Inflation model, quantum cosmology and the existence of multiple universes

AstroNuclPhysics Nuclear Physics - Astrophysics - Cosmology - Philosophy Gravity, black holes and physics

Chapter 5
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 1014 g/cm3, 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 tp 10-43 s, when the mass density reached ~1094 g/cm3. 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 Ep 1019 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 ~1015 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) ~ t1/2 of the standard model) and by cooling the universe, the energy density of relativistic particles (proportional to T4) 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 = jo, 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 = jo with disturbed symmetry.
b ) In the case that the effective potential V(j) has two local minima (one corresponds to a stable state j = jo 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 = jo; 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 =   [(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/a2 = (8pG/3)[V(j) + 1/2 .j2], 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 Lj = 1/2 (j;i)2 - 1/2 m2j2 - l/4 j4, 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 Too = - e, Tab = p.dab, where e = 1/2 .j2 + 1/2 m2j2, p = 1/2 .j2 - 1/2 m2j2. If the field j changes slowly enough so that .j2 << m2 j2, 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.gik 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 = jo 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) ~ t1/2, leter after with appropriate cooling in the mode of the dominant substance with expansion a(t) ~ t2/3.
   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" 1026 -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 e70-times 1028 -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/rcrit @ 1).
*) These estimates are based on the requirement that the total entropy S of the universe (which is approximately equal to S a3.T3f for a closed photon universe, where Tf is the "temperature" of radiation) increases from the original value of So ao3 .Tp3 during inflation expansion in the Planck period on the present entropy S a3.Tf 3 @ 1087 observable parts of the universe of size a 1028 cm containing relic radiation of temperature T f @ 2.7 K.

Fridman expansion in the standard model is slowing: d2a/dt2= d2(ao.t1/2)/dt2 = - 1/2 ao.t-2/3 < 0. In the inflation stage, however, expansion acceleration d2(ao.eHt)/dt2 = ao.H2.eHt positive. The physical cause is that at a large negative pressure p = - e = - r.c2, 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?".
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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 = jo 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 jo 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 = jo, 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 = jo 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 e2000 -times, which corresponds to the dimensions of the universe ~10800 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 <~ tp at densities r > ~ rp , when due to strong quantum-gravitational fluctuations of fields and space-time metrics it can be assumed that at t <~ tp all values of fields j (at which V(j) <~ mp4) 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  > ~  [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) ~ ao.eH.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 m2 j2, 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 <~ lp . 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 > ~ rp) lead to the formation of an inflation-expanding universe, it is significant only if the condition [3hc/8pG.V(j)] = H-1 <~ mp-2, i.e. V(j) > ~mp4 is met; the probability of quantum formation of the universe at V(j) << mp4 is significantly lower *). Given the condition Dl <~ mp-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 <~ lp @ 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. rp/r, where k is some constant. Thus, with a decrease in density below rp, 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".
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 "histor
ically 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 ,
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 Nm2/kg2, Planck's constant h = 6,6262.10-34 J s, electron charge e = 1, 60219.10-19 C, electron mass me  = 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 = e2/2eohc = 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, eo - 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".

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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.".

5.4. Standard cosmological model. Big Bang.   5.6. The future of the universe

Gravity, black holes and space-time physics :
Gravity in physics General theory of relativity Geometry and topology
Black holes Relativistic cosmology Unitary field theory
Anthropic principle or cosmic God
Nuclear physics and physics of ionizing radiation
AstroNuclPhysics Nuclear Physics - Astrophysics - Cosmology - Philosophy

Vojtech Ullmann