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(5.4) |
| 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. Forming the structure of the
universe.
5.5. Microphysics
and cosmology. Inflationary
universe.
5.6. The
future of the universe. Time
arrow. Dark matter. Dark
energy
5.7. Anthropic
principle and existence of multiple universes
5.8. Cosmology
and physics
5.1. Basic starting points and principles of cosmology
Cosmology deals with the issue of the
structure and development of the universe as a whole *) - a science standing on the
border of astronomy, physics and philosophy. These are questions
of the past of the Universe (or its origin), construction,
development of the Universe and its future (duration or
extinction). The dominant force in the universe is gravity. The physics of gravity and the structure
of spacetime therefore play the most important role in cosmology
and find significant application in it. In several paragraphs of
this chapter, we will try to briefly analyze the basic principles
and findings of relativistic cosmology, especially from this
physical point of view (further details can be found mainly in [288], as wel as
in [271], [200], [181], [215]).
*) The Greek word cosmos
(cosmos) means world, universe (Latin synonym
univesum); originally order, harmonic system
(opposite of chaos), also ornament, beautiful jewel. The
current usual meaning of Greek. cosmology
(cosmology) =
doctrine of the world, the universe. Related areas such as cosmogony
(the science of the origin of celestial bodies, especially
planets) or cosmography (the "topography" of
celestial bodies) are based on the same ethymology. And also cosmetics
in the sense of external beautification.
Mystical cosmology
From time immemorial, people have been interested not only in the
problems of present life and local properties of nature, but also
in eschatological issues and the global
structure of
the world (universe) - how big the universe is and what its its
shape, when and how did it originate and where
does it go, what laws are governed, what is its essence. In antiquity and the
Middle Ages, ideas about the structure and evolution of the
universe stood on mystical foundations and had little to do
with reality *).
*) The historical development of our
knowledge of the universe, in the context of the development of
the whole natural sciences, was discussed in more detail in §1.1
"Historical development of knowledge about
nature, the universe, gravity".
The questions of the construction and properties of the Universe
and the position of man in it have been (and still are) reflected
in various areas of human culture, philosophical and religious
trends ("Anthropic principle or
cosmic God").
Mystery: The
Origin of the Universe ?
In these earlier times, there was a particular emphasis
on the origin of the universe. Different
human cultures have
created their own stories describing the
origin of the world. Most of these creation myths (creation)
of the world presupposes the existence of a supernatural divine or absolute
force
capable of creating the world. In others is the universe eternal, there is always the endless past and
will exist forever. A common assumption was that the Universe
arose - either spontaneously or by divine intervention - from the
primordial nothingness or chaos, into which order was imprinted. From the point of view of
the scientific cognitive method, according to which each effect
arises from a cause, we can trace the chain of causes back in
time until we reach the "original
cause".
But the question arises: what caused this root cause? Why does
"something" exist at all, instead of nothing? A common
simple superficial answer refers to God the Creator. The current
best scientific answer is that our Universe (and
perhaps other "universes") appeared spontaneously from random quantum fluctuations in the primordial vacuum manifold (discussed in more detail in §5.5, section "Chaotic Inflation",
"The Origin of Multiple Universes")..
However, this initial quantum vacuum is not some
"nothingness" or emptiness, but in the spirit of
quantum field theory it contains constantly fluctuating physical
fields and their quantum - particles and antiparticles. From
"quantum nothingness" - from
"nothing" arose
"everything"..?.. But they are all just hypotheses..!..
Scientific
cosmology
It was not until Galileo's observations and Newton's law of
universal gravitation erased the seeming
abysmal difference between the laws of terrestrial nature and the
"heavenly" laws of the universe. It has begun to show that the universe and
earthly nature are governed by probably the same
fundamental laws; we just observe them from a different
"point of view". Since the days of Galileo and Newton,
the knowledge of the universe has been based on rational natural
(physical) laws, using calculations and predictions of the motion
of celestial bodies, with an emphasis on ever-refining
observations and confrontation with scientific experiments.
Astronomy and cosmology have thus become a scientific
discipline
in which theoretical ideas and models are constantly corrected in
order to gradually achieve the most accurate
agreement
with everything we observe in the universe. Even in the
above-mentioned most difficult question of the origin of the universe ...
Thus, the
way to understand the universe is as follows: to extrapolate
the physical laws resulting from experiments in our
laboratories to the processes taking place in space, and to
try to explain astronomically observed phenomena using these
laws. In astronomy and astrophysics, this approach has led to
impressive successes. Spectral analysis of radiation coming to us
from evnen the remotest observed objects in the
universe shows, that there to apply the
same laws
of classical and quantum mechanics, electrodynamics, atomistic,
thermodynamic and gravity as here on Earth. Although
this cannot be explicitly proven, it entitles us to believe that
the laws of physics apply even where we have not
yet "looked" - and perhaps even in places we will never
be able to see..!..
However, cosmology seeks
to extrapolate the laws of physics to the entire
universe at
any time in the past and future, and to explain its global
structure and evolution. The question arises as to the legitimacy of such a bold and far-reaching
extrapolation? *) - the universe as a whole would not have to
have the same properties as the part we observed. But if we want
to know megaworld, let's hope the material unity of the
world governed by the universal laws
of physics. Spectrometric analysis of radiation coming from
even the farthest reaches of the universe shows, that the natural
processes taking place here on Earth and in the whole observation
of the available universe are governed by the same physical
laws of mechanics, gravity, electrodynamics, atomistic, nuclear
physics, thermodynamics, plasma physics, etc.
*) When building the current standard
cosmological model (§5.4 "Standard
cosmological model. Big Bang. Formation of the structure of the
universe.") the
Einstein's equations are used to the whole Universe. However, the
general theory of relativity is reliably tested (experimentally
or observationally) only on much smaller scales
- here on Earth and in the solar system (bending of light rays in
the gravitational field of the Sun, twisting of Mercury
perihelion, Lense-Thirring effect of space-time entrainment
rotating by Earth, gravitational frequency feed), or processes in
small gravitationally collapsed compact objects; is summarized in
§2.10 "Experimental verification of the theory of relativity
and gravity"). However, galaxies
are many billions of times larger and the observable universe is
at least 1015 times larger. Admittedly, such far-reaching
extrapolation is not really substantiated..!?.. Unfortunately, we
can do nothing better. We have one option: to
try such an extrapolation and to see to what extent the
predictions from the resulting models correspond to the observed
facts; if so, it justifies the extrapolation used and at the same
time extends the validation of the given initial theory (here
general theory of relativity) to a larger scale.
The uniqueness of the
universe
In some important aspects, however, the universe (and thus the
methods of its study) is still different from other physical systems that
we encounter in nature. Above all, it is the uniqueness of the universe: the universe exists only in "one
edition", we can not do any experiments with it or observe
and compare (perhaps statistically) different variants of the
universe (we leave aside various
speculations about the possibility of multiple universes, we will
discuss below in §5.7 "Anthropic principle and existence of
multiple universes"). Because there is only one
universe and nothing outside of it, no system or observer can in
any way break out or "emerge" from the universe, stand
outside it, and examine it "from the outside" inward;
everything is an integral part of the universe.
When studying such a complex
object as the whole universe, we have to make a number of simplifications and idealizations - we create so-called cosmological models
(§5.2-5.5), which
capture some basic global features of the whole universe, but
abstract from the specific local structure of individual space
objects (such as stars, galaxies, even clusters of galaxies...).
Unimaginable size of
the universe !
The dimensions of the universe are completely beyond human
imagination, they cannot be compared to anything we are used to
on a human scale. It is very difficult, or even impossible for
us, to imagine the size of the universe. We have
nothing to compare with ("uniqueness of the universe")
and with such large distances and extensive spaces we have no
personal experience ...
Determining
the distances of space objects - a basic condition for cosmology
The cardinal problem of astronomy and astrophysics of outer space
is the correct determination of distances stars,
nebulae, star clusters, galaxies and other objects. Only in this
way can we determine the radiant powers of these objects, which
makes it possible to analyze the physical mechanisms that lead to
such energy powers. And also the space-time structure of the
universe. Distances in outer space are often determined by a
relatively, careful comparison of the luminosities of stars of a
certain type in our galaxy (the distance of which we more or less
know) and similar stars in other galaxies. We then extrapolate
this method to compare the brightness of closer and more distant
galaxies. The results are often burdened with considerable
inaccuracy. Contemporary astronomy has at its disposal four basic
interconnected methods for measuring the distances of space
objects: trigonometric method -
luminosity method - cepheids - supernovae Ia - red spectral shift
(it was discussed in more detail in §4.1, passage "Determining the distances of space
objects - a basic condition of astrophysics").
Cosmological principle
Most concepts of contemporary cosmology are based on the
so-called cosmological principle *), which is also sometimes
referred to as Copernicus' principle. Copernicus'
observation that the Earth was not the center of universe,
gradually generalize so that even the solar system or galaxy, or
the Local Group of galaxies, not only that they are not the
center of the universe, but they do not have any significant
position in the universe. The cosmological principle is then the
hypothesis that all positions in the universe are essentially
equivalent, no place in the universe is privileged. The cosmological principle can in
principle also be verified in the laboratory - it is closely
related to the reproducibility of laboratory physics experiments.
If we do an experiment and then repeat it after a long time (in the
same laboratory), we actually repeat it in another place in space
and in a different time, because the Earth has already reached
another place in space as part of its integration into several
moving systems. Neverheless, accordind
to experience, we get the
same results within the limits of accuracy, which testifies
in favor of the
cosmological principle - physical equivalence of all
places in the universe.
*) It is necessary to distinguish two
levels of the cosmological principle :
1. Homogeneity and isotropy at the level of validity
of physical laws, ie the assumption that physical laws
apply equally everywhere throughout the universe;
2. Homogeneity and isotropy in terms of (average) mass
distribution and other physical conditions in space.
At one time, the third version was also
discussed, the so-called perfect cosmological principle
requiring that the mean density of matter be the same not only in
different parts of the universe, but also in time. This incorrect
version of the cosmological principle became the basis for a
temporary erroneous hypothesis of a steady state of the
universe (see below).
The universe can be compared to a
kind of "island empire" in which matter is very unevenly distributed: elementary particles form
atoms, which cluster into stars and planets in which the density
is many orders of magnitude higher than in the environment; stars
are gravitationally grouped together with gas into huge stellar
"islands" - galaxies, which cluster in gravitationally
bound clusters and superclusters of galaxies. Neither these giant
stellar "islands" or "archipelago" in
the universe move randomly, but flows in a kind of "filaments",
among which are almost empty huge "bubble". The Universe
in these scales reminiscent of a kind of giant "cosmic spider web" (see §5.4,
part "Formation of large-scale structure of the
universe", Fig.5.5).
However, in the cosmological
study of the universe as a whole, it is necessary to disregard
the "local" irregularities of the distribution of
matter; these smaller structures are studied in classical
astronomy and astrophysics. If we average the density of mass distribution in areas of large dimensions compared to the
distance between galaxies and galaxy clusters (i.e. about 108
-1010 light-years), globally,
this "blurred"
mass will be distributed practically homogeneously and
isotropically. This is required by the cosmological principle
and confirmed by current astronomical observations *), including
relict radiation. The universe is therefore "more or less" homogeneous and isotropic - on
large dimensions it is the same in all places and looks the same
in all directions. In §5.4 and 5.5 we will see that, according to the standard cosmological model, this is due to the emergence of
the universe from the "big bang" and then the rapid
"blow-out" during the inflation phase.
*) How perfect is the homogeneity of the
universe ?
Of course, there are random differences in the distribution of
galaxies and galaxy clusters, but on large scales they fit into
an averagely homogeneous system. Astronomical observations made
in the 20th century showed the upper limit of the size of any
anomalous structure in the universe to be around 1÷1.2 billion
light years. However, in 2022, a structure 3.3 billion
light-years long (crescent-shaped, called the Giant Ark)
was observed. And there are indications for perhaps even larger
structures (such as the Great Wall of
Hercules manifesting in an increased density of GRB gamma-ray
bursts) that can occupy up to 10% of the
size of the observable universe.!... This suggests a greater
heterogeneity of the universe than previously thought, so
the traditional cosmological principle may need to be refined
and it will perhaps even lead to a modification of the
standard cosmological model..?..
Note:
For some time,
the Lambert-Charlier model of the hierarchical
structure of the universe was discussed, which was to remove some
cosmological paradoxes. According to him, the universe is formed
by a sequence of hierarchically arranged cosmic systems: stars -
galaxies - clusters of galaxies - ... etc., while the average
density of matter decreases rapidly during the transition to a
higher system. These structures, however, would be gravitationally unstable and would soon
disintegrated. Now these concepts have lost their relevance and
are not even in line with the new observational facts, which, on
the contrary, confirm the legitimacy of the cosmological
principle.
The universe is almost absolute emptiness !
Due to the huge size
of interstellar and intergalactic space, the current average
density of matter in the observable part of the universe is only
about 10-27 kg/m3, which corresponds to
only 3 protons in 1 m3. It's an almost perfect vacuum that we can't even
achieve under terrestrial laboratory conditions!
The whole universe is just a huge
emptiness, "polluted" by an almost negligible amount of
matter. This somewhat paradoxical statement applies not only to
vast cosmic scales, but also, in essence, to our terrestrial
nature. Everything around us is made up of only a small amount of
real - "solid", concentrated - matter. It starts with
the atom, which is not some solid mass sphere,
but consists of a very dense core measuring only 10-13 cm and an almost
empty electron shell. The nucleus, bearing more than 99.9% by
weight of the atom, is about 100,000 smaller than the whole atom.
Thus, an atom is actually an empty space, "polluted" by
several protons, neutrons and electrons. About 99.98% of each
atom is an empty vacuum. Even our body, which is built of these
atoms, is mostly formed by emptiness: the whole
"real" mass of our body could theoretically be
compressed into a ball with a diameter of about 1 mm, the rest would
be emptiness.
On the global scales of the universe, this "local"
emptiness is exacerbated by the very sparse distribution of
cosmic bodies and atoms of interstellar gases. It can be said
that matter in the universe represents only insignificant
"spots" in an otherwise completely empty and
"clean" space. In addition to large areas of virtually absolute
vacuum, however, there are unimaginably dense
clusters of matter in space , resulting from gravity at
the end of the life of very massive stars. They are neutron
stars (discussed in §4.2, section "Supernova
explosion. Neutron star. Pulsars").
With even greater gravitational compression, black holes
are formed, which, however, are again essentially "vacuum
objects" (as discussed in §4.2, section "Complete
gravitational collapse. Black hole.").
Skeptical
reflection :
The impossibility of physical travel
to distant space
- to other galaxies !
The gigantic vastness of the universe - the huge
distances to other galaxies (even
to different parts of our Galaxy) makes it
extremely difficult, if not impossible, to directly
(physically) visit these places. There are two
principle obstacles :
1. The slowness of space
vehicles
Our space rockets are "snails" reaching a maximum speed
of several tens of kilometers per second. At these speeds, it
would take hundreds of millions of years to travel to objects in
the distant universe. No hypothetical sci-fi possibilities like
"warp drive" or travel through "wormholes"
can be counted on; nothing like that works. The only future, in
principle, realistic possibility is thermonuclear
hydrogen fusion (section "Fusion
of atomic nuclei" in
§1.3 of the book "Nuclear Physics and Ionizing
Radiation"; it has an energy efficiency of about 0.7% m.c2),
which would be possible to achieve a maximum speed of about
20-22% of the speed of light. And that's an optimistic estimate,
assuming 100% lossless efficiency of all links in the fuel and
rocket chain (we won't be able to do
anything like that anytime soon!). Higher
speeds could hypothetically be achieved using antimatter
(see, however, the critical assessment in
the section "Antiparticles -
antiatoms - antimatter - antiworlds" in §1.5 of the mentioned monograph).
2.
Erosion of the
cosmic probe during movement through the interstellar
medium
Even if we managed to reach speeds close to the speed of light,
we would encounter a problem that is not usually analyzed :
Interstellar and intergalactic space appears to us as a high
vacuum, but it is not completely empty. Even
though there are only a few hydrogen and helium atoms per 1m3, at that high speed many
millions of high-energy particles would strike the probe every
second, destroying the probe's atoms and releasing
high-energy radiation that would further damage the spacecraft
and its electronic systems (and possibly
the crew in the case of a manned mission).
Even more dangerous damage would occur
upon collision with particles of cosmic dust. Not only would
there be a small hole that could be sealed, but there would be a
high-energy explosion that would melt and vaporize the wall of
the probe, accompanied by strong radiation. Also, when passing
through a planetary system with a higher density of
interplanetary gas, erosion could burn up the space probe in a
short time...
Conclusion : No macroscopic material object - no cosmic probe -
realistically, it is not able to fly to the intergalactic
distance! There is no way to fly through space faster
than about 20% the speed of light. And at this high speed, the
probe material will be eroded by the constant
collision of hydrogen and helium atoms in the interstellar medium
(as well as more severe damage from
collisions with cosmic dust grains). The lifetime
of the probe will only be on the order of tens to hundreds of
years, which is far from enough to reach intergalactic distances.
Even the hypothetical achievement of higher speeds would not
eliminate or reduce this erosion - the flight time would be
shortened, but the intensity of the erosion would increase...
Any space probe, traveling at speeds close to
the speed of light, would be vaporized by collisions with cosmic
matter particles, before reaching galactic distances...
When exploring the distant universe, we
will probably be forever dependent on the passive
detection and analysis of particles and radiation of
various kinds, emitted from these distant places (electromagnetic radiation, cosmic ray particles,
neutrinos, gravitational waves, ...).
However, thanks to constantly improving technologies for accurate
"passive" analysis of radiation from the most distant
and hidden regions of space, gradually we learn almost as much as if we were "physically there"... However, even here we encounter the
"Fundamental
limitation - the lack of photons", as discussed in §1.1, the
passage "Electromagnetic
radiation - the basic source of information about the universe".
And there is no question of
"settlement" the distant universe ! Similarly, a
physical visit to each other by possible extraterrestrial
civilizations located at great galactic distances will never
be possible (see also the discussion
"The search for
extraterrestrial life" in
the treatise "Anthropic Principle or Cosmic God"); a biological visit is of course completely
excluded, but a robotic one will not be possible either..!..
Quantum teleportation ?
The only, but for now completely sci-fi possibility, how we could
reach large interstellar distances in a certain sense could
perhaps be (quantum) teleportation :
1. Break down our body into atoms or
subatomic particles, with a detailed record of all their physical
and chemical bonds. 2. Send these particles at near-light
speed, including the structure information, to another target
part of the universe. 3.
At the destination, assemble
these particles into atoms, molecules, tissues and biological
structures, according to the sent plan.
The problem with this straightforward approach is how
much of the sent particles would actually make it to the distant
destination? - many of them would probably be destroyed by
collisions with cosmic rays and particles of interstellar matter.
Therefore, it would be more appropriate not to send actual
particles, but to send only quantum information
about them, using laser-encoded electromagnetic radiation; and
assemble an organism at the target location using particles and
atoms that are normally found there - information
teleportation.
However, we will not be able to attempt anything like
that in the foreseeable future...
Our modest
place in the universe
In people's daily lives, we observe that lack of knowledge leads
to arrogance and pride, better knowledge awakens modesty and
humility. So it is also in science. Every newfound knowledge of
the universe, space, and time pushes us away
from that privileged place in the center of the universe,
that we once proudly claimed. We now know that we are just
insignificant organisms living on a tiny grain of powder in a
vast cosmos. This should lead us to modesty, rejection of
religious and other false superstitions, to ennobling our
relationships with each other and with living and
non-living nature..!..
Newtonian cosmology. Static
universe.
In the 18th and 19th centuries, classical mechanics, together
with Newton's law of gravitation, celebrated great successes in
explaining all mechanical and gravitational phenomena not only on
Earth, but also made it possible to explain the structure and
dynamics of our cosmic environment - the solar system. Therefore,
it was offered to try to understand the structure of the universe as a whole on the same basis: In the cosmic space
there are stars spread, which exert Newtonian gravitational forces on each other. These
gravitational forces, according to the laws of mechanics, then
determine the movements of the
stars (or, in equilibrium, their immobility).
Back then, galaxies (except our Milky Way), interstellar matter,
or exoplanets around stars were not yet known...
The basic premise, seemingly
resulting from astronomical observations, was the static
nature of the universe, according to which the universe
is filled with "perennials" that are at rest (today we
know that this assumption does not correspond to reality at all).
If the universe were then a finite material system, due to gravity, all matter should cluster into one large
compact body. However, even the conception of the universe, which
represents an infinite Euclidean space on average
uniformly and statically filled with stars acting on each
other according to Newton's law of gravitation, encountered
insurmountable difficulties :
Photometric Paradox of the Night "Dark Sky"
The most famous is the so-called Olbers photometric paradox
formulated in 1826 - the "dark sky" paradox - "why
is it dark at night?". If the stars are uniformly
and statically distributed in the infinite universe, the sky
would have to shine day and night from horizon to horizon as
dazzlingly bright as the surface of the Sun *): for in every
spatial viewing angle, each surface element contains, on average,
a number of stars proportional to the square of the distance from
us, while the intensity of light from there is also inversely
proportional to the square of the distance. It can be imagined
even more vividly by looking at the sky in any direction, some
stars always stick to the surface (just
like in a vast pine forest, we see only trees in every direction). There should be a star shining in every direction -
the stars should cover the entire observed "firmament".
We cannot see individual distant stars, but the sum of their
light should be seen as a continuous glow. There would be neither
day nor night, but still only a blinding conflagration!
*) Most of the stars, about 70%, are red
dwarfs, so the night sky should be intensely yellow-red..?..
The assumption of light absorption by an interstellar substance
will not help here, because it would heat up with the absorbed
energy in the final time and from it would radiate in thermodynamic equilibrium with
radiation from stars.
The explanation of the photometric paradox from the
point of view of today's knowledge of astrophysics and cosmology
consists in three circumstances :
1.
The photometric paradox
arises only on the assumption that the stars shine for an
infinitely long time, as was thought at the time. Considering
that stars actually shine only for a finite time
(~106 -1010 years), the
photometric paradox does not arise even in an infinite
homogeneous universe. Considering the actual astronomically
observed average density of stars in the universe, the stars
do not have enough energy to fill the entire space with
light and turn the dark sky into a bright one.
2.
Even the age of the
universe is finite. The greatest distance from which
light can reach us is approximately 13.8 billion light years.
Anything beyond that distance is too far. There hasn't been
enough time in space yet for the light from these distant objects
to reach us. So the sky is dark also because the light from the
most distant stars has not yet reached Earth...
3.
We live in an expanding
universe. So with respect to very distant objects
(stars, galaxies, early hot universe) we are moving away at a
high speed (or they are moving away from us
quickly). As a result, any light emitted by
distant objects exhibits a spectral red shift - a decrease
in frequency. Visible light becomes infrared, later
radio waves. We cannot see this radiation with our eyes. However,
sensitive detectors installed on satellites can detect this
radiation, measure its frequency spectrum and angular
distribution in the sky (see §5.4. passage
"Microwave relic radiation - a
unique messenger of news about the early universe"), showing even small
inhomogeneities, from which later they developed the large-scale
structures of the universe. In these images (which
are an example of a master detection technique!) we can see how our sky is "illuminated" from
all directions by weak cosmic microwave radiation.
This radiation was originally emitted as visible light by a hot
gas at about 3000 °K at the beginning of the era of matter, but it comes
from so far away in the expanding universe that its frequency has
dropped about 1100-times to the microwave radio region.
So, generally speaking, our night sky is not completely
dark, but is permanently irradiated by weak microwave radiation,
corpuscular cosmic radiation ("Cosmic Rays"), radiation from stars, and temporarily also by solar
radiation reflected from the Moon and from the planets (mainly Venus, Mars, Jupiter, Saturn).
The Gravitational Paradox;
cosmological weakening of gravity ?
Furthermore, the gravitational paradox is manifested
here, consisting in the fact that that in the model of the universe as an
infinite Euclidean space evenly filled with matter (stars), the
gravitational potential would become infinitely large. Due to
symmetry, the homogeneously distributed mass to the infinity
should be in equilibrium, because gravitational forces act on the
same effect on any material element in the same way and their
effect is canceled. For a truly infinite case, however, these
forces from each of the direction of the infinite; the overall
strength, field strength, and integration potential diverge. If
the mass is to be in static equilibrium, the intensity of the
gravitational field E must be zero everywhere, so
according to Newton's law of gravity expressed in form
div E = - 4 p G r , or Dj = 4 p G r ,
the density of mass r must also be zero everywhere. Under Newton's law, therefore, only empty space could be a static "universe". Seeliger tried to modify Newton's law of universal gravitation by adding into Poisson's equation another "cosmological" member -L.j, causing "weakening" of gravity at great distances :
| Dj - L . j = 4 p G r . | (5.1) |
This equation has as a solution the potential (1.19) (now referred to as the Yukawa type) , which decreases to infinity so fast that the expressions for the potential and intensity of the gravitational field excited by a homogeneously distributed mass converge. The given equation is satisfied by a constant potential, which gives zero intensity of the gravitational field. In order for this modification of Newton's law not to affect the agreement with experimental data which exist within the solar system, must be "cosmological constant" L sufficiently small ( L <~10-45 m-2). In light of the findings later, Seeliger's attempt to overcome the gravitational paradox was unsuccessful. Instead of modifying Newton's law, the second basis of Newton's cosmology was to be modified - give up the assumption of the static nature of the universe; but something like that could hardly have occurred to anyone at the time. Until the 1920s, it was thought that the universe was immutable and eternal, consisting of one galaxy, the Milky Way, surrounded by infinite empty and dark space.
Relativistic cosmology
Since the interaction of cosmic objects located at great
distances from each other takes place mainly through gravity, it is not surprising that research in
the field of gravity helps to solve basic cosmological problems.
The creation of Einstein's general theory of relativity - the
modern physics of gravity - set completely new horizons in
cosmology, for which he laid a solid scientific basis. All cosmic
bodies distributed in the universe create
gravitational fields - they curve
spacetime
according to Einstein's GTR equations, and this curved
spacetime according to the gik metric
tensor in turn
determines the movements of matter in the universe (it is discussed in more detail below in the passage
"Relativistic cosmological model").
A.Einstein was well aware of
this, and so in 1917 he tried to apply his gravitational
equations to the universe as a
whole and
thus create a relativistic model of the universe. He
proceeded from the assumption of homogeneity and isotropy of the
distribution of matter in space. Moreover, he believed, in
accordance with the firm beliefs of physics and philosophy of the
time, that the universe was static. When used for static cosmology,
the original Einstein equation (2.50) behaved
similarly disadvantageously as the older Poisson equation - the
only homogeneous static solution here is the Minkowski spacetime
corresponding to empty flat space *).
*) Today we know that the
main source of difficulties in both Newton's and the original
Einstein's cosmological model is common: it is a presumption of static
(time invariability) of the universe. However, this assumption
seemed completely natural to all naturalists, including Einstein,
until the 1920s, and there was no doubt about its legitimacy.
It is worth noting that many basic
findings of relativistic cosmology regarding the dynamics of
space expansion, critical density, etc., can be obtained even
in Newtonian cosmology, if we do not
consider a homogeneous and isotropic distribution of matter in
space as static, but as
expanding (a kind of "vertical
upward throw" from each
point according to Hubble 's law, given in the initial
conditions). However, these contexts became clearer only later,
when the results of relativistic theory were already known.
Static Einstein's universe
Therefore, since Einstein did not find any solution compatible
with the static spherical universe, he decided to modify his
original gravitational equations Rik- (1/2) R.gik = 8p Tik by
introducing the so-called cosmological member L.gik , which could "stabilize" the universe. This
cosmologic member
which here plays a similar role as a member L.j in equation (5.1) of
Newton-Seeliger cosmology; but here it does not have to introduce
"from the outside" (ad hoc), but arises already when
deriving Einstein's equations of the gravitational field - see
§2.5. Based on such supplemented
gravitational equations Rik- (1/2) R.gik - L.gik = 8p Tik , Einstein's
cosmological model of the static universe was created,
discussed in more detail in §5.2 "Einstein's
and deSitter's universe. Cosmological
constant.". Although this
model has not proven to be realistic, it is often used to compare
the parameters of newer cosmological models (see
eg §5.3, section "Relative W-parameterization of cosmological models").
Later, when Hubble's observations
revealed that the static universe thezis was wrong,
Einstein called the cosmological contant as the "biggest
mistake of his life" **), which prevented him from
theoretically predicting the cosmological redshift caused by the
expansion of the universe.
**) Much later, however, some experts
welcomed the cosmological term and used it in theories attempting
to explain some of the problems of the original standard
cosmology. In §5.5 "Microphysics and Cosmology.
Inflation Universe." it
will be shown what role the cosmological member can play in the
so-called inflationary expansion of the very
early universe. And in §5.6 "Future of the
Universe. Arrow of Time. Hidden Matter.",
section "Accelerated Expansion of the
Universe? Dark Energy?"
we will see that the cosmological constant can explain the accelerated
expansion of the universe in its late evolution.
Dynamic expanding universe
In 1924-29, E.Hubble, while systematically observing
extragalactic "nebulae" with a telescope on Mount
Wilson (mirror diameter 2.5 meters), discovered that they were in fact
foreign galaxies, whose distance he
determined using the Cepheids contained in them (§4.1, passage "Variable
Stars"). Hubble found that the radiation spectra
of distant galaxies show a systematic shift toward the red
region, the magnitude of this redshift
not depending on the direction
in which the galaxy lies, but is approximately proportional to
the distance l of the galaxy :
| z =def. Dl / l = H . l , | (5.2) |
where l is the wavelength of light and the
coefficient of proportionality H
between the galaxy's velocity and its distance is is now called
the Hubble parameter or the Hubble speed.
The name Hubble constant *) is also used for it, but
this can be somewhat misleading :
*) It is a constant only in the sense that it does not
depend on the distance l . However, in the context of the
global evolution of the universe, its value of H(t) depends
on the time t .
Determining the
exact actual value of the Hubble coefficient H (t) is not very
easy. In our immediate vicinity, cosmological expansion has
little effect and the measurement results are distorted by local
galaxy motions. When measuring in outer space, we look back to
the past and it can be difficult to reliably extrapolate the
current value of H(t) if we do not know in advance the dynamics
of the expansion of the universe.
Note: At the same
time, G. Lemaitre was also dealing with the expansion of
the universe, who, among other things, he hypothesized a "primordial
atom" at the beginning of the universe, the splitting
of which released and began to expand all the matter of the
universe.
As the Hubble
constant H0, it is more adequate to take the value of the Hubble
parameter H(t) at the current time of evolution of the universe t~14×109 years, i.e. at
redshift z=0. Based on measurements of a larger number of
galaxies, the current value of the Hubble constant H0
~ 70 km/s/Mpc (megaparsec 1Mpc = 3.26 million light-years).
The measurement of
the Hubble constant and some differences in the values are
discussed in §5.4, the passage "How
fast is the universe expanding? - precise measurement of the
Hubble constant".
In addition, Hubble's
observations showed an approximately homogeneous and isotropic
average mass distribution in the visible part of space with a
density of about 10-31 -10-29
g/cm3.
The Hubble redshift, which is the same for all spectral lines and
wavelengths, is most naturally interpreted as a Doppler effect *) caused by rapid distancing
of far galaxies from
us. The farther apart the galaxies are, the
faster they move away each other. The inverse value of the Hubble
constant 1/H0 represents the so-called Hubble time -
the age of the universe derived from the instantaneous rate of
expansion, without taking into account the effect of gravity on
the dynamics of expansion; is about 14 billion years.
*) The Doppler effect
is a kinematic effect arising from the relative movement of a
wave source and an observer (wave detector). It generally applies
to all types of waves. If the wave source with a certain constant
frequency fo moves towards the observer (receiver), this observer
registers a higher frequency f than what source it
actually radiated. Conversely, when the source moves away from
the observer, the registered frequency is lower than the actual
one. The relative difference between the actual fo and the observed f
frequency (Doppler frequency shift) increases in proportion to
the velocity V of the source relative to the observer: f =
[1 + (V/v)] fo , where v is the propagation velocity of the
given wave; Df/fo = (f-fo)/f = V/v. The same applies to the wavelength l = v/f. By
measuring the difference between the frequencies
or wavelengths of the primary radiated wave and the received
wave, we can determine the mutual speed movement
of the source and the observer. For electromagnetic waves, of
course, v = c.
Note: This
rule also applies when the source of the received wave is the reflection
of the wave from a certain moving object (including a flowing gas
or liquid). It is used in radar technology and ultrasonic
sonography.
Global receding <-versus-> peculiar
motions of galaxies
From a global point of view, galaxies primarily perform a diverging
cosmological motion. However, individual galaxies are also
influenced by the gravitational action of other, surrounding
galaxies. This can cause local deviations in their
movement - so-called peculiar movements (lat. peculiaris = special, individual,
strange). Although the universe is
expanding overall, from a local point of view not completely
uniform, some galaxies can move faster or slower, depending
on their masses and distances from other nearby galaxies. The
local gravitational attraction can sometimes even overcome
the global cosmological expansion and some galaxies can move
towards each other.
An example is our Milky Way
galaxy and the neighboring galaxy in Andromeda, about
2.5 million light-years away, which are approaching each
other at about 110 km/s. In about 4 billion years, they will
"collide", or rather "penetrate",
and both galaxies will form one large elliptical or irregular
galaxy. There are many such groups of galaxies that are bound by
their own gravity and moving through space. Galaxy
"collisions" are discussed in §5.5, the passage "Gravitational
interactions and galaxy collisions"
and "Galaxy clusters".
Age and size of the universe
The age of the universe
For many centuries, the universe seemed to be like a philosopher
and a natural scientist as permanent and unchanging,
the age of the universe considered infinite (if we ignore some of the illusory value of about a
thousand years, derived from unsubstantiated religious
legends of the divine "creation of the world",
which, moreover, they were in ancient times invented from anthropocentric
backgrounds, without relation to the universe - the construction
of which people at the time had no idea).
This view changed dramatically after Hubble's discovery of the expansion
of the universe. If we project the observed moving away
of all galaxies from each other into the past,
against the flow of time, we inevitably come to the moment when
all these galaxies had to be close together (figuratively
"at one point") --> the
universe cannot be infinitely old, the age of
the universe is finite. The event when the universe
"freed" itself from highly compresed condition and
began its expansion evolution is now called "big
bang" - is discussed in
detail in §5.4 "Standard cosmological model.
Big Bang. Formation of the structure of the universe.".
The total age of the universe - the
time elapsed since its creation - is determined or estimated by
basically two approaches :
1. Analysis of
the dynamics of the expansion of the universe
in principle, it makes it possible to determine retrospectively
the time "t = 0" from which the
evolution of the universe began. The basic way here is to use the
inverse value of the Hubble constant : 1 / H
represents the so-called Hubble time - the age
of the universe derived from the instantaneous rate of expansion,
without taking into account the effect of gravity on the dynamics
of expansion; is about 14 billion years (which
surprisingly agrees quite well with more complex methods) . .... Within the standard cosmological model, the exact
determination of the age of the universe lies in the problem of
determining the values of cosmological parameters
(§5.3, passage "Relative Omega-parameterization of cosmological
models") - this allows in this model the idea of "running
the cosmological clock back in time" up to the moment t
= 0 (t0). This extrapolation can be performed exactly on the
basis of Fridman's equation (5.23). This can be
illustrated by the above Hubble time 1/H :
t 0 = ( 1
/ H ) .
F (Omega) ,
multiplied by the correction factor F(Omega),
which is a function of the "Omega"
cosmological parameters dependent on the specific density and
composition of matter in space. Relict microwave radiation
measurements are now used to accurately determine the age of the
universe (coefficient F) (§5.4, passage "Microwave relic radiation -
messenger of early space news"). Minor fluctuations in the cosmic microwave background
make it possible to fine-tune the values of the "Omega"
cosmological parameters. According to new measurements, the
original range of 13-15 billion years has been specified to 13.8
billion years.
2. The age of
objects in the universe
The universe must be at least as old as the oldest objects in it...
If we can determine or estimate the age of such objects, it sets
a limit for the minimum age of the universe. To
determine the true age of the universe, we must add the
time of origin to this value of this analyzed object
from the big bang, if we are able to reliably estimate it. The
search for the oldest stars is important for
this analysis. These occur mainly in globular clusters,
where they formed at about the same time, soon after the
beginning of the universe (they can therefore serve as "cosmic
clocks"). The oldest globular clusters contain active
stars only less than 0.7 times the mass of the Sun (the more massive ones have long since burned out), whose age is estimated at 11-18 billion years
(considerable uncertainty in this estimate is due to inaccuracy
of the distances of the star clusters and ignorance of some
details of dynamics stellar evolution).
Another alternative method turns to
the chemical evolution of the universe - nucleosynthesis.
Uses radioactive dating using radionuclides with
extremely long half-lives (from a general
point of view of nuclear physics, the principle of this method is
discussed in §1.4 " Radionuclides ", part
"Radioisotope
(radiometric) dating" in
monograph "Nuclear physics and ionizing radiation physics"). For dating minerals on
Earth and in meteorites, the isotope rubidium Rb-87 is most often
used, which with a half-life of 47 billion years is converted to
strontium Sr-87, whose representation is compared to Sr-86. For
meteorites, this is 4.56 billion years old, which is considered
the age of the solar system. For interstellar gas and old stars,
the isotope pair with Re-187 was used, which with a half-life of
40 billion years is transformed into Os-187, then the pair U-235
and U-236, or the ratio of Uranium-238 to Thorium-232.
The size of the universe
Determining the "size of the universe"
is also a difficult and debatable task. The area astronomically
observable from us from Earth - the observable universe
- is constantly increasing with the improvement of observation
technology. The most distant objects are observed at a distance
of almost 13 billion light-years. By analyzing the redshift of
relic radiation and the rate of expansion, it is estimated that with
the inclusion of the cosmological expansion of the universe,
the observable universe is a sphere with a radius of about 45
billion light-years. This expansion made it possible for us to
observe light from a galaxy now even 40 billion light-years away (with a correspondingly large spectral redshift), while this light traveled to us in only about 13
billion years. Including the dynamics of space expansion
(hypothesis of accelerated expansion -
§5.6, section "Accelerated
expansion of space? Dark energy?"), the diameter of the
universe could be even about 100 billion years! This would be the
size of the space that matter reached during expansion from the
beginning of the universe; if the universe is open, it has no
boundaries...
This distance value
corresponds to the event horizon - an interface
beyond which we can no longer be seen in principle. If an object
were at a greater distance than the light could have covered
during the existence of the universe, then such light has not yet
reached us - and due to the expansion of the universe, it will
not even reach it! Such extremely distant objects lie
forever outside our observable universe.
Moreover, if the conclusions
of inflationary
cosmology leading to the multiverse - the existence
of more universes (§5.5, part
"Chaotic inflation", passage "The
emergence of more universes")
were valid, the question of "the size of the whole universe"
would be unsolvable and irrelevant
..!..
It is estimated that there are about
1021-1023 stars in the
observable universe, in more than 1012 galaxies.
Cosmological
expansion of univese
The kinematic explanation of the cosmological spectral shift
using the Doppler effect of rapidly receding galaxies is adequate
from the local point of view of classical physics or special
theory of relativity. Hubble's rule that the farther galaxies
are, the faster they move away from us (and from each other)
suggests that this is not the movement of galaxies through space
in the classical (mechanical) sense. Rather, they appear to be
carried away by the ever-expanding geometric "fabric"
of space itself.
From the point of view of the
globally curved space-time, which the universe is according to
the general theory of relativity, the expansion of space
as such, which carries the distant galaxies to
even greater distances, and these galaxies themselves do
not move relative to this space (the galaxies' own
motions are small at relatively relativistic speeds and are
irrelevant here - due to the Doppler effect, they cause very
little additional - positive or negative - spectral
shift to cosmological redshift). Both of these explanations are
equivalent only when observing not too distant galaxies.
The superluminal rate
of expansion of space ?
.According to current relativistic cosmology, a short period of
so-called inflationary expansion of the universe
took place at the beginning of the evolution of the universe
(§5.5 "Microphysics and cosmology. Inflationary
universe. "), when the
germinal universe swelled exponentially. It expanded much faster
than the speed of light. It would seem to be in conflict with
the special theory of relativity, but this is not the case
here: nothing moved at super-light speeds
through space - the space itself expanded very rapidly
and carried a physical field with it. What drove him to this
rapid spontaneous expansion is not completely known, it is
assumed that it was the so-called dark energy (§5.6
"The future of the universe. Time
arrow. Dark matter. Dark
energy. "), thanks to
which it is observed even in the late phase (here slow - gradual)
so-called accelerated expansion of the universe.
An alternative explanation
for the redshift; aging light ?
Some alternative explanations for the
redshift have also emerged , trying to find another mechanism for
losing the energy of light quanta from distant cosmic objects.
The simplest explanation would be the loss of energy by the interaction of photons with intergalactic matter. However, such collisions of
photons with other particles would also lead to a change in their
momentum, ie to their scattering and thus to the blurring of the image of the source, which is not observed - the
images of even the most distant objects are sharp. The most
common hypothesis was the "aging" or "fatigue" of photons from distant galaxies during their long
journey through space - photon could spontaneously emit some
particles carrying away part of its energy (eg a
neutrino-antineutrino pair). However, no such process has ever
been observed in the laboratory, and in addition, the probability
of spontaneous photon decay would have to be energy dependent
(inversely proportional to the photon energy), so the redshift
would be different in different parts of the spectrum. Nothing
like this, however, not observed, red shift for all wavelengths
equally (exact measurements showed that the red shift of radio
waves, l = 21 cm in distant galaxies is
the same as the shift in the optical field). In addition, the emission of
photon particles would lead to a change in their momentum and
thus in the direction of photon motion, which would cause blur images of distant sources, similar to
intergalactic absorption. Also, the assumption that the redshift
has a locally gravitational origin does not hold up to a more
detailed analysis - light would have to be emitted from areas
near the horizon of a compact formation that would certainly
collapse soon at such a mass (as a galaxy).
All these alternative explanations turned out to be ad hoc hypotheses,
explaining only some aspects of the phenomenon; they do not
correspond to current knowledge and are now abandoned. Only the mechanism of the
Doppler effect, or global expansion of space, faithfully explains
all the basic properties of the phenomenon - the same relative
shift value for light of all colors and electromagnetic waves of
all frequencies and the absence of blurring of observed distant
objects or blurring of their spectral lines.
According to the cosmological principle of
homogeneity and isotropy, ie the equality of all observers, every observer
everywhere must see that distant galaxies diverge from him - in
other words, the universe as a whole
expands *). Hubble's
discovery thus showed that there was no need to look for static
solutions for the distribution of matter and fields in space; on
the contrary, dynamic solutions will better reflect reality.
These findings proved to be in full agreement with the earlier
(1922) found Fridman solution of Einstein's equations by which
the solution of gravitational equations even without
a cosmological term is also three-dimensional
homogeneous and isotropic space that is not static, but its
radius of curvature changes with time.
*) No specific place is the center of expansion of the universe,
respectively each location is this center of expansion. On a
cosmological scale, everything starts from everything ...
From a local and
kinematic point of view, we can imagine the redshift as a Doppler
effect. From the global point of view of relativistic cosmology,
an alternative but essentially equivalent explanation emerges:
the cosmological redshift can be attributed to the
"expansion" of space during the time that light from
its source propagates through this space. The wavelength of light
increases as it moves through space - at different times and at
different speeds depending on how fast the space was expanding.
The magnitude of the redness, ie, the extension of the
wavelengths, is proportional to how much the universe has
expanded during the time that light traveled to us. The resulting
red shift from thus, it depends on the distance of the
observed object and on the dynamics (history) of the expansion of
space. The measurement of the spectral shift in galaxies and
quasars lying at different distances thus in principle provides
information on the temporal dynamics of the expansion of space -
information on the history of the
expansion of the universe; however, the
objective and accurate determination of these large distances is
a difficult astronomical problem.
The most distant galaxies and
quasars observed so far reach redshift values around 5. The
largest possible redshift can be observed in relic radiation: zrelict »
1100 - this value results from the ratio of the temperatures
of end of radiation era of 3000 ° (when the radiation separated
from matter) and the current temperature relic radiation 2.7 °:
3000/2.7 » 1100; these
temperatures are inversely proportional to the mean wavelength of
the respective radiation.
Energy and the Law of Conservation of Energy
in an expanding universe
In classical physics and in everyday life, energy
is a cardinal quantity that we can measure, transform it between
different types, use it, but we cannot create or destroy it - the
law of conservation of energy applies. Energy is neither
created nor destroyed, it is only redistributed.
The global energy of the entire universe
is a complex and debatable issue. What could she relate to? The
prevailing opinion is that the amount of energy in the universe
is constant and comes from a mysterious process of the
creation of the universe - the big bang. In §5.4 "The
Standard Cosmological Model. The Big Bang. Formation of the
Structure of the Universe."
and 5.5 ("Microphysics and cosmology. Inflationary
universe.") we will see,
that in the very first moments of the creation of the universe,
processes were probably taking place during which the law of
conservation of energy could not be spoken of. Energy is a
quantity that does not exist by itself, but is always relative
to other objects, particles, systems. And in these first stages
of "chaos" there were no such objects yet. Only after
the end of the inflationary phase and the onset of the hadron
era, the (local) law of conservation of energy probably becomes
applicable.
Even though the universe is probably
infinite, that doesn't mean it has infinite energy. Energy is not
evenly distributed in the universe, there are areas where it is
more or less. Although the total amount of energy in the universe
does not change, its density decreases during the expansion. And
eventually it will be so low that it will be almost zero
everywhere and the universe will reach a state of maximum
entropy. Then nothing will happen anymore, no
stars and planets will be formed, no life -> "heat
death" of the universe (§5.6 "The
future of the universe. The arrow of time. Hidden matter. Dark
energy.").
As the universe expands, the light (and electromagnetic radiation in general) that passes through, it also expands - spectral
redshift. This means it loses energy because longer wavelengths
have lower energy. When the spectrum of electromagnetic radiation
is redshifted during its journey through expanding space, its
energy decreases due to the increase in wavelength. The
question arises, where did this part of the lost energy
"go"? Is she lost forever? - is energy escaping from
space? Isn't this a violation of the law of conservation of
energy? Such a contradiction would arise from the point of view
of classical physics or STR. In the general theory of relativity,
however, the concept of energy is more complex (see §2.8 "Specific properties of
gravitational energy"). In locally inertial frames of reference, the law of
conservation of (non-gravitational) energy continues to apply.
However, in curved spacetime, what we call energy may not
itself be conserved in general. And so it is also in
"time-curved" space-time, in which the expansion of
space takes place. Here, the "geometric"
(gravitational), electromagnetic and kinematic contribution to
the quantity that we are used to using in classical physics as
"energy", is combined.
The all-pervading medium in space is the
gravitational field. As the universe expands, so does gravity.
The energy that light loses as it travels through expanding space
is balanced by the energy that gravity gains as the universe
expands. The total energy of the system remains the same,
only its distribution and form changes.
Hot early universe , "big
bang", background radiation
From the properties of Friedman solution
came G.Gamov, which between 1946-1956 expressed and developed
the hypothesis of the
"hot universe", according to which the
temperature in the universe in the early stages after the "big bang" (Big
bang - the singular origin of the universe corresponding to time
t=0 in Fridman's model - see §3.3) reached billions of degrees, and
during this hot stage all chemical elements from hydrogen to
uranium were formed by nuclear synthesis reactions; today we know
that nucleosynthesis was more complicated - see §5.4, section
"Primordial
nucleosynthesis"
and §4.1, section "Thermonuclear reactions in stars".
The hot early universe was filled
with high-energy quantum, but as a result of the expansion of the
universe, the energy of each photon was constantly decreasing; now the
spectral energy distribution of these
"relict" photons (left over from
the hot early stage)
should correspond to blackbody radiation heated to several °K,
which corresponds to radio waves of the centimeter band. This hypothesis not
initially given greater attention until 1965, when A.Penzias and
R.Wilson in the analyzing noise of
the radio telescopic
receiving antenna discovered cosmic
background radiation - weak microwave electromagnetic
radiation, which comes isotropically
from all directions of the sky, is non-polarized,
time constant (independent of the year season). Further measurements showed
that its spectrum corresponded to the radiation of an absolutely
black body at a temperature of about 2.7 °K. It is a relic radiation, a "cooled" remnant of the
radiation era after the Big Bang, the "thermal
afterglow" of the Big Bang. This confirmed the concept of an
expanding universe with a very hot early period. Relativistic
cosmology has thus irrevocably shown a that the universe
is a dynamic object, evolving not only in this
parts (evolution of
stars and galaxies), but also as a
whole.
Steady-state theory of the
universe
The idea of an expanding and generally evolving universe was
initially met with distrust and resistance from astronomers. As
an alternative to the theory of expanding universe and the Big
Bang in 1948 F.Hoyle, H.Bondi and T.Gold proposed theory
steady state of space (TSS Theory steady-state
universe), called theory of stationar universe
or solid state of the universe. It is based on the so-called perfect
cosmological principle, requiring that (on a large
scale) the mean density of matter be the same not only in
different parts of the universe, but be the same over time.
Steady state theory does not deny the spatial evolution
(expansion) of the universe, but seeks to preserve a static
(time-invariant) solution of cosmological equations - to preserve
the universe eternal in time, not changing its appearance,
without the temporal beginnings of the universe (the
objection was accentuated: if the universe had its time
beginning, what was before him?). The universe is
expanding, but the density of matter does not change in it,
because in the "gaps" of the growing space, new
matter "from nothing" is constantly
being created (a hypothetical "C-field" has
been introduced). To maintain a steady state (against the
existing expansion), the formation of a new mass at the rate of 1
hydrogen atom per 1 m3 would suffice.in 5 billion years (such a small increase
cannot be confirmed or refuted). The erroneous
of the steady state theory of the universe became apparent in the
1960s, when observations of quasars and radio galaxies showed
that they were only at great distances and therefore existed in
the distant past, while according to the steady state theory they
should occur evenly everywhere. The definitive refutation of the
stationary universe theory came with the discovery of relict
microwave radiation, which unequivocally supported the
theory of the hot beginning of the universe and the
"dilution" of matter and radiation as it expanded.
When astronomers aim powerful telescopes at distant objects, they can observe the evolution of the universe in a way. This is due to the finite, constant and fixed speed of light. Distant galaxies whose light came to us billions of years ago look different from similar galaxies relatively close to us. By observing ever greater distances, we also penetrate the ever greater "depths of time". And we observe that the universe previously looked different then now...
Further significant development of cosmology was stimulated by the application of knowledge of nuclear physics and elementary particle physics to processes in space, especially to the hot early universe. Nuclear astrophysics has emerged that can convincingly explain the entire "chemical evolution" of the universe, ie both the nuclear reactions in the stars and the initial nucleosynthesis in the early hot universe. Fridman's solution, supplemented by a detailed theory of physical processes in the early hot universe, gave rise to the standard cosmological model (§5.4 "Standard cosmological model. Big Bang. Forming the structure of the universe."), which broadly explains the observed structure and evolution of the universe. In recent years, the efforts of cosmologists have focused mainly on the study of the earliest stages of the evolution of the universe just after the Big Bang - quantum cosmology and the hypothesis of inflationary expansion of the very early universe have emerged to solve some problems of the standard model (§5.5 "Microphysics and cosmology. Inflationary universe.").
Relativistic cosmological model
The process of constructing a relativistic cosmological model
consists of the following main stages :
If space-time can be found that is an exact solution of Einstein's equations for the real distribution of matter and well describes the global properties of the universe (agrees with the findings of the visible part of the universe obtained by observation), such a solution can be considered an adequate cosmological model.
Matter in
the universe
First we
notice stage c). Cosmology deals with the
properties of the universe on large
cosmological scales, larger than about 109
light-years. From the point of view of these scales, the
dimensions of astronomical objects (observed in the sky) are
quite insignificant (galaxies with typical
dimensions of 100,000 light-years are ten thousand times smaller
than this basic scale, galaxy clusters a thousand times smaller). From this large-scale point of
view, galaxies and their clusters are only a kind of tiny "dust particles", whose internal structure does not
play a proper role from the point of view of the whole. From a
cosmological point of view, then, we can imagine the present
universe as a space filled with sparsely distributed
"dust" *).
*) This "sparse spreading" is
valid at the present stage, in the beginning of the evolution of
the universe it was a "dense spreading" of high-energy
particles and radiation!
In cosmology, therefore, it is
abstracted from specific local structures, as matter is usually
considered "dust" or "gas" (ideal liquid) -
it can be both an intergalactic gas in the usual sense, and a
relativistic "gas" of photons, or a gas whose
"molecules" are stars, galaxies or clusters of
galaxies. The uniform distribution of the averaged mass in space
(cosmological principle) is similar to the homogeneity of a gas
(or liquid), which is very inhomogeneous at molecular scales, but
from a macroscopic point of view it appears
perfectly homogeneous. In the cosmological approximation,
therefore, we can consider the whole universe to be filled with
an ideal "gas", whose molecules are galaxies or rather
clusters of galaxies, photons of radiation, intergalactic gas.
The energy-momentum tensor of such a cosmologically distributed
mass in space is therefore expressed in the form corresponding to
an ideal fluid (derived in §1.6, passage "Energy-momentum tensor")
| T ik = (p + r ) u i u k - p. g ik . | (5.3) |
When modeling the mass filling the universe in the form of an ideal fluid, it is necessary to know the dependence of the density r on the pressure p, ie the equation of state, for solving the equations of space-time evolution of the universe. However, to analyze the basic issues of global evolution, it is sufficient to limit ourselves to two extreme cases :
Analysis of the evolution of the universe for this basic substance will be in terms of relativistic cosmology, the structure of spacetime performed primarily in §5.3 "Fridman dynamic models of the universe", from the perspective of a particular physical cosmology then §5.4 "Standard cosmological model. Big Bang. Formation of the structure of the universe.", §5.5 "Microphysics and Cosmology. Inflationary Universe" and §5.6 "Future of the Universe. Arrow of Time. Dark Matter. Dark Energy".
Geometry
of the universe
In models based on the cosmological principle, three-dimensional
space must be homogeneous and isotropic, ie all points and all
directions are equal here, they are no different. In differential
geometry, it is shown [214], [155] that such three-dimensional
space (except planar Euclidean space) is a space with constant curvature R, independent of spatial
coordinates or a direction, that is spherically
symmetric
with respect to the each point; therefore, any point can be
chosen as the origin r = 0 of the spatial coordinates.
This
basic geometric aspect can be illustrated for clarity on a 2D
analogy with two-dimensional area. Homogeneous and
isotropic 2D surfaces can be of three types :
--> 2D Euclidean space is flat
(non-curved), it is the simplest special case of the more general
Riemann space, it has zero curvature everywhere. In Cartesian
coordinates (x, z), the length element according to the
Pythagorean theorem is simply dl 2 = dx2 + dy2.
In the polar coordinates (r, J) given by the
transformations x = r.cos J , y = r.sin J, the length element is
dl 2 = dr 2 + r 2 d J 2 .
--> 2D sphere - the surface of a sphere of
radius R , the spherical surface is a
Riemannian space with positive constant curvature, in which the
length element in polar coordinates has the form
dl 2 = [dr2/(1-r2/R2)] + r2dJ2 .
--> 2D " saddle
" surface is a Riemannian space with
negative constant curvature, in which the length element in polar
coordinates has the form
dl 2 = [dr2/(1+r2/R2)] + r2dJ2 .
The length element in a two-dimensional homogeneous
isotropic space with constant curvature can therefore be written
in polar coordinates in the general form
dl 2 = [ dr 2 / (1 - k.r 2 / R 2 ) ] + r 2 d J 2 ,
where the curvature parameter k = + 1, 0, -1 is introduced.
Analogously, the length element dl in three-dimensional
space with constant curvature, it can generally be expressed in spherical
coordinates in the form
|
(5.4) |
where the quantity R -> a (with a
dimension of length) indicates
the radius of curvature of the space (the
radius of curvature of space is
customary to denote R
; however, this would be confused with
scalar curvature R ,
so in cosmology it is customary to denote curvature space of space a ). The
parameter k = 1, 0, -1 characterizes the global type of
space curvature :
| k = + 1 ® space with positive constant
curvature; k = 0 ® Euclidean flat space; k = - 1 ® space with constant negative curvature . |
A more detailed analysis of the space-time geometry of the universe using this metric, but the time variable a = a(t), in Einstein's gravitational equations will be performed in §5.3 "Fridman's dynamic models of the universe".
Topology of the universe
The local geometry of space-time is determined
by the distribution of matter in the universe - matter~energy
curves space-time, in which bodies and particles then move along
geotedics, representing the straightest possible trajectories.
The curvature of spacetime is described by Einstein's equations,
the application of which to the universe under appropriate
simplifying assumptions leads to Fridman's equations (5.23)
describing a universe whose space can have positive, negative or
zero curvature, as mentioned above; see §5.3.
However, this local geometry generally
says nothing about the global shape, ie the overall
topology of space. In standard relativistic cosmology, a
simply continuous universe (with a sphere topology) is
considered, on which Einstein's, DeSitter's or Fridman's
cosmological models work. Theoretically, however, the universe
could have a more complex, multi-conected topology,
with different topological tunnels or identifications of
different parts, as has already been discussed in §3.3, the
passage "Time Travel";
such a universe could even look like an "emmental"...
The complex multiple conected
topological structure of the space of the finite universe would
have interesting implications for what the observer sees in such
a universe: in principle, he could see multiple images of
galaxies, stars, and himself, as in a mirror maze. And in time at
different stages of development. It could not be
ruled out that when we observe a distant galaxy, it could be our
own Galaxy a long time ago billions of years ago! However, it
would be very difficult to astronomically recognize that the two
galaxies observed are one and the same galaxy, represented by the
passage of light through the complex topological structure of the
universe *), if not hopeless! We would see them from different
angles and especially, due to the spatial scales of many billions
of light years, in completely different time stages of
development, changed beyond recognition ...
*) Incomparably more difficult than it is with multiple imaging
due to gravitational lensing (§4.3 ,
passage "Gravitational
lenses. Optics of black holes.")
.
A certain way to
obtain at least partial indications for certain topological
structures of the universe could be a detailed measurement of the
properties of microwave relic radiation - its
homogeneity, fluctuations (depending on the angular distance and
wavelength), polarization. Already at the time of the separation
of radiation from matter, there were nuclei of future structures
in the universe, so these photons passed through places with
different gravitational potentials, which led to small changes in
their energy and wavelength - a slight cooling or heating. These fluctuations
should be visible even now, as slightly warmer and colder
"spots" in the otherwise isotropic distribution of
relic radiation - they represent a kind of "paleontological
imprint" of the structures of the early universe. The
temperature difference is very small, of the order of 10-5 degrees, so the
relevant projects of their data measurement are still being
prepared *) - see §5.4, passage "Microwave relic
radiation - a unique messenger of early space informations".
*) For a detailed study of relic radiation,
a satellite was launched in 1989 COBE (Cosmic Background
Explorer) and in 2001 the WMAP satellite (Wilkinson Microwave
Anisotropy Probe); even more accurate PLANCK probe in 2007.
All these
theoretical speculations about a more complex topology have no
justification in astronomical observations, so we will
stick to the interpretation of relativistic cosmology the
simplest and, from the current point of view, the natural
assumption of a simply continuous topological structure of the
universe.
A certain exception will perhaps only be
discussions about the possibility of the existence of
multiple universes (§5.5 "Microphysics
and cosmology. Inflationary universe." and §5.7 "Anthropic principle and the
existence of multiple universes");
however, this will not be the introduction of some a priori
complex topology, but of hypothetical topological properties
"induced" by turbulent quantum-gravitational
processes at the beginning of the universe.
Correct and
erroneous cosmological ideas about the universe ?
The development of cosmology was accompanied by many mistakes.
During our knowledge of nature and the universe, there were a
number of ideas and concepts, most of which were partially or
completely erroneously. In the beginning, it was
a misconception of the Earth as a flat plate:
the view of a man standing in a free landscape really suggested a
flat area, possibly wrinkled by mountains. Later, the idea of the
globe standing as the center of the
universe, around which everything revolves:
we live on a cosmic "carousel" of rotating Earth, which
suggests the orbit of cosmic bodies around us - was refuted
by the Copernican heliocentric system. The idea of the central
position of the solar system in space still persisted. The Milky
Way astronomically appeared to be a whole universe that was
considered static. Stars used to be considered unchanging
"perennials" - all stars and planets are in a
state of infinite unchangingness and cyclical motion, from the
infinite past to the "ages of ages"..!..
Even A.Einstein initially believed in the global static
of the universe (see above the passage "Einstein's static universe" and §5.2 "Einstein's and
deSitter's universe. Cosmological
constant. "). Only
E.Hubble's observations of 1924-29 showed the existence of many
galaxies moving away from each other - a vast dynamic
expanding universe.
The current Standard
Cosmological Model (§5.4 "Standard
Cosmological Model. The Big Bang. Shaping the Structure of the
Universe.") is
very well astronomically and physically based, convincingly
explaining everything we observe in the universe. However, even
here there are some unresolved issues, such as the question of
the origin of the universe, or the mystery of dark
matter and even more mysterious dark energy (§5.6 "The future of the
universe. The arrow of time. Dark matter. Dark energy."). Only the more distant future will show
how these issues can be solved, or what we were wrong
about again, and what new phenomena and concepts
will appear ..?..
 |
 |
 |
| 4.9. Gravitational collapse - - The biggest disaster in nature |
5.2. Einstein's and deSitter's
universe. Cosmological
constant. |
| 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 | ||