in the very early universe. The entire Universe would then consist of many separate " mini-universes " (metagalaxies) with different properties. |
However, the concept of the inflationary universe also brings new important insights of a methodological (or even philosophical) nature. In cosmology, until now, most of the observed properties of the universe (homogeneity and isotropy, initial rate of expansion, scale of inhomogeneities for galaxy formation, entropy per baryon, etc.) have always had to be "built in manually" into the model as initial conditions. In the inflation model, however, the initial conditions are insignificant because inflationary expansion effects inthey "erase" all the details of the universe that was before the inflation phase. The avalanche-like expansion almost perfectly smoothes the universe. Once inflation begins, it will wipe out all traces of the previous state - leaving only a vast hot, dense and smooth early universe. According to the inflation model, therefore, the structure of the universe is not a product of initial conditions, but is exclusively the result of the fundamental laws of physics - the laws of gravity and quantum field theory. For the first time we encouter a physical theory which, in addition to the dynamics of evolution, resolves (or rather circumvents) the problem of initial conditions - let's compare with the mention in §3.3 (passage of Cauchy's problem) and §5.7 (anthropic principle in the existence of multiple universes); see also the analysis from a philosophical point of view in the work Anthropic Principle or the cosmic God .
Possibilities
of verifying the inflation model
It is, of course, not possible to directly examine or verify such
a deeply "history" event, such as inflation expansion
at the very beginning of the evolution of the universe. In any
case, we must rely only on circumstantial evidence or
indications. In favor of the inflationary hypothesis could speak
three observable evidence :
¨ Flatness
and uniformity of the universe
It is really watching, but it is an argument after the event that caused the inflationary scenario
actually devised ...
¨ Gaussian
spectrum of the scale density fluctuations substances ,
which vznikllo inflation stretching of stochastic quantum
fluctuations of the pre-inflationary epoch - was discussed above
in the passage " Germinal
inhomogeneities and large-scale structure of the universe". This division
inhomogeneities of which later became galaxies and clusters of
galaxies can be observed using a sufficiently accurate
measurement of fluctuations in the cosmic background radiation
(results will undoubtedly be refined).
¨ Primordial
gravitational waves
when so gigantic and fast storyline such as inflation, should be
intensive snaking curvature of space - should rise to massive primordial gravitational waves , which from that moment will
spread through space. Their original amplitude would be
proportional to the square of energy released during inflation.
with the expansion of the universe are weakening, and now appear
to be very weak and long relict
gravitational waves , beyond the possibility of detection in
the foreseeable future. While these gravitational waves still
relatively strong, the end of the era of radiation, however, can
cause partial polarization then generated (detaching) of
electromagnetic radiation, which now observe as microwave background (origin
and properties relict microwave cosmic background were analyzed
§ 5.4, passage " Microwave relic radiation -
messenger of early space news
") . With
sufficient accuracy and sensitivity of measuring this
polarization (especially its vortex mode
B ), it would
be possible to indirectly prove hypothetical inflationary
primordial gravitational waves (it is
discussed in §2.7, passage "Measurement of the polarization of relic
microwave radiation ")- and through them "
look " into the inflation phase.
Origin of natural constants
In addition to the variable values ??of the studied physical
quantities (forces, velocities, energies, potentials and field
intensities) and spatial and temporal coordinates, the laws of
physics include certain constant
factors ,
which never change, are always and
everywhere
to our knowledge. in space the same .
^{ }These primary natural constants are mainly: speed of light in vacuum c =
299 792,458 m / s, Newton's gravitational constant G = 6,672.10 ^{-11} Nm ^{2} / kg ^{2} , Planck's constant h =
6,6262.10 ^{-34} J s, electron charge e = 1 ,
60219.10 ^{-19} C, electron mass m _{e} = 9,10938.10 ^{-11} kg and a number of other constants
indicating the rest masses of elementary particles, their
electromagnetic properties, as well as a number of secondary
constants (derived, conversion factors).
^{ }Within current physical theories,
we have no explanation as to why these constants have
such special numerical values ??that do not follow any order?
Explaining or "deriving" these constants is one of the
main tasks of unitary theories , trying to create a complete
unified description of nature - the "theory of
everything" (see also §B.6 " Unification
of fundamental interactions. Supergravity. Superstrings. "). It is possible in
principle two solutions to the problem of physical constants
within the future unitary theory :
¨ Each natural constant has only one logically possible value. So far,
however, no theory has emerged that could predict such specific
values (or at least ratios of values) and derive from the
"primordial principles" ...
¨ The values of
natural constants are random and established as a result of
turbulent processes at the beginning of the evolution of the
universe fluctuations in the fields, which then
"froze". There is no explanation for their specific
values ??other than anthropic - that they form a rare
combination that allows for the evolution of matter that results
in the emergence of thinking life in the universe (see §5.7
"The Anthropic Principle and the Existence of
Multiple Universes "). With
different fluctuations, the values of these basic constants would
be completely different.
According to the latter option, our
observable universe could only be one of many isolated
"islands" surrounded by vast spaces without life -
where carbon atoms and DNA molecules, or even electrons and
protons, could not have formed. The laws of nature we observe
would be only a kind of "one edition" or "local
realization" of the general laws of nature (see also the
work " Anthropic Principle or Cosmic God ").
Variability
of natural constants ?^{ }
Possible variability is sometimes discussed basic
natural constants in time and possibly even in space, during the
evolution of the universe - the question of whether the values of
the basic natural constants (or their appropriate ratios or
combinations) were the same throughout the existence of the
universe? Experimental verification of this circumstance is
extremely difficult, as the possible variability of constants is
very slow (fractions per mille in a billion years). Accurate spectrometric analyzes of radiation coming from the outermost regions of space - and thus emitted more than
10-12 billion years ago -
would be a possibility .
^{ }Resolved fine structure of the
spectral lines is dependent on the so-called. Constant fine structure and a = e ^{2} /2 e _{of} h c =
0,0072973525376 = 1 / 137,03599968 , which is a dimensionless quantity
composed of the ratio of other natural constants: e - elementary charge of an electron, h - Planck's
constant (reduced), c - speed of light, e _{o} - electrical permittivity of vacuum (§ 1.1 "Atoms
and atomic nuclei", part " Structure of atoms " of the book " Nuclear physics and
physics of ionizing radiationThis very accurately measured
quantity may be a suitable tool for testing the constancy or
variability of fundamental natural "constants": any
deviations in the energy distribution of the fine structure of
spectral lines of radiation from outer space from the current
laboratory measured positions of these lines could indicate
constant variability, and The current spectrometric results do not show
the variability of the fine structure constant, see
Appendix A " Mach Principle and General Theory
of Relativity " for possible
variability of the gravitational constant .
Origin of
spacetime, vacuum, laws of physics ???
Even if we succeed in creating the coveted " complete
cosmological theory " (however so far it is only at
the level of hypotheses), we would still be left open to the two
most difficult and fundamental issues of cosmology and perhaps
the whole of physics and science :
1. What is the origin of spacetime and " vacuum
" , the fluctuations of which subsequently led to
the creation of the universe?
2. What is the origin of the basic laws of physics according to
which our universe was created and evolved? (eg quantum laws enabling the birth of energy "out
of nothing?)
^{ }The basic method of physics and science is reductionism - try to translate and explain
complex phenomena using simpler and more fundamental phenomena.
E.g. the ultimate goal of unitary field theory is to explain all
4 interactions using a single unitary field, the manifestation of
which would then be all elementary particles and the interactions
between them.
The simplest "field" is a vacuum - a
generally curved spacetime, geometrically characterized by a
general theory of relativity which is also the physics of
gravity, in which the laws of quantum field theory also apply.
Possibly. some more general manifold with
multiple dimensions, within which multidimensional unitary field
theories work. Here, quantum fluctuations of metrics or other
geometric structures can lead to the formation of a
"district", which, according to the laws of field
theory, including gravity, can initially expand exponentially
(inflation) and then Fridman - a new universe is born
. The existence of this initial (or permanent and all-pervading)
manifold must be postulated , as must the
validity of the basic physical quantum-gravitational laws that
"trigger" and control it all. The origin of these two primary
postulated starting points , and thus the origin
of the universe in terms of the reason for its
existence , we must probably leave in the transcendent
plane (and "God" ..?.) ; will be - perhaps forever? - shrouded in mystery
....
^{ }Some other philosophical and gnoseological
aspects of revealing natural laws, creating their models
and formulating physical theories are discussed in §1.1, passage
" Natural laws, models and
physical theories " and
in §1.0 " Physics - fundamental natural science" books" Nuclear Physics and Physics of
Ionizing Radiation ".
--------------------------------------------------
---------------------------------
Current note:
Some new alternative hypotheses bring to the process of
origin and evolution of the earliest phases of the universe new
research in superstring theory - see a brief
discussion in the passage " Astrophysical and cosmological consequences of
superstring theory " §
B.6 " Unification of fundamental interactions. Supergravity.
Superstrings. ".
Gravity, black holes and space-time physics : | ||
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Anthropic principle or cosmic God | ||
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