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 on 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 determined by the 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 "packed" on top of 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
of 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 produce 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, significant sucsess has
been made in the physics of elementary particles, especially the theory of electroweak
interactions, grandunification theory and superstrings,
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 unitary
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].
*)^{ }Unitary
because it tries to unite different types of
interactions - physical fields - electromagnetic, strong, weak
interactions into one unitary field. They are referred
to as calibration because they use special
"adaptation - calibration" transformations
of coordinates and field potentials in connection with symmetries
and conservation laws. It is analyzed in more detail in §B.6
"Unification of fundamental
interactions. Supergravity. Superstrings.".
^{ }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 cosmological consequences
of phase transitions
in grandunification calibration theories, which began in 1981 with the work af A.Guth [112], led to the hypothesis of the so-called inflationary expansion of the universe,
according to which the universe was expanded at an exponentially
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 the 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, some of
these vector bosons gain an effective rest mass, the respective 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; the
mutual transformation of quarks and leptons is almost impossible
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), the 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 mechanism
of the phase transition during the gradual cooling of a
superdense substance 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, but 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 (smooth) phase transition to a state with disturbed symmetry j = j_{o}, i.e. from a
"false" to a "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's model (§5.2) under the
"rule" of the large cosmological constant L *). The cosmological
constant, which Einstein first introduced and then
called it the "biggest mistake of his life",
was thus "rehabilitated" in the form
of an inflationary vacuum, which 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 interrelated 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 by the members 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 takes place according to the standard model of the hot universe in
the mode of first dominant
radiation, when a(t) ~ t^{1/2}, leter 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 gives the opportunity
to solve a number of cosmological problems, before
which the standard
model of the hot universe was until recently powerless.
*)^{ }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 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 by quantum effects, then
expands the exponential expansion into a large area, from which the now observable universe was created 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 the
single small causally related 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, thus
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 Dt meet the relation Dt >~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} » a_{o}^{3} .T_{p}^{3}
during inflation expansion 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 exponential
expansion, these
fluctuations expand to all possible scales and eventually lead to
the inhomogeneities dr of the mass density r in space. At the
same time, the "spectrum"
of these inhomogeneities dr/r is almost
independent of their spatial sizes - a 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. Compared to the standard model, the inflation
model leads to a more efficient
"generation" of baryon asymmetry, because
it takes place at the end of the strongly
unbalancd inflation
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 equilibrium 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 relicts,
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 universe
[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 equally
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 at the
same time almost
homogeneous. If the dimensions Dl of
the region, in which the field j is homogeneous, are larger than the size of the horizon in the de
Sitter model with energy density 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 it passes away and the phase of exponential
expansion thus ending .
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 Dl
<~ l_{p }. It is therefore the possibility that, as result of these fluctuations, is formed regions filled slowly
varying scalar field j. If size 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 field of curvature of space-time [174].
^{ }At the same time, 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[3hc/8pG.V(j)] = H^{-1} <~ m_{p}^{-2}, i.e. 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 Dl <~ m_{p}^{-1}, it follows that if the
described mechanism creates a Fridman universe, it will most
likely be a closed universe, starting its inflation expansion
from the characteristic size 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 some 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. At 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", besides it there could be many others ...
^{ }The idea of spontaneous quantum
formation of the universe ("Chaotic Inflation") leads
to other interesting possibilities and consequences. Indeed, 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 untangled
in our Universe. Along with our Universe (macroscopically
3 + 1-dimensional), perphas other "parallel" universes may coexist - with our universe 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 slight "grain
of sand" on the gigantic "beach" of the multiverse...
(further discussin in §5.7 "Anthropic
principle and existence of multiple universes").
For little refreshment, we can
mention the charming Indian legend of the creation of many
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 resulting 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 in all
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 concept 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" (is 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 what we
have so far called the universe, may be the
result of one "of our" big bang (or
quantum fluctuation) out of many other big
bangs, 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 as
circular 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 ...
Permanent 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 finally 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 again
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, other
universes could have formed 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-imensional 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 ...
What is the potential
benefit of the inflation concept ?
To summarize briefly, 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 irelevant, 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 ("Cauchy problem, causality and horizons", passage of Cauchy's problem)
and §5.7 ("Anthropic principle",
version "Existence of multiple universes?");
see also the analysis from a philosophical point of view in the
work "Anthropic principle
or the cosmic God".
^{ }In the concept of "eternal inflation", the universe as a whole is
constantly expanding at an exponential rate, but in some regions
this rapid expansion may be slowed or stopped (permanently or temporarily) by
some local process, such as quantum field fluctuation or the
curvature of spacetime. Although this local area is surrounded by
the rest of the universe, which still continues its exponential
expansion, specific physical laws can arise inside this "space bubble". The basic interactions could be
separated differently here, with a different development or
compactification of dimensions, with a different violation of
symmetries, which would lead to the fact that the basic particles
can acquire different masses and mutual interactions. This will
give rise to different physics and
chemistry,
different properties of atoms (or space
without the existence of stable atoms...). An infinite number of such separate
regions - "mini-universes", meta-galaxies, with different
properties
could hypothetically arise ...
^{ }And the concept of "chaotic inflation" even leads to the constant primary
emergence of completely new
"universes" always and everywhere..!.. However, we
must admit that all these opinions are already
very speculative,
outside of scientific astrophysics, rather at the level of "science fiction" ...
Possibilities
of verifying the inflation model
Of course, it is impossible to directly investigate or verify
such a deeply "historically forgoten" event as the inflationary
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
This is indeed observed, but it is an a posteriori argument, for which the inflationary scenario was actually
devised ...
¨ Gaussian
spectrum of the scale density fluctuations substances ,
which arosefrom the inflation expansion 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 distribution of 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 such a gigantic and fast action such
as inflation, there should be an intensive ripple
in the curvature of
space - massive primordial
gravitational waves should emerge, 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, they weaken, and now occur as very
weak and long-wave relict gravitational
waves, beyond
the possibility of detection in the foreseeable future. However,
at a time when these gravitational waves were still relatively
strong, at the end of the radiation era, they could have caused a
partial polarization of the then emerging
(separating) electromagnetic radiation, which we now observe as microwave relic radiation 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 even certain constant
factors,
which never change, are always and
everywhere in space the same to our knowledge to date.
^{ }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 "initial
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
"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 ?^{ }
Sometimes there is also a discussion about the possible variability
of basic natural constants in time and possibly 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.
^{ }The fine
structure of split e spectral lines depends on the
so-called fine structure constant a = e^{2}/2e_{o}hc =
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 radiation"). This 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
variability of a constant. 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 convert and explain the
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" in 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" in §
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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