THE UNIVERSE OR THE COSMOS
This high-resolution
image of the Hubble Ultra-Deep Field shows a diverse range
of galaxies, each
consisting of billions of stars. The equivalent area
of sky that the picture occupies is shown as a red box in the lower left
corner. The smallest, reddest galaxies, about 100, are some of the most distant
galaxies to have been imaged by an optical telescope, existing at the time
shortly after the Big Bang.
Solar system in the
Universe
Introduction
General
The universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar
terms include the cosmos or Kosmos, the world and nature.
Scientific observation of earlier stages
in the development of the universe, which can be seen at great distances,
suggests that the universe has been governed by the same physical laws and
constants through out most of its extent and history. There are various multiverse theories, in which physicists have
suggested that our universe might be one among many universes that likewise
exist.
According to the prevailing scientific
model of the universe, known as the Big Bang, the
universe expanded from an extremely hot, dense phase called the Planck epoch, in
which all the matter and energy of the observable universe was concentrated. Since the Planck epoch,
the universe has been expanding to its
present form, possibly with a brief period (less than 10−32 seconds)
of cosmic
inflation. Several independent experimental measurements support
this theoretical expansion and,
more generally, the Big Bang theory.
Recent observations indicate that this
expansion is accelerating because of dark energy, and
that most of the matter in the universe may be in a form which cannot be detected
by present instruments, called dark matter. The
common use of the "dark matter" and "dark energy" placeholder names for the unknown entities purported to
account for about 95% of the mass-energy density of
the universe demonstrates the present observational and conceptual shortcomings
and uncertainties concerning the nature and ultimate fate of
the universe.
Current interpretations of astronomical observations indicate
that the age of the universe is
13.75 ± 0.17 billion years, (whereas the decoupling of light and
matter happened already 380,000 years after the Big Bang), and that the
diameter of the observable universe is
at least 93 billion light years or 8.80×1026 metres.
According to general relativity, space can expand faster than the speed of
light, although we can view only a small portion of the universe due to the
limitation imposed by light speed. Since we cannot observe space beyond the
limitations of light (or any electromagnetic radiation), it is uncertain
whether the size of the universe is finite or infinite.
History
Throughout recorded history, several cosmologies and cosmogonies have been proposed to account for
observations of the universe. The earliest quantitative geocentric models were developed by the ancient Greek philosophers.
Over the centuries, more precise observations and improved theories of gravity
led to Copernicus's heliocentric model and the Newtonian model of the Solar System,
respectively.
Further improvements in astronomy led
to the realization that the Solar System is embedded in a galaxy composed
of billions of stars, the Milky Way, and that
other galaxies exist outside it, as far as astronomical instruments can reach.
Careful studies of the distribution of these galaxies and their spectral lines have led to much of modern cosmology.
Discovery of the Red shift and
cosmic microwave background radiation revealed that the universe is
expanding and apparently had a beginning.
Etymology,
synonyms and definitions
Etymology
The word universe derives from the Old French word Univers,
which in turn derives from the Latin word universum.
The Latin word was used by Cicero and
later Latin authors in many of the same senses as the modern English word is used. The Latin word derives
from the poetic contraction Unvorsum -first
used by Lucretius in Book IV of his De rerum natura (On
the Nature of Things) - which connects un, uni (the combining form of unus', or "one") with vorsum, versum.
An alternative interpretation of unvorsum is "everything rotated as
one" or "everything rotated by one". In this sense, it may be
considered a translation of an earlier Greek word for the universe,περιφορά, (periforá,
"circumambulation"), originally used to describe a course of a meal,
the food being carried around the circle of dinner guests. This Greek word refers to celestial spheres,
an early Greek model of the universe. Regarding Plato's Metaphor of the sun, Aristotle suggests that the rotation of the
sphere of fixed stars inspired by the prime mover,
motivates, in turn, terrestrial change via the Sun. Careful astronomical and physical measurements (such as theFoucault pendulum)
are required to prove the Earth rotates on its axis.
Synonyms
A term for "universe" in
ancient Greece
Definition
Broadest
definition
The broadest definition of the universe
can be found in De divisione naturae by
the medieval philosopher and theologian Johannes Scotus Eriugena, who defined it as simply everything:
“everything that is created and
everything that is not created”.
Definition
as reality
More customarily, the universe is
defined as everything that exists, (has existed, and will exist). According to
our current understanding, the universe consists of three principles: spacetime, forms of energy, including momentum and matter, and the physical laws that relate them.
Definition
as connected space-time
It is possible to conceive of
disconnected space-times, each
existing but unable to interact with one another. An easily visualized metaphor
is a group of separate soap bubbles, in
which observers living on one soap bubble cannot interact with those on other
soap bubbles, even in principle. According to one common terminology, each
"soap bubble" of space-time is denoted as a universe, whereas our
particular space-time is denoted as the universe, just as we call our moon the Moon. The entire collection of these
separate space-times is denoted as the multiverse. In
principle, the other unconnected universes may have differentd imensionalities and topologies of space-time,
different forms of matter and energy, and different physical laws and physical constants,
although such possibilities are currently speculative.
Definition
as observable reality
According to a still-more-restrictive
definition, the universe is everything within our connected space-time that could have a chance to interact
with us and vice versa. According to the general theory of relativity, some regions of space may
never interact with ours even in the lifetime of the universe, due to the
finite speed of light and the ongoing expansion of space. For example, radio messages sent from Earth
may never reach some regions of space, even if the universe would live forever;
space may expand faster than light can traverse it. It is worth emphasizing
that those distant regions of space are taken to exist and be part of reality
as much as we are; yet we can never interact with them. The spatial region
within which we can affect and be affected is denoted as the observable universe. Strictly speaking, the observable
universe depends on the location of the observer. By traveling, an observer can
come into contact with a greater region of space-time than an observer who
remains still, so that the observable universe for the former is larger than
for the latter. Nevertheless, even the most rapid traveler will not be able to
interact with all of space. Typically, the observable universe is taken to mean
the universe observable from our vantage point in the Milky Way Galaxy.
Historical models
Many models of the cosmos (cosmologies)
and its origin (cosmogonies) have been proposed, based on the then-available
data and conceptions of the universe. Historically, cosmologies and cosmogonies
were based on narratives of gods acting in various ways.
Mythology
Creation
Many cultures have stories describing the origin of the
world, which may be roughly grouped into common types. In one type of story,
the world is born from a world egg; such
stories include the Finnish epic poem Kalevala, the Chinese story
of Pangu or
the Indian Brahmanda Purana.
In related stories, the creation idea is caused by a single entity emanating or
producing something by him- or herself, as in the Tibetan Buddhism concept of Adi-Buddha, the ancient Greek story of Gaia (Mother Earth), the Aztec goddess Coatlicue myth, the ancient Egyptian god Atum story,
or the Genesis creation narrative.
In another type of story, the world is
created from the union of male and female deities, as in the Maori story of Rangi and Papa. In
other stories, the universe is created by crafting it from pre-existing
materials, such as the corpse of a dead god - as from Tiamat in
the Babylonian epic Enuma Elish or from the giant Ymir in Norse mythology -
or from chaotic materials, as in Izanagi and Izanami in Japanese mythology.
In other stories, the universe emanates
from fundamental principles, such as Brahman and Prakrti, or the yin and yang of the Tao.
Philosophical
models
From the 6th century BCE, the pre-Socratic Greek philosophers developed the earliest known
philosophical models of the universe. The earliest Greek philosophers noted
that appearances can be deceiving, and sought to understand the underlying
reality behind the appearances. In particular, they noted the ability of matter
to change forms (e.g., ice to water to steam) and several philosophers proposed
that all the apparently different materials of the world are different forms of
a single primordial material, or arche.
Thales' student, Anaximander,
proposed that everything came from the limitless apeiron. Anaximenes proposed Air on account
of its perceived attractive and repulsive qualities that cause the arche to
condense or dissociate into different forms. Anaxagoras,
proposed the principle of Nous (Mind).
Heraclitus proposed fire (and spoke
of logos). Empedocles proposed the elements: earth, water,
air and fire. His four element theory became very popular. Like Pythagoras, Plato believed
that all things were composed of number, with the Empedocles' elements
taking the form of the Platonic solids.
Democritus, and later philosophers - most
notably Leucippus-proposed
that the universe was composed of indivisible atoms moving
through void (vacuum).
Aristotle did not believe that was feasible
because air, like water, offers resistance to motion.
Air will immediately rush in to fill a void, and moreover, without resistance,
it would do so indefinitely fast. Aristotle responded to these paradoxes by
developing the notion of a potential countable infinity, as well as the
infinitely divisible continuum. Unlike the eternal and unchanging cycles of
time, he believed the world was bounded by the celestial spheres, and thus
magnitude was only finitely multiplicative.
Although Heraclitus argued for eternal
change, his quasi-contemporary Parmenides made the radical suggestion that all
change is an illusion, that the true underlying reality is eternally unchanging
and of a single nature. Parmenides denoted this reality as (The One). Parmenides' theory seemed
implausible to many Greeks, but his student Zeno of Elea challenged them with several famousparadoxes.
The Indian philosopher Kanada, founder of the Vaisheshika school, developed a theory of atomism and proposed that light and heatwere varieties of the same substance. In
the 5th century AD, the Buddhist atomist philosopher Dignāga proposed atoms to
be point-sized, durationless, and made of energy. They denied the existence of
substantial matter and proposed that movement consisted of momentary flashes of
a stream of energy.
The theory of temporal finitism was inspired by the doctrine of
Creation shared by the three Abrahamic religions: Judaism, Christianity and Islam. The Christian philosopher, John Philoponus,
presented the philosophical arguments against the ancient Greek notion of an
infinite past and future. Philoponus' arguments against an infinite past were
used by the early Muslim philosopher, Al-Kindi (Alkindus); the Jewish philosopher, Saadia Gaon (Saadia ben Joseph); and the Muslim theologian, Al-Ghazali (Algazel). Borrowing from Aristotle's Physics and Metaphysics,
they employed two logical arguments against an infinite past, the first being
the "argument from the impossibility of the existence of an actual
infinite", which states:
"An actual infinite cannot
exist."
"An infinite temporal regress of
events is an actual infinite."
"An infinite temporal regress of
events cannot exist."
The second argument, the "argument
from the impossibility of completing an actual infinite by successive
addition", states:
"An actual infinite cannot be
completed by successive addition."
"The temporal series of past
events has been completed by successive addition."
"The temporal series of past
events cannot be an actual infinite."
Both arguments were adopted by
Christian philosophers and theologians, and the second argument in particular
became more famous after it was adopted by Immanuel Kant in his thesis of the first antinomy concerning time.
Astronomical
models
Theories of an impersonal universe
governed by physical laws were first proposed by the Greeks and Indians. Over
the centuries, improvements in astronomical observations and theories of motion
and gravitation led to ever more accurate descriptions of the universe.
Later Greek philosophers, observing the motions of
the heavenly bodies, were concerned with developing models of the universe
based more profoundly on empirical evidence.
The first coherent model was proposed
by Eudoxus of Cnidos.
According to Aristotle's physical interpretation of the model, celestial spheres eternally rotate with uniform motion around
a stationary Earth. Normal matter, is entirely contained within the terrestrial sphere.
This model was also refined by Callippus and after concentric spheres were
abandoned, it was brought into nearly perfect agreement with astronomical
observations by Ptolemy. The
success of such a model is largely due to the mathematical fact that any
function (such as the position of a planet) can be decomposed into a set of
circular functions (the Fourier modes).
Other Greek scientists, such as the Pythagorean philosopher Philolaus postulated that at the center of the
universe was a "central fire" around which the Earth, Sun, Moon and Planets revolved in uniform circular motion. The Greek astronomer Aristarchus of Samos was
the first known individual to propose a heliocentric model of the universe. Though the
original text has been lost, a reference in Archimedes' book The Sand Reckoner
describes Aristarchus' heliocentric theory. Archimedes wrote: (translated into English)
You King Gelon are aware the 'universe'
is the name given by most astronomers to the sphere the center of which is the
center of the Earth, while its radius is equal to the straight line between the
center of the Sun and the center of the Earth. This is the common account as
you have heard from astronomers. But Aristarchus has brought out a book
consisting of certain hypotheses, wherein it appears, as a consequence of the
assumptions made, that the universe is many times greater than the 'universe'
just mentioned. His hypotheses are that the fixed stars and the Sun remain
unmoved, that the Earth revolves about the Sun on the circumference of a
circle, the Sun lying in the middle of the orbit, and that the sphere of fixed
stars, situated about the same center as the Sun, is so great that the circle
in which he supposes the Earth to revolve bears such a proportion to the
distance of the fixed stars as the center of the sphere bears to its surface.
Aristarchus thus believed the stars to
be very far away, and saw this as the reason why there was no visible parallax,
that is, an observed movement of the stars relative to each other as the Earth
moved around the Sun. The stars are in fact much farther away than the distance
that was generally assumed in ancient times, which is why stellar parallax is
only detectable with telescopes. The geocentric model, consistent with
planetary parallax, was assumed to be an explanation for the unobservability of
the parallel phenomenon, stellar parallax. The rejection of the heliocentric
view was apparently quite strong, as the following passage from Plutarch
suggests (On the Apparent Face in the Orb of the Moon):
Cleanthes [a contemporary of Aristarchus and
head of the Stoics] thought it was the duty of the Greeks to indict Aristarchus
of Samos on the charge of impiety for putting in motion the Hearth of the universe
[i.e. the earth],…supposing the heaven to remain at rest and the earth to
revolve in an oblique circle, while it rotates, at the same time, about its own
axis.
The only other astronomer from
antiquity known by name who supported Aristarchus' heliocentric model was Seleucus of Seleucia, a Hellenistic astronomer who
lived a century after Aristarchus. According to Plutarch, Seleucus
was the first to prove the heliocentric system through reasoning, but it
is not known what arguments he used. Seleucus' arguments for a heliocentric
theory were probably related to the phenomenon of tides. According to Strabo ,
Seleucus was the first to state that the tides are
due to the attraction of the Moon, and that the height of the tides depends on
the Moon's position relative to the Sun Alternatively, he may have proved the
heliocentric theory by determining the constants of a geometric model for the heliocentric theory and
by developing methods to compute planetary positions using this model, like
what Nicolaus Copernicus later did in the 16th century. During the Middle Ages,
heliocentric models may have also been proposed by the Indian astronomer, Aryabhata, and by
thePersian astronomers, Albumasar and Al-Sijzi.
Model of the Copernican universe byThomas Digges in 1576, with the amendment that the
stars are no longer confined to a sphere, but spread uniformly throughout the
space surrounding the planets.
The Aristotelian model was accepted in
the Western world for roughly two millennia, until
Copernicus revived Aristarchus' theory that the astronomical data could be
explained more plausibly if the earth rotated
on its axis and if the sun were
placed at the center of the universe.
In the center rests the sun. For who would place this lamp
of a very beautiful temple in another or better place than this wherefrom it
can illuminate everything at the same time?
Nicolaus Copernicus, in Chapter 10, Book 1
of De Revolutionibus Orbium Coelestrum (1543)
As noted by Copernicus himself, the
suggestion that the Earth rotates was very old, dating at least to Philolaus (c.450 BC), Heraclides Ponticus (c.350 BC) and Ecphantus the Pythagorean. Roughly a century before
Copernicus, Christian scholar Nicholas of Cusaalso
proposed that the Earth rotates on its axis in his book, On Learned Ignorance (1440). Aryabhata
(476–550), Brahmagupta (598–668), Albumasar and Al-Sijzi, also
proposed that the Earth rotates on its axis. The first empirical evidence for
the Earth's rotation on its axis, using the phenomenon of comets, was given by Tusi(1201–1274) and Ali Qushji (1403–1474).
This cosmology was accepted by Isaac Newton, Christiaan Huygens and
later scientists. Edmund Halley (1720) and Jean-Philippe de Cheseaux (1744)
noted independently that the assumption of an infinite space filled uniformly
with stars would lead to the prediction that the nighttime sky would be as
bright as the sun itself; this became known as Olbers' paradox in the 19th century. Newton
The modern era of physical cosmology began
in 1917, when Albert Einstein first applied his general theory of
relativity to model the structure and dynamics of the universe.
The modern era of cosmology began with Albert Einstein's 1915 general theory of relativity, which made it possible to
quantitatively predict the origin, evolution, and conclusion of the universe as
a whole. Most modern, accepted theories of cosmology are based on general
relativity and, more specifically, the predicted Big Bang; however,
still more careful measurements are required to determine which theory is
correct.
Theoretical models
.jpg)
High-precision test
of general relativity by the Cassini space probe (artist's impression): radio signals sent between the Earth and the
probe (green wave) aredelayed by
the warping of space and time(blue
lines) due to the Sun's mass.
Of the four fundamental interactions, gravitation is dominant at cosmological length
scales; that is, the other three forces play a negligible role in determining
structures at the level of planetary systems, galaxies and larger-scale
structures. Since all matter and energy gravitate, gravity's effects are
cumulative; by contrast, the effects of positive and negative charges tend to
cancel one another, making electromagnetism relatively insignificant on
cosmological length scales. The remaining two interactions, the weak and strong nuclear forces, decline very rapidly with distance;
their effects are confined mainly to sub-atomic length scales.
General
theory of relativity
Given gravitation's predominance in
shaping cosmological structures, accurate predictions of the universe's past
and future require an accurate theory of gravitation. The best theory available
is Albert Einstein's
general theory of relativity, which has passed all experimental tests hitherto.
However, since rigorous experiments have not been carried out on cosmological
length scales, general relativity could conceivably be inaccurate.
Nevertheless, its cosmological predictions appear to be consistent with observations,
so there is no compelling reason to adopt another theory.
General relativity provides a set of
ten nonlinear partial differential equations for the spacetime metric (Einstein's field equations) that must be solved from the
distribution of mass-energy and momentum throughout the universe. Since these
are unknown in exact detail, cosmological models have been based on the cosmological principle, which states that the universe is
homogeneous and isotropic. In effect, this principle asserts that the
gravitational effects of the various galaxies making up the universe are
equivalent to those of a fine dust distributed uniformly through out the
universe with the same average density. The assumption of a uniform dust makes
it easy to solve Einstein's field equations and predict the past and future of
the universe on cosmological time scales.
Einstein's field equations include a cosmological constant (Λ),
that corresponds to an energy density of empty space. Depending on its sign,
the cosmological constant can either slow (negative Λ) or accelerate (positive Λ) the expansion of the universe. Although many scientists, including
Einstein, had speculated that Λ was zero, recent astronomical
observations of type Ia supernovae have detected a large amount of "dark energy"
that is accelerating the universe's expansion. Preliminary studies suggest that
this dark energy corresponds to a positive Λ,
although alternative theories cannot be ruled out as yet. Russian physicist Zel'dovich suggested
that Λ is a measure of the zero-point energy associated with virtual particles of quantum field theory, a pervasive vacuum energy that exists everywhere, even in empty
space. Evidence for such zero-point energy is observed in the Casimir effect.
Special
relativity and space-time
The universe has at least three spatial and
one temporal (time) dimension. It
was long thought that the spatial and temporal dimensions were different in
nature and independent of one another. However, according to the special theory of relativity, spatial and temporal separations
are interconvertible (within limits) by changing one's motion.
To understand this interconversion, it
is helpful to consider the analogous interconversion of spatial separations
along the three spatial dimensions. Consider the two endpoints of a rod of
length L. The length can
be determined from the differences in the three coordinates Δx, Δy and Δz of
the two endpoints in a given reference frame using the Pythagorean theorem. In a rotated reference frame, the
coordinate differences differ, but they give the same length.
Thus, the coordinates differences (Δx,
Δy, Δz) and (Δξ, Δη, Δζ) are not intrinsic to the rod, but merely reflect the
reference frame used to describe it; by contrast, the length L is an intrinsic property of the rod.
The coordinate differences can be changed without affecting the rod, by
rotating one's reference frame.
The analogy in spacetime is called the interval between two
events; an event is defined as a point in spacetime, a specific position in
space and a specific moment in time. The spacetime interval between two events
is given by where c is the speed of light. According to special relativity, one can change a spatial and time
separation (L1, Δt1) into another (L2,
Δt2) by changing one's reference frame, as long as the change
maintains the spacetime interval s.
Such a change in reference frame corresponds to changing one's motion; in a
moving frame, lengths and times are different from their counterparts in a
stationary reference frame. The precise manner in which the coordinate and time
differences change with motion is described by the Lorentz transformation.
Solving
Einstein's field equations
The distances between the spinning
galaxies increase with time, but the distances between the stars within each
galaxy stay roughly the same, due to their gravitational interactions. This
animation illustrates a closed Friedmann universe with zero cosmological constant Λ;
such a universe oscillates between a Big Bang and a Big Crunch.
In non-Cartesian (non-square) or curved
coordinate systems, the Pythagorean theorem holds only on infinitesimal length
scales and must be augmented with a more general metric tensor gμν, which can vary
from place to place and which describes the local geometry in the particular
coordinate system. However, assuming the cosmological principle that
the universe is homogeneous and isotropic everywhere, every point in space is
like every other point; hence, the metric tensor must be the same everywhere.
That leads to a single form for the metric tensor, called the Friedmann–Lemaître–Robertson–Walker metric
where (r, θ, φ) correspond to a spherical coordinate system. This metric has only
two undetermined parameters: an overall length scale R that can vary with time, and a
curvature index k that can be only 0, 1 or -1,
corresponding to flat Euclidean geometry, or spaces of positive or negative curvature. In
cosmology, solving for the history of the universe is done by calculating R as a function of time, given k and the value of the cosmological constant Λ,
which is a (small) parameter in Einstein's field equations. The equation
describing how R varies with time is known as the Friedmann equation, after its inventor, Alexander Friedmann.
The solutions for R(t) depend on k and Λ,
but some qualitative features of such solutions are general. First and most
importantly, the length scale R of the universe can remain constant only if the universe is perfectly isotropic
with positive curvature (k=1) and has one precise value of density
everywhere, as first noted by Albert Einstein.
However, this equilibrium is unstable and since the universe is known to be
inhomogeneous on smaller scales, R must change, according to general relativity. When R changes, all the spatial distances in
the universe change in tandem; there is an overall expansion or contraction of
space itself. This accounts for the observation that galaxies appear to be
flying apart; the space between them is stretching. The stretching of space
also accounts for the apparent paradox that two galaxies can be 40 billion
light years apart, although they started from the same point 13.7 billion years
ago and never moved faster than the speed of light.
Second, all solutions suggest that
there was a gravitational singularity in
the past, when R goes to zero and matter and energy
became infinitely dense. It may seem that this conclusion is uncertain since it
is based on the questionable assumptions of perfect homogeneity and isotropy
(the cosmological principle) and that only the gravitational interaction is
significant. However, the Penrose–Hawking singularity theorems show that a singularity should exist
for very general conditions. Hence, according to Einstein's field equations, R grew rapidly from an unimaginably hot,
dense state that existed immediately following this singularity (when R had a small, finite value); this is
the essence of the Big Bang model of the universe. A common
misconception is that the Big Bang model predicts that matter and energy
exploded from a single point in space and time; that is false. Rather, space
itself was created in the Big Bang and imbued with a fixed amount of energy and
matter distributed uniformly throughout; as space expands (i.e., as R(t)increases), the density of
that matter and energy decreases.
“Space has no boundary - that is empirically more
certain than any external observation. However, that does not imply that space
is infinite...(translated, original German)- Bernhard
Riemann (Habilitationsvortrag,
1854)”
Third, the curvature index k determines the sign of the mean
spatial curvature of spacetime averaged over length scales greater
than a billion light years. If k=1, the curvature is positive
and the universe has a finite volume. Such universes are often visualized as a three-dimensional sphere S3 embedded in a four-dimensional space.
Conversely, if k is zero or negative, the universe may have infinite volume, depending on its
overall topology. It may
seem counter-intuitive that an infinite and yet infinitely dense universe could
be created in a single instant at the Big Bang when R=0, but exactly that is
predicted mathematically when k does not equal 1. For comparison, an
infinite plane has zero curvature but infinite area, whereas an infinite
cylinder is finite in one direction and a torus is
finite in both. A toroidal universe could behave like a normal universe with periodic boundary conditions, as seen in "wrap-around" video games such as Asteroids; a traveler crossing an outer
"boundary" of space going outwards would reappear instantly at another
point on the boundary moving inwards.
The ultimate fate of the universe is still unknown, because it depends
critically on the curvature index k and the cosmological constant Λ. If the universe is
sufficiently dense, k equals +1, meaning that its average
curvature throughout is positive and the universe will eventually recollapse in
a Big Crunch,
possibly starting a new universe in a Big Bounce.
Conversely, if the universe is insufficiently dense, k equals 0 or −1 and the universe will
expand forever, cooling off and eventually becoming inhospitable for all life,
as the stars die and all matter coalesces into black holes (the Big Freeze and
the heat death of the universe). As noted above,
recent data suggests that the expansion speed of the universe is not decreasing
as originally expected, but increasing; if this continues indefinitely, the
universe will eventually rip itself to shreds (the Big Rip).
Experimentally, the universe has an overall density that is very close to the
critical value between recollapse and eternal expansion; more careful
astronomical observations are needed to resolve the question.
Big
Bang model
Big Bang model
The prevailing Big Bang model accounts
for many of the experimental observations described above, such as the
correlation of distance and redshift of galaxies, the universal ratio of
hydrogen:helium atoms, and the ubiquitous, isotropic microwave radiation
background. As noted above, the redshift arises from the metric expansion of space; as the space itself expands, the
wavelength of aphoton traveling through space likewise
increases, decreasing its energy. The longer a photon has been traveling, the
more expansion it has undergone; hence, older photons from more distant
galaxies are the most red-shifted. Determining the correlation between distance
and redshift is an important problem in experimental physical cosmology.
Other experimental observations can be
explained by combining the overall expansion of space with nuclear and atomic physics. As
the universe expands, the energy density of the electromagnetic radiation decreases
more quickly than does that of matter, since the energy of a photon
decreases with its wavelength. Thus, although the energy density of the
universe is now dominated by matter, it was once dominated by radiation;
poetically speaking, all was light. As the universe expanded, its
energy density decreased and it became cooler; as it did so, the elementary particles of
matter could associate stably into ever larger combinations. Thus, in the early
part of the matter-dominated era, stable protons and neutrons formed, which then associated into atomic nuclei. At
this stage, the matter in the universe was mainly a hot, dense plasma of negative electrons, neutral neutrinos and positive nuclei. Nuclear reactions among the nuclei led to the present
abundances of the lighter nuclei, particularly hydrogen, deuterium, and helium. Eventually, the electrons and
nuclei combined to form stable atoms, which are transparent to most wavelengths
of radiation; at this point, the radiation decoupled from the matter, forming
the ubiquitous, isotropic background of microwave radiation observed today.
Other observations are not answered
definitively by known physics. According to the prevailing theory, a slight
imbalance of matter over antimatter was present in the universe's
creation, or developed very shortly thereafter, possibly due to the CP violation that has been observed by particle physicists.
Although the matter and antimatter mostly annihilated one another, producing photons, a small residue of matter
survived, giving the present matter-dominated universe. Several lines of
evidence also suggest that a rapid cosmic inflation of the universe occurred very early in
its history (roughly 10−35 seconds
after its creation). Recent observations also suggest that the cosmological constant (Λ)
is not zero and that the net mass-energy content of the universe is dominated
by a dark energyand dark matter that have not been characterized
scientifically. They differ in their gravitational effects. Dark matter
gravitates as ordinary matter does, and thus slows the expansion of the
universe; by contrast, dark energy serves to accelerate the universe's
expansion.
Size, age, contents, structure, and laws
The universe is immensely large and
possibly infinite in volume. The region visible from Earth (the observable universe) is a sphere with a radius of about 46
billion light years, based on where the expansion of space has taken the most distant objects observed. For
comparison, the diameter of a typical galaxy is
only 30,000 light-years, and the typical distance between two neighboring
galaxies is only 3 million light-years. As an
example, our Milky Way Galaxy is roughly 100,000 light years
in diameter, and our nearest
sister galaxy, the Andromeda Galaxy,
is located roughly 2.5 million light years away. There are probably more than 100
billion (1011) galaxies in
the observable universe. Typical
galaxies range from dwarfs with as few as ten million (107) stars up
to giants with one trillion (1012) stars, all orbiting
the galaxy's center of mass. A 2010 study by astronomers estimated that the
observable universe contains 300 sextillion (3×1023) stars.
The observable matter is spread
homogeneously (uniformly) throughout the universe, when averaged over
distances longer than 300 million light-years. However, on smaller length-scales,
matter is observed to form "clumps", i.e., to cluster hierarchically;
many atoms are
condensed into stars, most stars into galaxies, most
galaxies into clusters, superclusters and, finally, thel argest-scale structures such as the Great Wall of galaxies. The observable matter of the universe
is also spread isotropically,
meaning that no direction of observation seems different from any other; each
region of the sky has roughly the same content.[28] The universe is also bathed in a
highlyisotropic microwave radiation that
corresponds to athermal equilibrium blackbody spectrum of
roughly 2.725 kelvin. The hypothesis that the
large-scale universe is homogeneous and isotropic is known as the cosmological principle, which is supported by astronomical
observations.
The present overall density of the universe is very low, roughly
9.9 × 10−30 grams per
cubic centimetre. This mass-energy appears to consist of 73% dark energy, 23% cold dark matter and 4% ordinary matter.
Thus the density of atoms is on the order of a single hydrogen atom for every
four cubic meters of volume. The properties of dark energy and dark matter are
largely unknown. Dark matter gravitates as ordinary matter, and thus works to
slow the expansion of the universe; by contrast, dark energy accelerates its expansion.
The most precise estimate of the universe's age is
13.72 ±0.12 billion years old, based on observations of the cosmic microwave background radiation. Independent estimates (based on
measurements such as radioactive dating) agree at 13–15 billion years. The universe has not been the same at
all times in its history; for example, the relative populations of quasars and
galaxies have changed and space itself
appears to have expanded. This expansion accounts for how Earth-bound scientists
can observe the light from a galaxy 30 billion light years away, even if that
light has traveled for only 13 billion years; the very space between them has
expanded. This expansion is consistent with the observation that the light from
distant galaxies has been redshifted; the photonsemitted have been stretched to
longer wavelengths and lower frequency during their journey. The rate of this
spatial expansion isaccelerating, based on studies of Type Ia supernovae and corroborated by other data.
The relative fractions of different chemical elements - particularly the lightest atoms such as hydrogen, deuterium and helium - seem to be identical
throughout the universe and throughout its observable history. The universe
seems to have much more matterthan antimatter, an
asymmetry possibly related to the observations of CP violation. The universe appears to have no net electric charge,
and therefore gravity appears to be the dominant interaction
on cosmological length scales. The universe also appears to have neither net momentum nor angular momentum.
The absence of net charge and momentum would follow from accepted physical laws
(Gauss's law and the non-divergence of the stress-energy-momentum pseudotensor,
respectively), if the universe were finite.
The elementary particles from
which the universe is constructed. Six leptons and
six quarks comprise
most of thematter; for example,
the protons and neutrons of atomic nuclei are composed of quarks, and the
ubiquitous electron is a lepton. These particles interact
via the gauge bosonsshown
in the middle row, each corresponding to a particular type of gauge symmetry. The Higgs boson (as yet unobserved) is believed to
confer mass on
the particles with which it is connected. The graviton, a
supposed gauge boson for gravity, is not
shown.
The universe appears to have a smooth space-time continuum consisting
of three spatial dimensions and one temporal (time) dimension. On the average, space is observed to be very nearly flat
(close to zero curvature), meaning
that Euclidean geometry is
experimentally true with high accuracy throughout most of the Universe. Spacetime
also appears to have asimply connected topology, at least
on the length-scale of the observable universe. However, present observations
cannot exclude the possibilities that the universe has more dimensions and that
its spacetime may have a multiply connected global topology, in analogy with
the cylindrical or toroidaltopologies of two-dimensional spaces.
The universe appears to behave in a
manner that regularly follows a set ofphysical laws and physical constants.
According to the prevailingStandard
Model of physics, all
matter is composed of three generations of leptons and quarks, both of which are fermions. These elementary particles interact via at most three fundamental interactions: the electroweak interaction
which includes electromagnetism and the weak nuclear force; the strong nuclear force described
by quantum chromodynamics; and gravity, which is
best described at present by general relativity. The first two interactions can be
described by renormalized quantum field theory, and are mediated by gauge bosons that correspond to a particular type
of gauge symmetry. A
renormalized quantum field theory of general relativity has not yet been
achieved, although various forms of string theory seem promising. The theory of special relativity is
believed to hold throughout the universe, provided that the spatial and
temporal length scales are sufficiently short; otherwise, the more general
theory of general relativity must be applied. There is no explanation for the
particular values that physical constants appear to have throughout our
universe, such as Planck's constant h or the gravitational constant G.
Several conservation laws have been identified, such as the conservation of charge, momentum, angular momentum and energy; in many cases, these conservation laws can be related
to symmetries or mathematical identities.
Fine
tuning
It appears that many of the properties
of the universe have special values in the sense that a universe where these
properties only differ slightly would not be able to support intelligent life. Not
all scientists agree that this fine-tuning exists. In particular, it is not known under
what conditions intelligent life could form and what form or shape that would
take. A relevant observation in this discussion is that for an observer to
exist to observe fine-tuning, the universe must be able to support intelligent
life. As such theconditional probability of
observing a universe that is fine-tuned to support intelligent life is 1. This
observation is known as theanthropic principle and
is particularly relevant if the creation of the universe was probabilistic or if
multiple universes with a variety of properties exist.
Multiverse
theory
Some speculative theories have proposed
that this universe is but one of a set of disconnected universes,
collectively denoted as the multiverse,
challenging or enhancing more limited definitions of the universe. Scientific multiverse theories are
distinct from concepts such as alternate planes of consciousness and simulated reality,
although the idea of a larger universe is not new; for example, Bishop Étienne Tempier of Paris ruled in 1277 that God could
create as many universes as he saw fit, a question that was being hotly debated
by the French theologians.
Max Tegmark developed a four part classification
scheme for the
different types of multiverses that scientists have suggested in various
problem domains. An example of such a theory is the chaotic inflation model
of the early universe. Another is the many-worlds interpretation of quantum mechanics. Parallel worlds
are generated in a manner similar to quantum superposition and decoherence, with
all states of the wave function being
realized in separate worlds. Effectively, the multiverse evolves as a universal wavefunction. If the big bang that created our
multiverse created an ensemble of multiverses, the wave function of the
ensemble would be entangled in this sense.
The least controversial category of
multiverse in Tegmark's scheme is Level I,
which describes distant space-time events "in our own universe". If
space is infinite, or sufficiently large and uniform, identical instances of
the history of Earth's entire Hubble volume occur every so often, simply by
chance. Tegmark calculated our nearest so-called doppelgänger, is 1010115 meters away from us (a double exponential function larger than a googolplex). In principle, it would be impossible
to scientifically verify an identical Hubble volume. However, it does follow as
a fairly straightforward consequence from otherwise unrelated scientific
observations and theories. Tegmark suggests that statistical analysis
exploiting the anthropic principle provides
an opportunity to test multiverse theories in some cases. Generally, science
would consider a multiverse theory that posits neither a common point of
causation, nor the possibility of interaction between universes, to be an idle
speculation.
Shape of the universe
The shape or geometry of the universe includes both local geometry in
the observable universe and global geometry, which we may or may not be able to measure.
Shape can refer to curvature and topology. More
formally, the subject in practice investigates which 3-manifold corresponds to the spatial section in comoving coordinates of
the four-dimensional space-time of the universe. Cosmologists normally
work with a given space-like slice of spacetime called the comoving coordinates.
In terms of observation, the section of spacetime that can be observed is the
backward light cone (points within the cosmic light horizon, given time to reach a given observer).
If the observable universe is smaller than the entire universe (in some models
it is many orders of magnitude smaller), one cannot determine the global
structure by observation: one is limited to a small patch.
Among the Friedmann–Lemaître–Robertson–Walker (FLRW) models, the presently most
popular shape of the Universe found to fit observational data according to
cosmologists is the infinite flat model, while other FLRW models include the Poincaré
dodecahedral space and the Picard horn. The
data fit by these FLRW models of space especially include the Wilkinson Microwave Anisotropy Probe (WMAP) maps of cosmic background
radiation. NASA released the first WMAP cosmic background radiation data in
February 2003.
In 2009 the Planck observatory was
launched to observe the microwave background at higher resolution than WMAP,
possibly providing more information on the shape of the Universe. The data
should be released in late 2012.
The shape
of the universe is a matter
of debate in physical cosmology over the local and global
geometry of the universe which considers both curvature andtopology,
though, strictly speaking, it goes beyond both. In practice, more formally, the
debate seeks a 3-manifold that corresponds to the spatial
section (in comoving coordinates) of the 4-dimensional space-time of the universe.
The Wilkinson Microwave Anisotropy
Probe (WMAP) has confirmed
that theobservable universe is flat with only a 0.5% margin of
error.Within the Friedmann-Lemaître-Robertson-Walker (FLRW) model, the presently most
popular shape of the Universe found to fit observational data according to
cosmologists is the infinite flat model, while other FLRW models that fit the
data include the Poincaré dodecahedral space and the Picard horn.
Consideration of the shape of the
universe can be split into two; local geometry, which relates especially to
the curvature of the universe, especially in the observable universe, and global geometry, which relates to the
topology of the universe as a whole, measurement of which may not be within our
ability. If the observable universe encompasses the entire universe, we may
determine the global structure by observation. If the observable universe is
smaller than the entire universe (in some models it is many orders of magnitude
smaller or even infinitesimal), observation is limited to a part of the whole.
Possibly the universe is small in some dimensions and not in others (like a
cylinder). If a small closed loop, one would see multiple images of an object
in the sky, although not necessarily of the same age.
Cosmologists normally work with a given space-like slice of spacetime called thecomoving
coordinates, the existence of a preferred set of which is possible and
widely accepted in present-day physical cosmology. The section of spacetime
that can be observed is the backward light cone (all points within the cosmic light horizon, given time to reach a
given observer), while the related term Hubble
volume can be used to
describe either the past light cone or comoving space up to the surface of last
scattering. To speak of "the shape of the universe (at a point in
time)" is ontologically naive from the point of view of special relativity alone: due to the relativity of simultaneity we cannot speak of different points in
space as being "at the same point in time" nor, therefore, of
"the shape of the universe at a point in time".
Local geometry (spatial curvature)
The local
geometry is the curvature
describing any arbitrary point in the observable universe (averaged on a
sufficiently large scale). Many astronomical observations, such as those from supernovae and the Cosmic Microwave Background (CMB) radiation,
show the observable universe to be very close to homogeneous and isotropic and
infer it to be accelerating.
FLRW
model of the universe
In General Relativity, this is modelled by the Friedmann–Lemaître–Robertson–Walker
(FLRW) model. This model, which can be represented by the Friedmann equations, provides a curvature
(often referred to as geometry)
of the universe based on the mathematics of fluid
dynamics, i.e. it models the matter within the universe as a perfect fluid.
Although stars and structures of mass can be introduced into an "almost
FLRW" model, a strictly FLRW model is used to approximate the local
geometry of the observable universe.
Another way of saying this is that if
all forms of dark energy are ignored, then the curvature of the
universe can be determined by measuring the average density of matter within
it, assuming that all matter is evenly distributed (rather than the distortions
caused by 'dense' objects such as galaxies).
This assumption is justified by the
observations that, while the universe is "weakly" inhomogeneous and anisotropic (see the large-scale structure of the cosmos),
it is on average homogeneous and isotropic.
The homogeneous and isotropic universe
allows for a spatial geometry with a constant curvature. One aspect of local geometry
to emerge from General Relativity and the FLRW model is that the density
parameter, Omega (Ω), is related to the curvature of space. Omega is the
average density of the universe divided by the critical energy density, i.e.
that required for the universe to be flat (zero curvature).
The curvature of space is a
mathematical description of whether or not the Pythagorean theorem is valid for spatial coordinates. In
the latter case, it provides an alternative formula for expressing local
relationships between distances:
-If the curvature is zero, then Ω = 1,
and the Pythagorean theorem is correct;
-If Ω > 1, there is positive
curvature; and
-if Ω < 1 there is negative
curvature.
In the last two cases, the Pythagorean
theorem is invalid (but discrepancies are only detectable in triangles whose
sides' lengths are of cosmological
scale).
If you measure the circumferences of
circles of steadily larger diameters and divide the former by the latter, all
three geometries give the value π for small enough diameters but the ratio
departs from π for larger diameters unless Ω = 1:
For Ω > 1 (the sphere, see diagram)
the ratio falls below π: indeed, a great circle on a sphere has circumference
only twice its diameter.
For Ω < 1 the ratio rises above π.
Astronomical measurements of both
matter-energy density of the universe and spacetime intervals using supernova
events constrain the spatial curvature to be very close to zero, although they
do not constrain its sign. This means that although the local geometries of
spacetime are generated by the theory of relativity based on spacetime intervals, we can approximate 3-space by the familiarEuclidean geometry.
Possible
local geometries
There are three categories for the
possible spatial geometries of constant curvature, depending on the sign of the
curvature. If the curvature is exactly zero, then the local geometry is flat;
if it is positive, then the local geometry is spherical, and if it is negative
then the local geometry is hyperbolic.
The geometry of the universe is usually
represented in the system of comoving coordinates, according to which the
expansion of the universe can be ignored. Comoving coordinates form a single frame of reference according to which the universe has a
static geometry of three spatial dimensions.
Under the assumption that the universe
is homogeneous and isotropic,
the curvature of the observable universe, or the local geometry, is described
by one of the three "primitive" geometries (in mathematics these are
called the model geometries):
-3-dimensional Flat Euclidean geometry, generally notated as E3
-3-dimensional spherical geometry with a small curvature, often notated
as S3
-3-dimensional hyperbolic geometry with a small curvature
Even if the universe is not exactly
spatially flat, the spatial curvature is close enough to zero to place the radius at approximately the horizon of the
observable universe or beyond.
Global geometry
Global geometry covers
the geometry, in particular the topology, of
the whole universe - both the observable universe and beyond. While the local
geometry does not determine the global geometry completely, it does limit the
possibilities, particularly a geometry of a constant curvature. For this
discussion, the universe is taken to be a geodesic
manifold, free of topological defects; relaxing either of these
complicates the analysis considerably.
In general, local to global theorems in Riemannian geometry relate the local geometry to the
global geometry. If the local geometry has constant curvature, the global
geometry is very constrained, as described in Thurston geometries.
A global geometry is also called a
topology, as a global geometry is a local geometry plus a topology, but this
terminology is misleading because a topology does not give a global geometry:
for instance, Euclidean 3-space and hyperbolic 3-space have the same topology but different
global geometries.
Two strongly overlapping investigations
within the study of global geometry are whether the universe:
-Is infinite in extent or, more generally, is a compact
space;
-Has a simply or non-simply connected topology.
Detection
For a flat spatial geometry, the scale
of any properties of the topology is arbitrary and may or may not be directly
detectable. For spherical and hyperbolic spatial geometries, the curvature
gives a scale (either by using the radius of curvature or its inverse), a fact noted by Carl Friedrich Gauss in an 1824 letter to Franz
Taurinus.
The probability of detection of the
topology by direct observation depends on the spatial curvature: a small
curvature of the local geometry, with a corresponding radius of curvature
greater than the observable horizon, makes the topology difficult or impossible
to detect if the curvature is hyperbolic. A spherical geometry with a small
curvature (large radius of curvature) does not make detection difficult.
Analysis of data from WMAP implies that on the scale to the
surface of last scattering, the density parameter of the Universe is within
about 2% of the value representing spatial flatness.
Compactness
of the global shape
Formally, the question of whether the
universe is infinite or finite is whether it is an unbounded or bounded metric space. An infinite universe
(unbounded metric space) means that there are points arbitrarily far apart: for any distance d, there are points that are of
a distance at least d apart. A finite universe is a bounded
metric space, where there is some distance d such that all points are within
distance d of each other. The smallest such d is called the diameter of the universe, in which case the
universe has a well-defined "volume" or "scale."
A compact
space is a stronger
condition: in the context of Riemannian manifolds, it is equivalent to being
bounded and geodesically complete. If we assume that the
universe is geodesically complete, then boundedness and compactness are
equivalent (by the Hopf–Rinow theorem), and they are thus used
interchangeably, if completeness is understood.
If the spatial geometry is spherical, the topology is compact. For a flat
or a hyperbolic spatial geometry, the topology can be either compact or
infinite: for example, Euclidean space is flat and infinite, but the torus is flat and compact.
In cosmological models (geometric
3-manifolds), a compact space is either a spherical geometry, or has infinite fundamental
group(and thus is called "multiply connected", or more strictly non-simply
connected), by general results on geometric 3-manifolds.
Compact geometries can be visualized by
means of closed geodesics: on a
sphere, a straight line, when extended far enough in the same direction, will
reach the starting point.
Note that on a compact geometry, not
every straight line comes back to its starting point. For instance, a line of
irrational slope on a torus never returns to its origin. Conversely, a
non-compact geometry can have closed geodesics: on an infinite cylinder, which
is a non-compact flat geometry, a loop around the cylinder is a closed
geodesic.
If the geometry of the universe is not
compact, then it is infinite in extent with infinite paths of constant
direction that, generally do not return and the space has no definable volume,
such as the Euclidean
plane.
Open
or closed
When cosmologists speak of the universe
as being "open" or "closed", they most commonly are referring
to whether the curvature is negative or positive. These meanings of open and
closed, and the mathematical meanings, give rise to ambiguity because the terms
can also refer to a closed
manifold i.e. compact without
boundary, not to be confused with a closed set.
With the former definition, an "open universe" may either be an open
manifold, i.e. one that is not compact and without boundary,[8] or a closed manifold, while a
"closed universe" is necessarily a closed manifold.
In the Friedmann-Lemaître-Robertson-Walker (FLRW) model the universe is
considered to be without boundaries, in which case "compact universe"
could describe a universe that is a closed manifold.
The latest research shows that even the
most powerful future experiments (like SKA, Planck..) will not be able to distinguish
between flat, open and closed universe if the true value of cosmological
curvature parameter is smaller than 10−4. If the true value of the
cosmological curvature parameter is larger than 10−3 we will be able to distinguish between
these three models even now.
Flat
universe
In a flat universe, all of the local
curvature and local geometry is flat. It is generally assumed that it is
described by a Euclidean
space, although there are some spatial geometries that are flat and bounded
in one or more directions (like the surface of a cylinder, for example).
The alternative two-dimensional spaces
with a Euclidean metric are the cylinder and
the Möbius
strip, which are bounded in one direction but not the other, and the torus and Klein
bottle, which are compact.
In three dimensions, there are 10
finite closed flat 3-manifolds, of which 6 are orientable and 4 are
non-orientable. The most familiar is the 3-Torus.
See the doughnut theory of the universe.
In the absence of dark energy, a flat
universe expands forever but at a continually decelerating rate, with expansion
asymptotically approaching some fixed rate. With dark energy, the expansion
rate of the universe initially slows down, due to the effect of gravity, but
eventually increases. The ultimate fate of the universe is the same as that of an open
universe.
A flat universe can have zero total energy and thus can come from nothing.
Spherical
universe
A positively curved universe is
described by spherical geometry, and can be thought of as a
three-dimensional hypersphere,
or some other spherical 3-manifold (such as the Poincaré dodecahedral space), all of
which are quotients of the 3-sphere.
Analysis of data from the Wilkinson Microwave Anisotropy
Probe (WMAP) looks for
multiple "back-to-back" images of the distant universe in the cosmic
microwave background radiation. It may be possible to observe multiple images
of a given object, if the light it emits has had sufficient time to make one or
more complete circuits of a bounded universe. Current results and analysis do
not rule out a bounded global geometry (i.e. a closed universe), but they do
confirm that the spatial curvature is small, just as the spatial curvature of
the surface of the Earth is small compared to a horizon of a
thousand kilometers or so. If the universe is bounded, this does not imply
anything about the sign of its curvature.
In a closed universe lacking the repulsive
effect of dark energy,
gravity eventually stops the expansion of the universe, after which it starts
to contract until all matter in the observable universe collapses to a point, a
final singularity termed the Big Crunch,
by analogy with Big Bang. However, if the universe has a large amount of dark
energy (as suggested by recent findings), then the expansion of the universe
could continue forever.
Based on analyses of the WMAP data,
cosmologists during 2004–2006 focused on the Poincaré dodecahedral space (PDS),
but horn topologies (which are hyperbolic) were also deemed compatible with the
data.
Hyperbolic
universe
A hyperbolic universe is described by hyperbolic geometry, and can be thought of
locally as a three-dimensional analog of an infinitely extended saddle shape.
There are a great variety of hyperbolic 3-manifolds, and their
classification is not completely understood. For hyperbolic local geometry,
many of the possible three-dimensional spaces are informally called horn topologies, so called
because of the shape of the pseudosphere,
a canonical model of hyperbolic geometry.
Spherical
Expanding Universe (Milne model)
-
Universe in an
expanding sphere. The galaxies
furthest away are moving fastest and hence experience length contraction and so
become smaller to an observer in the centre.
If the Universe is contained within an
ever expanding sphere (which may have started from a single point), it can
still appear infinite for all practical purposes. Because of length contraction the galaxies further away, which are
travelling away from the observer the fastest, will appear smaller. In this way
an infinite Universe fits within a finite sphere as long as the sphere is
expanding continually. The question of whether the Universe is infinite can
depend on the coordinate system used. For example, you could choose a
coordinate system in which the galaxies are equally spaced out and don't have length contraction, in which case the Universe
could be said to be infinite in size. Whichever galaxy the observer is on, the
other galaxies moving away from it will appear length contracted. An observer
can never get to the edge of the Universe if it is expanding at the speed of
light. At the edge of the sphere matter becomes infinitely dense, but because
it is moving away from the observer close to the speed of light due to time
dilation its effect on the
rest of the Universe is negligible. As the spherical Universe expands, matter
that was near the edge is now in the middle of the sphere.
Proposed
models
Various models have been proposed for
the global geometry of the universe. In addition to the primitive geometries,
these proposals include the:
-Poincaré dodecahedral space, a positively curved
space, colloquially described as "soccerball-shaped", as it is the
quotient of the 3-sphere by the binary icosahedral group, which is very
close to icosahedral symmetry, the symmetry of a soccer
ball. This was proposed by Jean-Pierre Luminet and colleagues in 2003 and an optimal
orientation on the sky for the model was estimated in 2008.
-Picard horn,
a negatively curved space, colloquially described as "funnel-shaped",
for the horn geometry.
References
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