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 construction
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). It is beyond the scope of this book to discuss in
detail the issues of contemporary relativistic cosmology, which,
moreover, are now evolving very rapidly. However, since the
physics of gravity and the structure of spacetime play
the most important role for cosmology and find significant
application in it, we will try to analyze the basic principles
and knowledge of relativistic cosmology at least briefly from
this physical point of view (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 shape
is, when and how it was created and where it goes governs 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.
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 variety
(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
Galileo's observations and Newton's law of universal gravitation erased the
apparent 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 throughout the
observation of the available universe follow the same physical
laws of mechanics, gravity, electrodynamics, atomistic, nuclear
physics, thermodynamics, physics, plasma, etc.
*) When building the now standard
cosmological model (§5.4 " standard
cosmological model. Big Bang. Formation of the structure of the
universe. ") to
Einstein's equations apply 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 10^{15} 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...).
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
distributionand 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).
Our humble
place in the universe
In everyday life, we observe that lack of knowledge leads to
arrogance and pride, better knowledge awakens modesty and
humility. So it is 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 used to personalize. We now know that we are just tiny
organisms living on a tiny grain of powder in a vast cosmos ...
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 10^{8}
-10^{10} 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
(especially relic 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 this is due to
the emergence of the universe from the "big bang" and
then the rapid "blowing" during the inflation phase.
*) At one 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.
^{ }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 / m^{3} , which corresponds
to only 3 protons in 1 m^{3} . It's an almost perfect vacuum that we can't even
achieve under terrestrial laboratory conditions!
The universe is almost
absolute emptiness!^{
}
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. Pulsary
"). 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. ").
Newtonian cosmology. Static
universe.
In the 18th and 19th centuries, classical mechanics, together
with Newton's law of gravitation, celebrated great success 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. The basic premise, supposedly
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, all matter
should be clustered by gravity into one large compact body.
However, even Newton's conception of the universe, which
represents an infinite Euclidean space on average evenly and
statically filled with stars acting on each other according to
Newton's law of gravitation, has encountered insurmountable
difficulties.
^{ }The best known is the so-called Olbers photometric paradox formulated in 1826 - the paradox of the
"dark sky" - "why is
it dark at night?". If the stars are evenly and
statically distributed in an infinite universe, the sky would
have to shine as bright as the surface of the Sun day and night
from horizon to horizon *): in each spatial angle of view, each
area element contains on average a number of stars proportional
to a square distance from us, while the intensity of light from
there is also inversely proportional to the square of the
distance. It can be even more clearly imagined that
the view of the sky in any direction always sticks to the surface
of some stars (similar to a large pine forest we see only trees
in each direction). A star should shine in every direction -
the stars should cover the entire observed “celestial
vault.” We do not see individual distant stars, but the sum
of their light should be seen as a continuous glow, not day or
night, but still just a blinding hearth!
*) Most stars, about 70%, are red dwarfs,
so the night sky should be intense yellow-red.
Note: The photometric paradox arises only if the
stars shine indefinitely, as was thought at the time. Considering
that the stars actually shine are finite time (~ 10 ^{6} -10 ^{10} years), the photometric paradox does not
arise even in an infinite homogeneous universe. The stars
do not have enough energy to fill the entire space with light and
turn the dark sky into glowing. Furthermore, the sky is dark
because light from the farthest stars has not yet reached Earth.
^{ }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 photometric paradox is
successfully explained by the expansion
of the universe
.
^{ }Furthermore, there is a gravitational
paradox consisting in the fact 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 must be E 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 Poisson's equation to add 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 ordee 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. 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 arelativistic 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). These connections are not cleared until much later
after a plot, when the
results were already known relativistic theory.
Therefore, since
Einstein did not find any solution compatible with the static
spherical universe, he decided to modify his original
gravitational equations R _{ik} - (1/2) R g _{ik} = 8p T_{ik }by
introducing the so-called cosmological term L .g _{ik} , which could
"stabilize" the universe. This cosmologic member which 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
the thus completed gravitational equations R_{ik}- (1/2) R.g_{ik} - L.g_{ik} = 8p T_{ik} , 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 "biggest
mistake of his life" **) , which prevented him from
theoretically predicting the cosmological redshift caused by the
expansion of the universe.
**) Much later, however, many experts have welcomed
the cosmological member and used it in theories attempting to explain some of the
problems of standard cosmology . In §5.5 it will be shown
what role the cosmological
term can play in the so-called inflationary
expansion of the very early
universe .
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 was determined by
Cepheids (§4.1). 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 º 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 called the Hubble
constant *); a
more appropriate name would be Hubble
speed .
Based on measurements of a larger number of galaxies, the value
of the Hubble constant H » 70 km/s /Mpc is based (megaparsec: 1Mpc = 3.26
million light-years) . *) 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 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 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.
^{ }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 / cm ^{3} . 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 are. 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.
*) 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 moves at a certain
constant frequency f _{o} towards the observer (receiver), this observer
registers a higher frequency fthan what source it actually
publishes. Conversely, when the source moves away from the
observer, the registered frequency is lower than the actual one.
The relative difference between the actual f _{o} 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)] f _{o} , where v is the propagation velocity of the
given wave; D f / f _{o} = (f-f _{o} ) / f = V / v. The same applies to the wavelength l = v / f. By
measuring the difference between the frequencies
or wavelengths of the primary transmitted 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.
Age and size 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 distance 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
"stabbed" itself from highly inflated 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 (t _{0} ). 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 " space
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 cluster 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 "
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 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. An astronomically
observable region from Earth - an 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
the observable universe is a sphere with a radius of about 40
billion light-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
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
..!..
Cosmological
expansion of space
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.
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 - foton 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 feed rate in opti c Kem art). 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. It also believed that the
redshift of a local gravitational origin in from when a more detailed
analysis does not hold water - the light would have to be emitted
from areas near term compact unit that, when such a large mass
(such a galaxy), certainly soon collapsed.
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 to Einstein's equations by which
the solution gravitational equations 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: z
_{relict }» 1100 - this value results from the ratio of end-era
temperatures 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.
Cosmological
redshift and the law of conservation of energy^{ }
During the redshift of the spectrum of electromagnetic radiation
during its travel through expanding space, its energy
decreases due to the increase in wavelength . The
question arises, where did this part of the lost energy
"go"? Isn't that contrary to 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 reference frames, the law of conservation of
(non-gravitational) energy continues to apply. However, in curved
spacetime, what we call energy may not be maintained
in general. And so it is in "time-curved" space-time,
in which space expands. This combines geometric
("gravitational"), electromagnetic and kinematic
contribution to a quantity that we are used to using as
"energy" in classical physics.
Hot early universe , "big
bang", background radiation
From the properties of Friedman solution
came G.Gamov , which between 1946-1956 and expressed hypothézu
developed " hot universe "
, according
to which the temperature in the space 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 s attention until 1965, when
A.Penzias and R.Wilson when analyzing noise radioteleskopické
receiving antenna discovered cosmic
background radiation - weak microwave electromagnetic
radiation coming from all directions isotropic sky is
unpolarized, time constant (independent of year time). 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 eternally eternal, not changing its appearance,
without the temporal origin 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 1m ^{3} would suffice.in 5
billion years (such a small increase cannot be confirmed or
refuted). The erroneous theory of the steady
state 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 it manages to find space-time, which is the exact solutions of Einstein's equations for the fair distribution of mass, yet well describes global properties of the Universe (agrees with the findings of the visible part of the universe obtained by observation), can be regarded as being 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 10 ^{9} 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 " Fridmanovy 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} = dx ^{2} + dy ^{2}
. 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} = [ dr ^{2 }/ (1-r ^{2} / R ^{2} ) ] + r ^{2} d J ^{2} .
--> 2D " saddle
" surface is a Riemannian space with
negative constant curvature, in which the length element in polar
coordinates has the form
dl ^{2} = [dr ^{2 }/ (1 + r ^{2} / R ^{2} ) ] + r ^{2} d J ^{2} .
^{ }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 - kr ^{2} / R ^{2} ) ]
+ r ^{2} d J ^{2} ,
where the curvature parameter k = + 1.0, -1.
^{ }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 "...." ..
^{ }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.
*) 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.
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 |