Some verses from Qur-an, and their interpretation are incorporated into this topic,
which is taken primarily from Wikipedia, the free encyclopedia. (http://en.wikipedia.org/wiki/Inflation_(cosmology))
In physical
cosmology,
cosmic inflation, cosmological inflation or just inflation is the theorized exponential expansion of the universe at the end of the grand unification epoch, 10^{−36} seconds after the Big Bang, driven by a negative-pressure vacuum energy density.^{[1]} The term "inflation" is
also used to refer to the hypothesis that inflation occurred, to the theory of
inflation, or to the inflationary
epoch. The
inflationary hypothesis was proposed by American physicist Alan Guth in 1980.
Inflation :
(http://physics.uoregon.edu/~jimbrau/BrauImNew/Chap27/6th/27_11Figure-F.jpg)
In physical
cosmology, the inflationary epoch was the
period in the evolution of the early universe when, according to inflation theory, the universe underwent an extremely rapid
exponential expansion. This rapid
expansion increased the linear dimensions of the early universe by a factor
of at least 10^{26} (and possibly a much larger factor), and so
increased its volume by a factor of at least 10^{78}. ([1]) |
في علم الكونيات الفيزيائي ، الحقبة التضخمية هي
الفترة في تطور الكون المبكر . أثناءها
، و وفقًا لنظرية التضخم ، فقد خضع الكون لتوسع أسي سريع للغاية. أدى هذا التوسع
السريع إلى زيادة قطر الكون المبكر بمعامل لا يقل عن10^{26} (وربما أكبر بكثير) ، وبالتالي
زاد حجمه بعامل لا يقل عن 10^{78}. |
Inflation is Referred to by the Verses:
(ثُمَّ اسْتَوَى
إِلَى السَّمَاءِ وَهِيَ دُخَانٌ فَقَالَ لَهَا وَلِلْأَرْضِ ائْتِيَا طَوْعًا
أَوْ كَرْهًا قَالَتَا أَتَيْنَا طَائِعِينَ * فَقَضَاهُنَّ سَبْعَ سَمَاوَاتٍ فِي يَوْمَيْنِ) [فصّلت آية 11-12
].
Allâh says: "Moreover, He
comprehended in His design the Sama (upper part of universe), and it had
been smoke: He said to it and to Ardh (lower - interior - part of the Universe;
not earth): 'Come ye, willingly or unwillingly.' They said: 'We do come, in
willing obedience'. So He completed them as seven firmaments in two Days
(Periods) …" (Surah 41, Verses 11-12).
(وَالسَّمَاءَ بَنَيْنَاهَا
بِأَيْيدٍ وَإِنَّا لَمُوسِعُونَ _{*} وَالأرْضَ فَرَشْنَاهَا
فَنِعْمَ الْمَاهِدُونَ) ] 48-47
الذّاريات[.
" We have built The Sama - Firmament - with might, We
indeed Have vast power; to create the vastness of Space and continue to expand
it * And We have spread out Ardh - Ground; interior or lower part
of the Universe; the dark matter holding the galaxies -: How excellently We do
spread out!" (Surah No. 51, verse 47- 48).
(أَأَنْتُمْ
أَشَدُّ خَلْقًا أَمْ السَّمَاءُ بَنَاهَا _{*} رَفَعَ سَمْكَهَا
فَسَوَّاهَا)
[النّازعات 27-28]
(What!
Are ye the more difficult to create or the Samaa (Firmaments) (above)? (Allah)
hath constructed it: On high hath He
raised its canopy, and He hath given it order and perfection.) (Surah 79, Verses 27-28).
(وَالسَّمَاءَ رَفَعَهَا وَوَضَعَ
الْمِيزَانَ) (الرحمن 7)
(And
the Firmament has He raised high, and He has set up the Balance (of Justice),) (S. 55, V. 7)
- (وَإِلَى
السَّمَاءِ كَيْفَ رُفِعَتْ) سورة الغاشية آية رقم 18 .
(And at the Sama – Firmaments ; sky; galaxies -, how it is raised
high? ) (S. 88, V. 18).
وإنّ كون النظام معزول ومغلق هو بعض مما تتضمنه الآية
الكريمة: (وَالسَّمَاءِ
ذَاتِ الرَّجْعِ) (الطارق آية 11) ، على اعتبار أنّ السّماء
هنا هي البناء.
This adiabatic (closed) system is likely to
be among things indicated by the following verse:
(By the Firmament which returns ),
(Surah 86, verse 11)
As a direct consequence of this expansion, all of the
observable universe originated in a small causally
connected
region. Inflation answers the classic conundrum of the big bang cosmology: why does the universe
appear flat, homogeneous and isotropic in accordance with the cosmological principle when one would expect, on the basis of the physics of the
Big Bang, a highly curved, heterogeneous universe? Inflation also explains the
origin of the large-scale structure of the cosmos. Quantum
fluctuations
in the microscopic inflationary region, magnified to cosmic size, become the
seeds for the growth of structure in the universe (see galaxy formation and evolution and structure
formation).^{[2]}
While the detailed particle physics mechanism responsible for inflation
is not known, the basic picture makes a number of predictions that have been
confirmed by observation. Inflation is thus now considered part of the standard
hot big bang cosmology. The hypothetical particle or field thought to be responsible for
inflation is called the inflaton.
Overview
Main article: Metric expansion of space
While special
relativity
constrains objects in the universe from moving faster than the speed of light
with respect to each other, there is no such constraint in general
relativity.
For example, an object which crosses the event horizon and falls into a black hole can be thought of as moving faster
than light from the point of view of an outside observer. An expanding universe
generally has a cosmological
horizon, and
like a black hole event horizon, this marks the boundary to the part of the
universe that an observer can see. The horizon
is the boundary beyond which objects are moving away too fast to be visible
from Earth.
(فَلَا أُقْسِمُ بِمَا
تُبْصِرُونَ * وَمَا لَا تُبْصِرُونَ)
(الحاقة س 69، الآيتان 38-39)
"Furthermore
I swear by what ye see * And what ye see not." (S. 69 V 38-39)
Also the word horizon is
mentioned by: Two Qur-anic verses, and by some
authentic Hadiths
For details, see (horizon).
There are two ways to describe a spacetime with a horizon, global and local. The global picture includes
regions beyond the horizon, which are invisible
to us, while the local picture is the picture from one point of view only.
These two perspectives are related by a process of extension, wherever there is
a horizon, a solution of General Relativity can
go on by assuming that nothing special happens there. The local and global
points of view have a different notion of time. From the local point of view,
time stops at the horizon. From the global point
of view, time marches on, and surfaces of constant time cross the horizon. Ignoring quantum mechanics, the two pictures
are equivalent: any statement can be translated freely back and forth.
For cosmology in the global point of view, the observable
universe is
one causal patch of a much larger unobservable universe; there are parts
of the universe which cannot communicate with us yet. These parts of the
universe are outside our current cosmological horizon.
(فَلَا أُقْسِمُ بِمَا
تُبْصِرُونَ * وَمَا لَا تُبْصِرُونَ)
(الحاقة س 69، الآيتان 38-39)
"Furthermore
I swear by what ye see * And what ye see not." (S. 69 V 38-39)
(عَالِمُ
الْغَيْبِ وَالشَّهَادَةِ الْكَبِيرُ الْمُتَعَالِ) (الرعد س 13 ، 9)
[9] He knoweth the
Unseen and that which is open: He is the Great, the most High.
وَقَوْله"
عَالِم الْغَيْب وَالشَّهَادَة " أَيْ يَعْلَم كُلّ شَيْء مِمَّا يُشَاهِدهُ
الْعِبَاد وَمِمَّا يَغِيب عَنْهُمْ وَلَا يَخْفَى عَلَيْهِ مِنْهُ شَيْء"
(بن كثير).
(عَالِمِ
الْغَيْبِ وَالشَّهَادَةِ فَتَعَالَى عَمَّا يُشْرِكُونَ) (المؤمنون 23، 92)
[92] He knows what
is hidden and what is open; too high is He for the partners they attribute
to Him!
" عَالِم الْغَيْب وَالشَّهَادَة
" أَيْ يَعْلَم مَا يَغِيب عَنْ الْمَخْلُوقَات وَمَا يُشَاهِدُونَهُ "
فَتَعَالَى عَمَّا يُشْرِكُونَ " أَيْ تَقَدَّسَ وَتَنَزَّهَ وَتَعَالَى
وَعَزَّ وَجَلَّ عَمَّا يَقُول الظَّالِمُونَ وَالْجَاحِدُونَ (بن كثير).
(هُوَ
اللَّهُ الَّذِي لَا إِلَهَ إِلَّا هُوَ عَالِمُ الْغَيْبِ وَالشَّهَادَةِ هُوَ
الرَّحْمَنُ الرَّحِيمُ) (الحشر 59، 22)
[22] Allah is He, than Whom there is no other
god; Who knows (all things) both secret and open; He, Most Gracious,
Most Merciful.
In the standard hot big bang model, without inflation, the
cosmological horizon moves out, bringing new
regions into view. As we see these regions for the first time, they look no
different from any other region of space we have already seen: they have a
background radiation which is at nearly the exact same temperature as the
background radiation of other regions, and their space-time curvature is
evolving lock-step with ours. This presents a mystery: how did these new
regions know what temperature and curvature they were supposed to have? They
couldn't have learned it by getting signals, because they were not in
communication with our past light cone before.^{[3]}^{[4]}
Inflation answers this question by postulating that all the
regions come from an earlier era with a big vacuum energy, or cosmological
constant. A space with a cosmological constant is qualitatively different:
instead of moving outward, the cosmological horizon
stays put. For any one observer, the distance to the cosmological
horizon is
constant. Space is expanding exponentially, two nearby observers very quickly
separate so far so fast that they can no longer communicate. In the global
point of view, the spatial slices are expanding very fast to cover huge
volumes. In the local point of view, things are constantly falling into the
cosmological horizon, which is a fixed distance
away, and everything becomes homogeneous very quickly.
In either view, as the scalar field slowly relaxes to the
vacuum, the cosmological constant goes to zero, and space begins to expand
normally. The new regions which come into view during the normal expansion
phase, in the global point of view, are exactly the same regions which were
pushed out of the horizon during inflation, and
so they are necessarily at nearly the same temperature and curvature, because
they come from the same little patch of space. In the local point of view, the
cosmological horizon still is at the big bang,
and inflation is always going on in a thin skin where time is nearly stopped,
and the same process produces new regions as it always did, up to small
fluctuations.
Inflation from the global point of view is often called eternal inflation:
(وَالسَّمَاءَ بَنَيْنَاهَا
بِأَيْيدٍ وَإِنَّا لَمُوسِعُونَ ) ]
47 الذّاريات[.
" We have built The Sama - Firmament - with might, We
indeed Have vast power; to create the vastness of Space and continue to expand
it" (Surah No. 51, verse 47).
On a global constant-time slice, regions with inflation have
an exponentially growing volume, while regions which are not inflating don't.
This means that the volume of the inflating part of the universe in the global
picture is always unimaginably larger than the part that has stopped inflating.
If the probability of different regions is counted by volume, one should expect
that inflation will never end, or applying boundary conditions that we exist to
observe it, that inflation will end as late as possible. Weighting by volume is
unnatural in the local point of view, and in the local point of view inflation
is not eternal, it eventually ends from the point of view of any single
observer. This second point of view gives a meaning to the probability
distribution on the anthropic
landscape,
and naively seems more compatible with the holographic principle.
The theory of inflation in any picture explains why the
temperatures and curvatures of different regions are so nearly equal, and it
predicts that the total curvature of a space-slice at constant global time is
zero. This prediction means that the total ordinary matter, dark matter, and
residual vacuum energy in the universe have to add up to the critical density,
a prediction which is very accurately confirmed. More strikingly, inflation
allows physicists to calculate the minute differences in temperature of
different regions from quantum fluctuations during the inflationary era, and
these quantitative predictions have also been confirmed.
Space expands
To say that space expands exponentially means that two inertial observers are moving farther apart with accelerating velocity.
In stationary coordinates for one observer, a patch of an inflating universe
has the following polar metric:^{[5]}^{[6]}
This is just like an inside-out black hole metric—it has a zero in the dt component on a fixed radius sphere
called the cosmological
horizon.
Objects are drawn away from the observer at r = 0 towards the cosmological horizon,
which they cross in a finite proper time. This means that any inhomogeneities
are smoothed out, just as any bumps or matter on the surface of a black hole horizon are swallowed and disappear.
Since the space–time metric has no explicit time
dependence, once an observer has crossed the cosmological horizon, observers closer in take its place. This
process of falling outward and replacement points closer in are always steadily
replacing points further out—an exponential expansion of space–time.
This steady-state exponentially expanding spacetime is called
a de
Sitter space,
and to sustain it there must be a cosmological constant, a vacuum energy proportional to Λ everywhere.
The physical conditions from one moment to the next are stable: the rate of
expansion, called the Hubble parameter, is nearly constant. Inflation is
often called a period of accelerated expansion because the distance
between two fixed observers is increasing exponentially (i.e. at an
accelerating rate as they move apart), while Λ can stay approximately constant (see deceleration parameter).
Few inhomogeneities remain
Cosmological inflation has the important effect of smoothing
out inhomogeneities, anisotropies and the curvature of space. This pushes the universe into a very simple state, in which
it is completely dominated by the inflaton field, the source of the
cosmological constant, and the only significant inhomogeneities are the tiny
quantum fluctuations in the inflaton. Inflation also dilutes exotic heavy
particles, such as the magnetic monopoles predicted by many extensions to the Standard Model of particle physics. If the universe was only hot enough
to form such particles before a period of inflation, they would not be
observed in nature, as they would be so rare that it is quite likely that there
are none in the observable
universe.
Together, these effects are called the inflationary "no-hair theorem"^{[7]} by analogy with the no hair theorem for black holes.
The "no-hair" theorem works essentially because the
cosmological horizon is no different from a
black-hole horizon, except for philosophical
disagreements about what is on the other side. The interpretation of the
no-hair theorem is that the universe (observable and unobservable) expands by
an enormous factor during inflation. In an expanding universe, energy densities generally fall, or get diluted, as
the volume of the universe increases. For example, the density of ordinary
"cold" matter (dust) goes as the inverse of the volume: when linear
dimensions double, the energy density goes down by a factor of eight; the
radiation energy density goes down even more rapidly as the universe expands
since the wavelength of each photon is stretched (redshifted), in addition to the photons being
dispersed by the expansion. When linear dimensions are doubled, the energy
density in radiation falls by a factor of sixteen. During inflation, the energy
density in the inflaton field is roughly constant. However,
the energy density in inhomogeneities, curvature, anisotropies and exotic
particles is falling, and through sufficient inflation these become negligible.
This leaves an empty, flat, and symmetric universe, which is filled with
radiation when inflation ends.
Key requirement
A key requirement is that inflation must continue long enough
to produce the present observable universe from a single, small inflationary Hubble volume. This is necessary to ensure that
the universe appears flat, homogeneous and isotropic at the largest observable
scales. This requirement is generally thought to be satisfied if the universe
expanded by a factor of at least 10^{26} during inflation.^{[8]}
Reheating
At the end of inflation, a process called reheating
occurs, in which the potential energy of the inflaton field is converted into Standard Model particles, starting the radiation
dominated phase of the Universe. It is not known how long inflation lasted but
it is usually thought to be extremely short compared to the age of the
universe.
Motivation
Inflation resolves several
problems in
the Big Bang cosmology that were pointed out in
the 1970s.^{[9]} These problems arise from the
observation that to look like it does today, the universe would have to
have started from very finely
tuned, or
"special" initial conditions at the Big Bang. Inflation attempts to
resolve these problems by providing a dynamical mechanism that drives the
universe to this special state, thus making a universe like ours much more
likely in the context of the Big Bang theory.
Horizon problem
Main article: Horizon problem
The horizon problem^{[10]}^{[11]}^{[12]} is the problem of determining why
the universe appears statistically homogeneous and isotropic in accordance with
the cosmological principle. For example, molecules in a canister of gas are distributed
homogeneously and isotropically because they are in thermal equilibrium: gas
throughout the canister has had enough time to interact to dissipate
inhomogeneities and anisotropies. The situation is quite different in the big
bang model without inflation, because gravitational expansion does not give the
early universe enough time to equilibrate. In a big bang with only the matter and radiation known in the Standard Model, two widely separated regions of the
observable universe cannot have equilibrated because they move apart from each
other faster than the speed of light—thus have never come in to causal contact: in the history of the universe,
back to the earliest times, it has not been possible to send a light signal
between the two regions. Because they have no interaction, it is difficult to
explain why they have the same temperature (are thermally equilibrated). This
is because the Hubble
radius in a
radiation or matter-dominated universe expands much more quickly than physical
lengths and so points that are out of communication are coming into
communication. Historically, two proposed solutions were the Phoenix universe of Georges
Lemaître^{[13]} and the related oscillatory
universe of Richard
Chase Tolman,^{[14]} and the Mixmaster
universe of Charles Misner.^{[11]}^{[15]} Lemaître and Tolman proposed that a
universe undergoing a number of cycles of contraction and expansion could come
into thermal equilibrium. Their models failed, however, because of the buildup
of entropy over several cycles. Misner made the
(ultimately incorrect) conjecture that the Mixmaster mechanism, which made the
universe more chaotic, could lead to statistical homogeneity and
isotropy.
10000 Mpc=32600000000 Ly
Horizon problem: Universe was in contact before
inflation
(http://physics.uoregon.edu/~jimbrau/BrauImNew/Chap27/6th/27_12Figure-F.jpg)
Flatness problem
Main article: Flatness problem
Another problem is the flatness problem (which is sometimes called one of
the Dicke coincidences, with the other being
the cosmological constant problem).^{[16]}^{[17]} It had been known in the 1960s^{[}^{citation needed}^{]} that the density of matter in the
universe was comparable to the critical density necessary for a flat universe (that
is, a universe whose large scale geometry is the usual Euclidean
geometry,
rather than a non-Euclidean hyperbolic or spherical
geometry).
Therefore, regardless of the shape of the universe the contribution of spatial curvature to the expansion of
the universe could not be much greater than the contribution of matter. But as
the universe expands, the curvature redshifts away more slowly than matter and
radiation. Extrapolated into the past, this presents a fine-tuning problem because the contribution of
curvature to the universe must be exponentially small (sixteen orders of
magnitude less than the density of radiation at big bang nucleosynthesis, for example). This problem is exacerbated by recent
observations of the cosmic microwave background that have demonstrated that the
universe is flat to the accuracy of a few percent.^{[}^{citation needed}^{]}
Magnetic monopole problem
The magnetic monopole problem (sometimes called the exotic
relics problem) is a problem that suggests that if the early universe were very
hot, a large number of very heavy, stable magnetic monopoles would be produced. This was a
problem with Grand
Unified Theories, popular in the 1970s and 1980s, which proposed that at high
temperatures (such as in the early universe) the electromagnetic force, strong and weak nuclear forces are not actually fundamental forces
but arise due to spontaneous symmetry breaking from a much simpler gauge theory.^{[18]} These theories predict a number of
heavy, stable particles which have not yet been observed in nature. The most
notorious is the magnetic monopole, a kind of stable, heavy "knot" in
the magnetic field.^{[19]}^{[20]} Monopoles are expected to be
copiously produced in Grand Unified Theories at high temperature,^{[21]}^{[22]} and they should have persisted to
the present day, to such an extent that they would become the primary
constituent of the universe.^{[23]}^{[24]} Not only is that not the case, but
all searches for them have so far turned out fruitless, placing stringent
limits on the density of relic magnetic monopoles in the universe.^{[25]} A period of inflation that occurs
below the temperature where magnetic monopoles can be produced would offer a
possible resolution of this problem: monopoles would be separated from each
other as the universe around them expands, potentially lowering their observed
density by many orders of magnitude.
Precursors
In the early days of General
Relativity, Albert Einstein introduced the cosmological constant to allow a static solution which was a three dimensional sphere with a uniform density
of matter. A little later, Willem de Sitter found a highly symmetric inflating
universe, which described a universe with a cosmological constant which is
otherwise empty.^{[26]} Einstein's solution is unstable, and
if there are small fluctuations, it eventually turns into de Sitter's.
In the early 1970s Zeldovich noticed the serious flatness and horizon problems of big bang cosmology; before his
work, cosmology was presumed to be symmetrical on purely philosophical grounds.
In the Soviet Union, this and other considerations led Belinski and Khalatnikov to analyze the chaotic BKL singularity in General Relativity. Misner's Mixmaster
universe
attempted to use this chaotic behavior to solve the cosmological problems, with
limited success.
In the late 1970s, Sidney Coleman applied the instanton techniques developed by Alexander Polyakov and collaborators to study the fate of the false vacuum in quantum field theory. Like a
metastable phase in statistical mechanics—water below the freezing temperature
or above the boiling point—a quantum field would need to nucleate a large
enough bubble of the new vacuum, the new phase, in order to make a transition.
Coleman found the most likely decay pathway for vacuum decay and calculated the
inverse lifetime per unit volume. He eventually noted that gravitational
effects would be significant, but he did not calculate these effects and did
not apply the results to cosmology.
In the Soviet Union, Starobinsky noted that quantum
corrections to general relativity should be important in the early universe,
and these generically lead to curvature-squared corrections to the Einstein–Hilbert action. The solution to Einstein's equations in the presence of
curvature squared terms, when the curvatures are large, can lead to an
effective cosmological constant, so he proposed that the early universe went
through a deSitter phase, an inflationary era.^{[27]} This resolved the problems of
cosmology, and led to specific predictions for the corrections to the microwave
background radiation, corrections which were calculated in detail shortly
afterwards.
In 1978, Zeldovich noted the monopole problem, which was an
unambiguous quantitative version of the horizon
problem, this time in a fashionable subfield of particle physics, which led to
several speculative attempts to resolve it. In 1980, working in the west, Alan Guth realized that false vacuum decay in
the early universe would solve the problem, leading him to propose scalar
driven inflation. Starobinski's and Guth's scenarios both predicted an initial
deSitter phase, differing only in the details of the mechanism.
Early inflationary models
Inflation was proposed in January, 1980 by Alan Guth as a mechanism for resolving these
problems.^{[28]}^{[29]}. At the same time, Alexei Starobinsky argued that quantum corrections to
gravity would replace the initial singularity of the universe with an exponentially
expanding deSitter phase.^{[30]} In October 1980 Demosthenes Kazanas suggested that exponential expansion
could eliminate the particle horizon and perhaps solve the horizon problem,^{[31]} and Sato suggesting that an
exponential expansion could eliminate domain walls (another kind of exotic relic.)^{[32]} In 1981 Einhorn and Sato^{[33]} published a model similar to Guth's
and showed that it would resolve the puzzle of the magnetic monopole abundance in Grand Unified Theories. Like Guth, they concluded that such a model not only
required fine tuning of the cosmological constant, but also would very likely
lead to a much too granular universe, i.e., to large density variations
resulting from bubble wall collisions.
The physical size of the Hubble radius (solid line) as a
function of the linear expansion (scale factor) of the universe. During
cosmological inflation, the Hubble radius is constant. The physical wavelength
of a perturbation mode (dashed line) is also shown. The plot illustrates how
the perturbation mode grows larger than the horizon
during cosmological inflation before coming back inside the horizon, which grows rapidly during radiation
domination. If cosmological inflation had never happened, and radiation
domination continued back until a gravitational singularity, then the mode would never have been outside the horizon in the very early universe, and no causal mechanism could have ensured that
the universe was homogeneous on the scale of the perturbation mode.
Guth proposed that as the early universe cooled, it was
trapped in a false
vacuum with a
high energy density, which is much like a cosmological constant. As the very early universe cooled it was trapped in a metastable state (it was supercooled) which it could only decay out of
through the process of bubble nucleation via quantum tunneling. Bubbles of true vacuum spontaneously form in the sea of
false vacuum and rapidly begin expanding at the speed of light. Guth recognized that this model was
problematic because the model did not reheat properly: when the bubbles
nucleated, they did not generate any radiation. Radiation could only be
generated in collisions between bubble walls. But if inflation lasted long
enough to solve the initial conditions problems, collisions between bubbles
became exceedingly rare. In any one causal patch, it is likely that only one
bubble will nucleate.
Slow-roll inflation
The bubble collision problem was solved by Andrei Linde^{[34]} and independently by Andreas Albrecht and Paul Steinhardt^{[35]} in a model named new inflation
or slow-roll inflation (Guth's model then became known as old
inflation). In this model, instead of tunneling out of a false vacuum
state, inflation occurred by a scalar field rolling down a potential energy
hill. When the field rolls very slowly compared to the expansion of the
universe, inflation occurs. However, when the hill becomes steeper, inflation
ends and reheating can occur.
Effects of asymmetries
Eventually, it was shown that new inflation does not produce
a perfectly symmetric universe, but that tiny quantum fluctuations in the inflaton are created. These tiny fluctuations
form the primordial seeds for all structure created in the later universe.
These fluctuations were first calculated by Viatcheslav Mukhanov and G. V. Chibisov in the Soviet Union in analyzing Starobinsky's similar
model.^{[36]}^{[37]}^{[38]} In the context of inflation, they
were worked out independently of the work of Mukhanov and Chibisov at the
three-week 1982 Nuffield Workshop on the Very Early Universe at Cambridge University.^{[39]} The fluctuations were calculated by
four groups working separately over the course of the workshop: Stephen Hawking;^{[40]} Starobinsky;^{[41]} Guth and So-Young Pi;^{[42]} and James M. Bardeen, Paul Steinhardt and Michael Turner.^{[43]}
Observational status
Inflation is a concrete mechanism for realizing the cosmological principle which is the basis of the standard model of physical
cosmology: it accounts for the homogeneity and isotropy of the observable
universe. In addition, it accounts for the observed flatness and absence of
magnetic monopoles. Since Guth's early work, each of these observations has
received further confirmation, most impressively by the detailed observations
of the cosmic microwave background made by the Wilkinson Microwave Anisotropy Probe (WMAP) spacecraft.^{[44]} This analysis shows that the
universe is flat to an accuracy of at least a few percent, and that it is
homogeneous and isotropic to a part in 10,000.
This is being indicated by the following verse:
(الَّذِي خَلَقَ سَبْعَ
سَمَاوَاتٍ طِبَاقًا مَا تَرَى فِي خَلْقِ الرَّحْمَانِ مِنْ تَفَاوُتٍ فَارْجِعْ
الْبَصَرَ هَلْ تَرَى مِنْ فُطُورٍ _{*} ثُمَّ ارْجِعْ الْبَصَرَ كَرَّتَيْنِ يَنقَلِبْ
إِلَيْكَ الْبَصَرُ خَاسِئًا وَهُوَ حَسِيرٌ) [ الملك 3-4].
[3] He Who
created the seven Samawat (sky, Firmament) one above
another: no want of proportion wilt thou see in the Creation of (Allah) Most
Gracious. So turn thy vision again: seest thou any flaw? [4] Again turn thy vision a second time:
(thy) vision will come back to thee dull and discomfited, in a state worn out.
إنّ غياب التفاوت والفطور وتمام التسوية جعلت من بناء السّماء جرماً هائلاً ضخماً، أملساً، مصقولاً (94-89) ، ومتجانساً (Homogeneous)،
ومتماثل المناحي الاتّجاهيّة (Isotropic). وبالتالي
فلعلّ بناء السّماء ( شكل) هو مصدر إشعاع الخلفيّة الكوني الميكرويّ (Cosmic
Microwave Background Radiation) (شكل ، شكل ، شكل)
الذي يمتلك في جميع المناحي والاتّجاهات درجة الحرارة (Mather et al. 1999, ApJ, 512,
511):
_{}
( شكل ، شكل). تمثّل الألوان التغاير
الطّفيف في درجة حرارة إشعاع الخلفيّة: المناطق الحمراء أسخن، بينما الزرقاء أبرد
بمقدار 0.0002 درجة (http://www.nasa.gov/topics/universe/features/wmap_five.html).
يعكس تردّد إشعاع الخلفيّة انخفاض درجة حرارة بناء
السّماء، وبالتالي يشير إلى انعدام إمكانيّة الرؤية البصريّة للبناء (125).
ومن إعجاز هذه الآية الكريمة أنّ رقمها 3، وعدد كلماتها 18 وترتيب كلمة تفاوت في هذه الآية هو 12. وبحساب بسيط:
Among the miraculous aspects of this
verse is that its number is 3, and it has a total of 18 words, and
the order of the word (Tafawote: flaw) is 12.
Calculation based on words gives
_{}
ولو حسبنا الحروف لحصلنا على الرقم:
Calculation based on letters counting
gives:
_{}
This number is almost the same as the
temperature of the CMBR.
وبالتالي
فإنّ هذا نوع من الإعجاز العلمي والإعجاز العددي؛ إذ تشير الآية وبأكثر من وجه إلى
التغاير الطفيف في إشعاع الخلفية الكوني، والذي يعكس تسوية البناء السماوي.
In addition, inflation predicts that the structures visible
in the universe today formed through the gravitational collapse of perturbations which were formed as quantum mechanical
fluctuations in the inflationary epoch. The detailed form of the spectrum of
perturbations called a nearly-scale-invariant Gaussian random field (or Harrison-Zel'dovich spectrum) is very specific and has
only two free parameters, the amplitude of the spectrum and the spectral
index which measures the slight deviation from scale invariance predicted
by inflation (perfect scale invariance corresponds to the idealized de Sitter
universe).^{[45]} Inflation predicts that the observed
perturbations should be in thermal
equilibrium
with each other (these are called adiabatic or isentropic
perturbations). This structure for the perturbations has been confirmed by the
WMAP spacecraft and other cosmic microwave background experiments,^{[44]} and galaxy surveys, especially the ongoing Sloan Digital Sky Survey.^{[46]} These experiments have shown that
the one part in 10,000 inhomogeneities observed have exactly the form predicted
by theory. Moreover, there is evidence for a slight deviation from scale
invariance. The spectral index, n_{s} is equal to one for a scale-invariant spectrum. The simplest models of
inflation predict that this quantity is between 0.92 and 0.98.^{[47]}^{[48]}^{[49]}^{[50]} From the data taken by the WMAP
spacecraft it can be inferred that n_{s} = 0.963 ±
0.012,^{[51]} implying that it differs from one at
the level of two standard
deviations (2σ). This is considered an important
confirmation of the theory of inflation.^{[44]}
A number of theories of inflation have been proposed that
make radically different predictions, but they generally have much more fine tuning than is necessary.^{[47]}^{[48]} As a physical model, however,
inflation is most valuable in that it robustly predicts the initial conditions
of the universe based on only two adjustable parameters: the spectral index
(that can only change in a small range) and the amplitude of the perturbations.
Except in contrived models, this is true regardless of how inflation is
realized in particle physics.
Occasionally, effects are observed that appear to contradict
the simplest models of inflation. The first-year WMAP data suggested that the
spectrum might not be nearly scale-invariant, but might instead have a slight
curvature.^{[52]} However, the third-year data
revealed that the effect was a statistical anomaly.^{[44]} Another effect has been remarked
upon since the first cosmic microwave background satellite, the Cosmic Background Explorer: the amplitude of the quadrupole moment of the cosmic microwave background
is unexpectedly low and the other low multipoles appear to be preferentially
aligned with the ecliptic plane. Some have claimed that this is a signature of non-Gaussianity and thus
contradicts the simplest models of inflation. Others have suggested that the
effect may be due to other new physics, foreground contamination, or even publication bias.^{[53]}
An experimental program is underway to further test inflation
with more precise measurements of the cosmic microwave background. In
particular, high precision measurements of the so-called "B-modes" of
the polarization of the background radiation will be evidence of the gravitational radiation produced by inflation, and they will also show whether the
energy scale of inflation predicted by the simplest models (10^{15}–10^{16} GeV) is correct.^{[48]}^{[49]} These measurements are expected to
be performed by the Planck
spacecraft,
although it is unclear if the signal will be visible, or if contamination from
foreground sources will interfere with these measurements.^{[54]} Other forthcoming measurements, such
as those of 21 centimeter radiation (radiation emitted and absorbed from neutral hydrogen before
the first
stars turned
on), may measure the power spectrum with even greater resolution than the
cosmic microwave background and galaxy surveys, although it is not known if
these measurements will be possible or if interference with radio sources on earth and in the galaxy will be
too great.^{[55]}
Dark Energy
Dark energy makes up approximately 70% of the universe and
appears to be associated with the vacuum in space. It is distributed evenly
throughout the universe, not only in space but also in time – in other words,
its effect is not diluted as the universe expands. The even distribution means
that dark energy does not have any local gravitational effects, but rather a
global effect on the universe as a whole. This leads to a repulsive force,
which tends to accelerate the expansion of the universe. The rate of expansion
and its acceleration can be measured by observations based on the Hubble law.
These measurements, together with other scientific data, have confirmed the
existence of dark energy and provide an estimate of just how much of it exists.
(http://home.web.cern.ch/about/physics/dark-matter)
تشكل الطاقة
المظلمة ما يقرب من 70% من مكونات الكون، ويبدو أنها ترتبط
مع الفراغ الكوني. يتم توزيعها بالتساوي في جميع أنحاء الكون، وليس فقط في الفضاء
ولكن أيضا في الزمان. وبعبارة أخرى، لا يضعف
تأثيرها مع توسع الكون. التوزيع المنتظم للطاقة المظلمة يعني أنه ليس لديها أي
آثار جاذبية محلية، وإنما لها تأثير على نطاق الكون ككل. وتأثيرها يبدو كقوة
طاردة، أو قوّة تنافر تعمل على تسريع توسع الكون. ويمكن قياس معدل التوسع والتسارع
الكوني من خلال الأرصاد واستنادا إلى قانون هابل. هذه القياسات، جنبا إلى جنب مع
بيانات علمية أخرى، أكدت وجود الطاقة المظلمة وحدّدت مقدارها.
Dark energy is persistent, which impart a constant impulse to
the expansion of the universe, which makes galaxies accelerate away. Dark energy doesn’t dilute away as the universe expands.
الطاقة المظلمة
هي ثابتة، وهي التي تبذل شغلاً وبدفع (impulse) ثابت يسهم في
توسع الكون، الأمر الذي يجعل المجرات تتباعد وبتسارع. الطاقة المظلمة لا تتناقص مع
توسّع الكون.
Dark energy is broadly similar to inflation, and is thought
to be causing the expansion of the present-day universe to accelerate. This continuous expansion indicated by the
verse:
(وَالسَّمَاءَ بَنَيْنَاهَا
بِأَيْيدٍ وَإِنَّا لَمُوسِعُونَ _{*} وَالأرْضَ فَرَشْنَاهَا
فَنِعْمَ الْمَاهِدُونَ) ] 48-47
الذّاريات[.
" We have built The Sama - Firmament - with might, We
indeed Have vast power; to create the vastness of Space and continue to expand
it * And We have spread out Ardh - Ground; interior or lower part
of the Universe; the dark matter holding the galaxies -: How excellently We do
spread out!" (Surah No. 51, verse 47- 48).
(وَالسَّمَاءَ
بَنَيْنَاهَا بِأَيْيدٍ وَإِنَّا لَمُوسِعُونَ): الآية فيها استمرارية، وبالتالي فالخالق سبحانه
قادر وذو سعة يرزق خلقه في كل حين، كما أنّه يوسع بناء السّماء في كلّ لحظة.
هذا وقد دلّ ظاهر الآية على أنّ السماء واسعة عندما خلقها الله عزّ وجلّ، ولا مانع من أنّ التوسّع فيها دائم مستمر
حتى فناء الكون يوم القيامة، وإبداله بكون آخر (يَوْمَ تُبَدَّلُ الأرْضُ غَيْرَ الأرْضِ وَالسَّمَاوَاتُ وَبَرَزُوا لِلَّهِ
الْوَاحِدِ الْقَهَّارِ) [
إبراهيم آية 48 ]. علماً أنّ تصور سعة السّماء من الوضوح والجلاء ومعروفة بالضرورة لكلّ إنسان مبصر،
فإنّ معنى الاستمرارية
في التوسعة يتبادر إلى الذهن من الآية نفسها، وليس في الآية ثمة دليل على حصر
التوسعة على وصف البناء عند خلقه، لأنّ قوله تعالى (وإنّا لَمُوسِعُونَ) مطلق غير مقيد
بزمن أو حال أو صفة.
ويؤكّد ذلك قوله تعالى: (إِنَّا نَحْنُ نَزَّلْنَا الذِّكْرَ وَإِنَّا لَهُ
لَحَافِظُونَ) [ الحِجْر
آية 9 ]. فالحفظ قطعاً صفة ملازمة
للذكر المنزّل، المحفوظ استمراراً على
مدى الزمان والمكان، وهذا الحفظ متعيّن محسوس مشاهد. ويدلّ على ذلك قوله تعالى : (وَأَنزَلْنَا مِنْ السَّمَاءِ
مَاءً بِقَدَرٍ فَأَسْكَنَّاهُ فِي الأرْضِ وَإِنَّا عَلَى ذَهَابٍ بِهِ لَقَادِرُونَ) [ المؤمنون آية 18 ]. فصفة القدرة ثابتة
مستقرة مستمرة، ولا
يمكن تقييدها بزمن الإنزال
فحسب، وإلا
اختلّ معنى القدرة. وكما هو معلومٌ، فإنّ صيغة اسم الفاعل الواردة (حافظون،
قادرون، كاتبون، مُوسِعُونَ) تدلُّ على الاستمرارية والانعتاق من الزّمن. (عمري 2002
، بناء السّماء ). وكذلك الآية
الكريمة: (وَالأرْضَ
فَرَشْنَاهَا فَنِعْمَ الْمَاهِدُونَ). ففي كلّ لحظة يتمّ فرش الأرض
(الأرضين السّبع : الحاضن الجاذبي للمجرّات) ومهادها ، مما يؤدّي إلى التباعد
المستمرّ بين المجرّات.
" We
have built The Sama - Firmament - with might, We indeed Have vast power;
to create the vastness of Space and continue to expand it * And We have
spread out Ardh - Ground; interior or lower part of the Universe; the
dark matter holding the galaxies -: How excellently We do spread out!"
(Surah No. 51, verse 47- 48).
However, the energy scale of dark energy is much lower, 10^{−12} GeV, roughly 27 orders
of magnitude
less than the scale of inflation.
Theoretical status
In the early proposal of Guth, it was thought that the inflaton was the Higgs field, the field which explains the mass
of the elementary particles.^{[29]} It is now known that the inflaton cannot be the Higgs field.^{[56]} Other models of inflation relied on
the properties of grand unified theories.^{[35]} Since the simplest models of grand unification have failed, it is now thought by
many physicists that inflation will be included in a supersymmetric theory like string theory or a supersymmetric grand unified
theory. A promising suggestion is brane inflation. At present, however, whilst
inflation is understood principally by its detailed predictions of the initial
conditions
for the hot early universe, the particle physics is largely ad hoc
modelling. As such, despite the stringent^{[}^{weasel words}^{]} observational tests inflation has
passed, there are many open questions about the theory.
Fine-tuning problem
One of the most severe challenges for inflation arises from
the need for fine
tuning in
inflationary theories. In new inflation, the slow-roll conditions must
be satisfied for inflation to occur. The slow-roll conditions say that the inflaton potential must be flat (compared to the large vacuum energy) and that the inflaton particles must have a small mass.^{[57]} In order for the new inflation
theory of Linde, Albrecht and Steinhardt to be successful, therefore, it seemed
that the universe must have a scalar field with an especially flat potential
and special initial conditions.
Andrei Linde
Andrei Linde proposed a theory known as chaotic inflation in which he suggested that the
conditions for inflation are actually satisfied quite generically and inflation
will occur in virtually any universe that begins in a chaotic, high energy
state and has a scalar field with unbounded potential energy.^{[58]} However, in his model the inflaton field necessarily takes values
larger than one Planck unit: for this reason, these are often called large
field models and the competing new inflation models are called small
field models. In this situation, the predictions of effective field theory are thought to be invalid, as renormalization should cause large corrections that
could prevent inflation.^{[59]} This problem has not yet been
resolved and some cosmologists argue that the small field models, in which
inflation can occur at a much lower energy scale, are better models of
inflation.^{[60]} While inflation depends on quantum
field theory (and the semiclassical approximation to quantum gravity) in an important way, it has not
been completely reconciled with these theories.
Robert Brandenberger has commented on fine-tuning in
another situation.^{[61]} The amplitude of the primordial
inhomogeneities produced in inflation is directly tied to the energy scale of
inflation. There are strong suggestions that this scale is around 10^{16} GeV or 10^{−3} times the Planck energy. The natural scale is naïvely the
Planck scale so this small value could be seen as another form of fine-tuning
(called a hierarchy
problem): the
energy density given by the scalar potential is down by 10^{−12} compared to the Planck density. This is not usually considered to
be a critical problem, however, because the scale of inflation corresponds
naturally to the scale of gauge unification.
Eternal inflation
Main article: Chaotic inflation
Cosmological inflation seems to be eternal the way it is
theorised. Although new inflation is classically rolling down the potential,
quantum fluctuations can sometimes bring it back up to previous levels. These
regions in which the inflaton fluctuates upwards expand much
faster than regions in which the inflaton has a lower potential energy, and
tend to dominate in terms of physical volume. This steady state, which first
developed by Vilenkin,^{[62]} is called "eternal
inflation". It has been shown that any inflationary theory with an
unbounded potential is eternal.^{[63]} It is a popular belief among
physicists that this steady state cannot continue forever into the past.^{[64]}^{[65]}^{[66]} The inflationary spacetime, which is
similar to de
Sitter space,
is incomplete without a contracting region. However, unlike de Sitter space,
fluctuations in a contracting inflationary space will collapse to form a gravitational singularity, a point where densities become infinite. Therefore, it is
necessary to have a theory for the universe's initial conditions. Linde,
however, believes inflation may be past eternal.^{[67]}
That inflation will last tell the end of the
world, is stated by the Qur'anic verse:
(وَالسَّمَاءَ بَنَيْنَاهَا
بِأَيْيدٍ وَإِنَّا لَمُوسِعُونَ _{*} وَالأرْضَ فَرَشْنَاهَا
فَنِعْمَ الْمَاهِدُونَ) ] 48-47
الذّاريات[.
" We
have built The Sama - Firmament - with might, We indeed Have vast power;
to create the vastness of Space and continue to expand it * And We have
spread out Ardh - Ground; interior or lower part of the Universe; the
dark matter holding the galaxies -: How excellently We do spread out!"
(Surah No. 51, verse 47- 48).
Initial conditions
Some physicists have tried to avoid the initial conditions
problem by proposing models for an eternally inflating universe with no origin.^{[68]}^{[69]}^{[70]}^{[71]} These models propose that whilst the
universe, on the largest scales, expands exponentially it was, is and always
will be, spatially infinite and has existed, and will exist, forever.
Other proposals attempt to describe the ex nihilo creation of
the universe based on quantum cosmology and the following inflation.
Vilenkin put forth one such scenario.^{[62]} Hartle and Hawking offered the no-boundary
proposal for
the initial creation of the universe in which inflation comes about naturally.^{[72]}
Alan Guth has described the inflationary
universe as the "ultimate free lunch":^{[73]}^{[74]} new universes, similar to our own,
are continually produced in a vast inflating background. Gravitational
interactions, in this case, circumvent (but do not violate) neither the first law of thermodynamics (energy
conservation)
nor the second law of thermodynamics (entropy and the arrow of time problem). However, while there is
consensus that this solves the initial conditions problem, some have disputed
this, as it is much more likely that the universe came about by a quantum
fluctuation. Donald Page was an outspoken critic of inflation because of this
anomaly.^{[75]} He stressed that the thermodynamic arrow of time necessitates low entropy initial conditions, which would be
highly unlikely. According to them, rather than solving this problem, the
inflation theory further aggravates it – the reheating at the end of the
inflation era increases entropy, making it necessary for the initial state of
the Universe to be even more orderly than in other Big Bang theories with no
inflation phase.
Hawking and Page later found ambiguous results when they
attempted to compute the probability of inflation in the Hartle-Hawking initial
state.^{[76]} Other authors have argued that,
since inflation is eternal, the probability doesn't matter as long as it is not
precisely zero: once it starts, inflation perpetuates itself and quickly
dominates the universe.^{[}^{citation needed}^{]} However, Albrecht and Lorenzo Sorbo
have argued that the probability of an inflationary cosmos, consistent with
today's observations, emerging by a random fluctuation from some pre-existent
state, compared with a non-inflationary cosmos overwhelmingly favours
the inflationary scenario, simply because the "seed" amount of
non-gravitational energy required for the inflationary cosmos is so much less
than any required for a non-inflationary alternative, which outweighs any
entropic considerations.^{[77]}
Another problem that has occasionally been mentioned is the
trans-Planckian problem or trans-Planckian effects.^{[78]} Since the energy scale of inflation
and the Planck scale are relatively close, some of the quantum fluctuations
which have made up the structure in our universe were smaller than the Planck
length before inflation. Therefore, there ought to be corrections from
Planck-scale physics, in particular the unknown quantum theory of gravity.
There has been some disagreement about the magnitude of this effect: about
whether it is just on the threshold of detectability or completely
undetectable.^{[79]}
Reheating
The end of inflation is called reheating or thermalization
because the large potential energy of the inflaton field decays into particles and
fills the universe with electromagnetic radiation. Because the nature of the inflaton is not known, this process is still
poorly understood, although it is believed to take place through a parametric resonance.^{[80]}^{[81]}
Non-eternal inflation
Another kind of inflation, called hybrid inflation, is
an extension of new inflation. It introduces additional scalar fields, so that
while one of the scalar fields is responsible for normal slow roll inflation,
another triggers the end of inflation: when inflation has continued for sufficiently
long, it becomes favorable to the second field to decay into a much lower
energy state.^{[82]} Unlike most other models of
inflation, many versions of hybrid inflation are not eternal.^{[83]}^{[84]}
In hybrid inflation, one of the scalar fields is responsible
for most of the energy density (thus determining the rate of expansion), while
the other is responsible for the slow roll (thus determining the period of
inflation and its termination). Thus fluctuations in the former inflaton would
not affect inflation termination, while fluctuations in the latter would not
affect the rate of expansion. Therefore hybrid inflation is not eternal. When
the second (slow-rolling) inflaton reaches the bottom of its potential, it changes
the location of the minimum of the first inflaton's potential, which leads to a
fast roll of the inflaton down its potential, leading to termination of
inflation.
Inflation and string cosmology
The discovery of flux compactifications have opened the way for reconciling inflation and string
theory.^{[85]} A new theory, called brane inflation suggests that inflation arises from
the motion of D-branes^{[86]} in the compactified geometry,
usually towards a stack of anti-D-branes. This theory, governed by the Dirac-Born-Infeld
action, is
very different from ordinary inflation. The dynamics are not completely understood.
It appears that special conditions are necessary since inflation occurs in
tunneling between two vacua in the string landscape. The process of tunneling between
two vacua is a form of old inflation, but new inflation must then occur by some
other mechanism.
Inflation and loop quantum gravity
When investigating the effects the theory of loop
quantum gravity would have on cosmology, a loop quantum cosmology model has evolved that provides a possible mechanism for
cosmological inflation. Loop quantum gravity assumes a quantified spacetime. If
the energy density is larger than can be held by the quantified spacetime, it
is thought to bounce back.
Alternatives to inflation
String theory requires that, in addition to the
three spatial dimensions we observe, there exist additional dimensions that are
curled up or compactified (see also Kaluza-Klein
theory).
Extra dimensions appear as a frequent component of supergravity models and other approaches to quantum gravity. This raises the question of why
four space-time dimensions became large and the rest became unobservably small.
An attempt to address this question, called string gas cosmology, was proposed by Robert Brandenberger and Cumrun Vafa.^{[87]} This model focuses on the dynamics
of the early universe considered as a hot gas of strings. Brandenberger and
Vafa show that a dimension of spacetime can only expand if the strings that
wind around it can efficiently annihilate each other. Each string is a
one-dimensional object, and the largest number of dimensions in which two
strings will generically
intersect
(and, presumably, annihilate) is three. Therefore, one argues that the most
likely number of non-compact (large) spatial dimensions is three. Current work
on this model centers on whether it can succeed in stabilizing the size of the
compactified dimensions and produce the correct spectrum of primordial density
perturbations. For a recent review, see^{[88]}^{[89]}
The ekpyrotic and cyclic models are also considered competitors to
inflation. These models solve the horizon problem through an expanding epoch well before
the Big Bang, and then generate the required spectrum of primordial density
perturbations during a contracting phase leading to a Big Crunch. The universe passes through the Big
Crunch and emerges in a hot Big Bang phase. In this sense they are
reminiscent of the oscillatory
universe
proposed by Richard
Chace Tolman:
however in Tolman's model the total age of the universe is necessarily finite,
while in these models this is not necessarily so. Whether the correct spectrum
of density fluctuations can be produced, and whether the universe can
successfully navigate the Big Bang/Big Crunch transition, remains a topic of
controversy and current research.
Philosophy of cosmology
Philosophers of science John Earman and Jesús Mosterín ^{[90]} have claimed that inflationary
cosmology is flawed. Writing in 1999, they said that:
(a) results showing that inflation is likely to occur under
generic conditions in the universe were not forthcoming (b) cosmic no hair
theorems showing that inflation is effective in ironing out generic
nonuniformities were not forthcoming (and in our reckoning are probably not
true) and (c) in the straightforward version of inflationary cosmology ... the
presence of enough inflation... is difficult to reconcile with a low value of Ω_{0}_{ }^{[91]}
Their second point contradicts the well-accepted uniqueness
and homogenization properties of deSitter space.^{[}^{citation needed}^{]} Their third point is a
non-sequitur—the presence of inflation is what guarantees that the initial
value of Ω_{0} will be small.^{[}^{citation needed}^{]} But it is the first point that
contains the essential philosophical position—they claim that inflation is no
better as a starting point for cosmology than the standard big-bang, except in
ways that are not accessible to experimental test.
Since the standard FRW big-bang picture can be fixed to match
observations by a certain amount of fine-tuning, Earman and Mosterin reckon
that this type of fine tuning is no worse or no better as an explanation of
experimental results than the tuning you need to match a scalar inflaton model
to the same data. This conclusion is not shared by mainstream cosmologists,^{[}^{citation needed}^{]} who view the fine-tuning of many
causally disconnected patches to almost, but not quite, the same temperature
and curvature as something that requires a dynamical explanation. This reflects
a difference in philosophy, limits on fine-tuning have long been used by
practicing scientists as criteria for a good theory, but are not given a
central role in standard philosophies of science.
Notes
1.
^ Liddle and Lyth (2000) and Mukhanov
(2005) are recent cosmology textbooks with extensive discussions of inflation.
Kolb and Turner (1988) and Linde (1990) miss some recent developments, but are
still widely used. Peebles (1993) provides a technical discussion with
historical context. Recent review articles are Lyth and Riotto (1999) and Linde
(2005). Guth (1997) and Hawking (1998) give popular introductions to inflation
with historical remarks.
2.
^ Tyson, Neil deGrasse and Donald
Goldsmith (2004), Origins: Fourteen Billion Years of Cosmic Evolution,
W. W. Norton & Co., pp. 84-5.
3.
^ Using Tiny Particles To Answer Giant
Questions.
Science Friday, 3 April 2009.
4.
^ See also Faster
than light#Universal_expansion.
5.
^ Melia, Fulvio (2007), The Cosmic
Horizon, MNRAS, 382, 1917--1921.
6.
^ Melia, Fulvio et al. (2009), The
Cosmological Spacetime, IJMP-D, 18, 1889--1901.
7.
^ Kolb and Turner (1988).
8.
^ This is usually quoted as 60 e-folds
of expansion, where e^{60} ≈ 10^{26}. It is equal
to the amount of expansion since reheating, which is roughly E_{inflation}/T_{0},
where T_{0} = 2.7 K is the temperature of the cosmic
microwave background today. See, e.g. Kolb and Turner (1998) or Liddle
and Lyth (2000).
9.
^ Much of the historical context is
explained in chapters 15–17 of Peebles (1993).
10.
^ Misner, Charles W.; Coley, A A;
Ellis, G F R; Hancock, M (1968). "The isotropy of the universe". Astrophysical
Journal 151: 431. doi:10.1088/0264-9381/15/2/008.
11.
^ ^{a} ^{b} Misner, Charles; Thorne, Kip S. and
Wheeler, John Archibald (1973). Gravitation. San Francisco: W. H.
Freeman. pp. 489–490, 525–526. ISBN 0-7167-0344-0.
12.
^ Weinberg, Steven (1971). Gravitation
and Cosmology. John Wiley. pp. 740, 815. ISBN 0-471-92567-5.
13.
^ Lemaître, Georges (1933). "The
expanding universe". Ann. Soc. Sci. Bruxelles 47A: 49.
14.
^ R. C. Tolman (1934). Relativity,
Thermodynamics, and Cosmology. Oxford: Clarendon Press. LCCN 340-32023. Reissued (1987) New York: Dover
ISBN 0-486-65383-8.
15.
^ Misner, Charles W.; Leach, P G L
(1969). "Mixmaster universe". Phys. Rev. Lett. 22: 1071–74. doi:10.1088/1751-8113/41/15/155201.
16. ^ Dicke, Robert H. (1970). Gravitation
and the Universe. Philadelphia: American Philosopical Society.
17.
^ Dicke, Robert H.; P. J. E. Peebles
(1979). "The big bang cosmology – enigmas and nostrums". in ed. S. W.
Hawking and W. Israel. General Relativity: an Einstein Centenary Survey.
Cambridge University Press.
18.
^ The importance of grand unification
has waned somewhat since the early 1990s, as the simplest theories have been
ruled out by proton
decay
experiments. However, many people still believe that a supersymmetric Grand Unified Theory is built into string theory, so it is still seen as a triumph
for inflation that it is able to deal with these relics. See, e.g. Kolb
and Turner (1988) and Raby, Stuart (2006). "Grand Unified Theories". in ed. Bruce Hoeneisen. Galapagos
World Summit on Physics Beyond the Standard Model. http://arxiv.org/abs/hep-ph/0608183.
19.
^ 't Hooft, Gerard (1974).
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20.
^ Polyakov, Alexander M. (1974).
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194–5.
21.
^ Guth, Alan (1980). "Phase
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44: 631–635; Erratum ibid.,44:963, 1980. doi:10.1103/PhysRevLett.44.631.
22.
^ Einhorn, Martin B (1980). "Are
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23.
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24.
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25.
^ See, e.g. Yao,
W.–M. (2006).
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27.
^ Starobinsky, A. A. - Spectrum Of
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28.
^ SLAC seminar, "10-35 seconds after the Big Bang", 23rd
January, 1980. see Guth (1997), pg 186
29. ^ ^{a} ^{b} A. H. Guth, "The Inflationary
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30.
^ Starobinsky, Alexei A. (1980).
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31.
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32.
^ Sato, K. (1981). "Cosmological
baryon number domain structure and the first order phase transition of a
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33.
^ Einhorn, Martin B (1981).
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Transition". Nucl. Phys. B180: 385–404. doi:10.1016/0550-3213(81)90057-2.
34.
^ A. Linde, "A New Inflationary
Universe Scenario: A Possible Solution Of The Horizon, Flatness, Homogeneity,
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35.
^ ^{a} ^{b} A. Albrecht and P. J. Steinhardt,
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36.
^ See Linde (1990) and Mukhanov
(2005).
37.
^ Mukhanov, Viatcheslav F. (1981).
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38.
^ Mukhanov, Viatcheslav F. (1982).
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39.
^ See Guth (1997) for a popular
description of the workshop, or The Very Early Universe, ISBN 0521316774 eds Hawking, Gibbon & Siklos for
a more detailed report
40.
^ Hawking, S.W. (1982). "The
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41.
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42.
^ Guth, A.H. (1982).
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43.
^ Bardeen, James M. (1983).
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44. ^ ^{a} ^{b} ^{c} ^{d} See, e.g. Spergel, D.N.
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45.
^ Perturbations can be represented by Fourier modes of a given wavelength. Each Fourier mode is normally
distributed
(usually called Gaussian) with mean zero. Different Fourier components are
uncorrelated. The variance of a mode depends only on its wavelength in such a
way that within any given volume each wavelength contributes an equal amount of
power to the spectrum of perturbations.
Since the Fourier transform is in three dimensions, this means that the
variance of a mode goes as k^{−3} to compensate for the
fact that within any volume, the number of modes with a given wavenumber k
goes as k³.
46.
^ Tegmark, M. (August 2006). Cosmological constraints from the SDSS luminous red galaxies. http://arxiv.org/abs/astro-ph/0608632.
47.
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48.
^ ^{a} ^{b} ^{c} Boyle, Latham A.; Steinhardt, PJ;
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49.
^ ^{a} ^{b} Tegmark, Max (2005). "What does inflation really predict?". JCAP 0504: 001. doi:10.1088/1475-7516/2005/04/001. http://www.arxiv.org/abs/astro-ph/0410281.
50.
^ This is known as a "red"
spectrum, in analogy to redshift, because the spectrum has more power
at longer wavelengths.
51.
^ Seven-Year Wilkinson Microwave
Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. January 2010. http://adsabs.harvard.edu/abs/2010arXiv1001.4538K.
52.
^ Spergel, D. N.; Verde, L.; Peiris,
H. V.; Komatsu, E.; Nolta, M. R.; Bennett, C. L.; Halpern, M.; Hinshaw, G. et
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53.
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54.
^ Rosset, C.; (PLANCK-HFI
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55. ^ Loeb, A.; Zaldarriaga, M (2004). "Measuring the small-scale power spectrum of
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56.
^ Guth, Alan (1997). The Inflationary Universe.
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57.
^ Technically, these conditions are
that the logarithmic derivative of the potential, ε = (1 / 2)(V' / V)^{2}
and second derivative η = V'' / V − (1 / 2)(V'
/ V)^{2} are small, where V is the potential and the
equations are written in reduced
Planck units.
See, e.g. Liddle and Lyth (2000).
58.
^ Linde, Andrei D.; Postma, M (1983).
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59.
^ Technically, this is because the inflaton potential is expressed as a Taylor
series in φ/m_{Pl}, where φ is the inflaton and m_{Pl} is the
Planck mass. While for a single term, such as the mass term m_{φ}^{4}(φ/m_{Pl})²,
the slow roll conditions can be satisfied for φ much greater than m_{Pl},
this is precisely the situation in effective field theory in which higher order
terms would be expected to contribute and destroy the conditions for inflation.
The absence of these higher order corrections can be seen as another sort of
fine tuning. See e.g. Alabidi, Laila; Lyth, David H (2006). "Inflation models and observation". JCAP 0605: 016. doi:10.1088/1475-7516/2006/05/016. http://www.arxiv.org/abs/astro-ph/0510441.
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