In physical cosmology, cosmic inflation, cosmological
inflation, or just inflation, is a theory
of exponential expansion of space in the early
universe. The inflationary epoch lasted from
10−36 seconds after the conjectured Big
Bang singularity to sometime between 10−33
and 10−32 seconds after the singularity.
Following the inflationary period, the universe
continues to expand, but at a less rapid rate.Inflation
theory was first developed in 1979 by theoretical
physicist Alan Guth at Cornell University.
It was developed further in the early 1980s.
It 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). Many
physicists also believe that inflation explains
why the universe appears to be the same in
all directions (isotropic), why the cosmic
microwave background radiation is distributed
evenly, why the universe is flat, and why
no magnetic monopoles have been observed.
The detailed particle physics mechanism responsible
for inflation is unknown. The basic inflationary
paradigm is accepted by most physicists, as
a number of inflation model predictions have
been confirmed by observation; however, a
substantial minority of scientists dissent
from this position. The hypothetical field
thought to be responsible for inflation is
called the inflaton.In 2002, three of the
original architects of the theory were recognized
for their major contributions; physicists
Alan Guth of M.I.T., Andrei Linde of Stanford,
and Paul Steinhardt of Princeton shared the
prestigious Dirac Prize "for development of
the concept of inflation in cosmology". In
2012, Alan Guth and Andrei Linde were awarded
the Breakthrough Prize in Fundamental Physics
for their invention and development of inflationary
cosmology.
== Overview ==
Around 1930, Edwin Hubble discovered that
light from remote galaxies was redshifted;
the more remote, the more shifted. This was
quickly interpreted as meaning galaxies were
receding from earth. If earth is not in some
special, privileged, central position in the
universe, then it would mean all galaxies
are moving apart, and the further away, the
faster they are moving away. It is now understood
that the universe is expanding, carrying the
galaxies with it, and causing this observation.
Many other observations agree, and also lead
to the same conclusion. However, for many
years it was not clear why or how the universe
might be expanding, or what it might signify.
Based on a huge amount of experimental observation
and theoretical work, it is now believed that
the reason for the observation is that space
itself is expanding, and that it expanded
very rapidly within the first fraction of
a second after the Big Bang. This kind of
expansion is known as a "metric" expansion.
In the terminology of mathematics and physics,
a "metric" is a measure of distance that satisfies
a specific list of properties, and the term
implies that the sense of distance within
the universe is itself changing, although
at this time it is far too small an effect
to see on less than an intergalactic scale.
The modern explanation for the metric expansion
of space was proposed by physicist Alan Guth
in 1979, while investigating the problem of
why no magnetic monopoles are seen today.
He found that if the universe contained a
field in a positive-energy false vacuum state,
then according to general relativity it would
generate an exponential expansion of space.
It was very quickly realized that such an
expansion would resolve many other long-standing
problems. 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 theory largely resolves
these problems as well, thus making a universe
like ours much more likely in the context
of Big Bang theory.
No physical field has yet been discovered
that is responsible for this inflation. However
such a field would be scalar and the first
relativistic scalar field proven to exist
was only discovered in 2012 - 2013 and is
still being researched. So it is not seen
as problematic that a field responsible for
cosmic inflation and the metric expansion
of space has not yet been discovered. The
proposed field and its quanta (the subatomic
particles related to it) have been named the
inflaton. If this field did not exist, scientists
would have to propose a different explanation
for all the observations that strongly suggest
a metric expansion of space has occurred,
and is still occurring (much more slowly)
today.
== Theory ==
An expanding universe generally has a cosmological
horizon, which, by analogy with the more familiar
horizon caused by the curvature of Earth's
surface, marks the boundary of the part of
the Universe that an observer can see. Light
(or other radiation) emitted by objects beyond
the cosmological horizon in an Accelerating
universe never reaches the observer, because
the space in between the observer and the
object is expanding too rapidly.
The observable universe is one causal patch
of a much larger unobservable universe; other
parts of the Universe cannot communicate with
Earth yet. These parts of the Universe are
outside our current cosmological horizon.
In the standard hot big bang model, without
inflation, the cosmological horizon moves
out, bringing new regions into view. Yet as
a local observer sees such a region for the
first time, it looks no different from any
other region of space the local observer has
already seen: its background radiation is
at nearly the same temperature as the background
radiation of other regions, and its space-time
curvature is evolving lock-step with the others.
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 previously in communication
with our past light cone.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. With exponentially expanding
space, two nearby observers are separated
very quickly; so much so, that the distance
between them quickly exceeds the limits of
communications. The spatial slices are expanding
very fast to cover huge volumes. Things are
constantly moving beyond the cosmological
horizon, which is a fixed distance away, and
everything becomes homogeneous.
As the inflationary field slowly relaxes to
the vacuum, the cosmological constant goes
to zero and space begins to expand normally.
The new regions that come into view during
the normal expansion phase are exactly the
same regions that were pushed out of the horizon
during inflation, and so they are at nearly
the same temperature and curvature, because
they come from the same originally small patch
of space.
The theory of inflation thus explains why
the temperatures and curvatures of different
regions are so nearly equal. It also predicts
that the total curvature of a space-slice
at constant global time is zero. This prediction
implies that the total ordinary matter, dark
matter and residual vacuum energy in the Universe
have to add up to the critical density, and
the evidence supports this. More strikingly,
inflation allows physicists to calculate the
minute differences in temperature of different
regions from quantum fluctuations during the
inflationary era, and many of these quantitative
predictions have been confirmed.
=== Space expands ===
In a space that expands exponentially (or
nearly exponentially) with time, any pair
of free-floating objects that are initially
at rest will move apart from each other at
an accelerating rate, at least as long as
they are not bound together by any force.
From the point of view of one such object,
the spacetime is something like an inside-out
Schwarzschild black hole -- each object is
surrounded by a spherical event horizon. Once
the other object has fallen through this horizon
it can never return, and even light signals
it sends will never reach the first object
(at least so long as the space continues to
expand exponentially).
In the approximation that the expansion is
exactly exponential, the horizon is static
and remains a fixed physical distance away.
This patch of an inflating universe can be
described by the following metric:
d
s
2
=
−
(
1
−
Λ
r
2
)
d
t
2
+
1
1
−
Λ
r
2
d
r
2
+
r
2
d
Ω
2
.
{\displaystyle ds^{2}=-(1-\Lambda r^{2})\,dt^{2}+{1
\over 1-\Lambda r^{2}}\,dr^{2}+r^{2}\,d\Omega
^{2}.}
This exponentially expanding spacetime is
called a de Sitter space, and to sustain it
there must be a cosmological constant, a vacuum
energy density that is constant in space and
time and proportional to Λ in the above metric.
For the case of exactly exponential expansion,
the vacuum energy has a negative pressure
p equal in magnitude to its energy density
ρ; the equation of state is p=−ρ.
Inflation is typically not an exactly exponential
expansion, but rather quasi- or near-exponential.
In such a universe the horizon will slowly
grow with time as the vacuum energy density
gradually decreases.
=== Few inhomogeneities remain ===
Because the accelerating expansion of space
stretches out any initial variations in density
or temperature to very large length scales,
an essential feature of inflation is that
it smooths out inhomogeneities, anisotropies
and reduces the curvature of space. This pushes
the Universe into a very simple state in which
it is completely dominated by the inflaton
field and the only significant inhomogeneities
are tiny quantum fluctuations. 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" 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
down 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 (see the solution of the energy density
continuity equation for an ultra-relativistic
fluid). During inflation, the energy density
in the inflaton field is roughly constant.
However, the energy density in everything
else, including inhomogeneities, curvature,
anisotropies, exotic particles, and standard-model
particles is falling, and through sufficient
inflation these all become negligible. This
leaves the Universe flat and symmetric, and
(apart from the homogeneous inflaton field)
mostly empty, at the moment inflation ends
and reheating begins.
=== Duration ===
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 1026 during inflation.
=== Reheating ===
Inflation is a period of supercooled expansion,
when the temperature drops by a factor of
100,000 or so. (The exact drop is model dependent,
but in the first models it was typically from
1027 K down to 1022 K.) This relatively low
temperature is maintained during the inflationary
phase. When inflation ends the temperature
returns to the pre-inflationary temperature;
this is called reheating or thermalization
because the large potential energy of the
inflaton field decays into particles and fills
the Universe with Standard Model particles,
including electromagnetic radiation, starting
the radiation dominated phase of the Universe.
Because the nature of the inflation is not
known, this process is still poorly understood,
although it is believed to take place through
a parametric resonance.
== Motivations ==
Inflation resolves several problems in Big
Bang cosmology that were discovered in the
1970s. Inflation was first proposed by Alan
Guth in 1979 while investigating the problem
of why no magnetic monopoles are seen today;
he found that a positive-energy false vacuum
would, according to general relativity, generate
an exponential expansion of space. It was
very quickly realised that such an expansion
would resolve many other long-standing problems.
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 ===
The horizon problem 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
and thus have never come into causal contact.
In the early Universe, it was not possible
to send a light signal between the two regions.
Because they have had no interaction, it is
difficult to explain why they have the same
temperature (are thermally equilibrated).
Historically, proposed solutions included
the Phoenix universe of Georges Lemaître,
the related oscillatory universe of Richard
Chase Tolman, and the Mixmaster universe of
Charles Misner. 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.
=== Flatness problem ===
The flatness problem is sometimes called one
of the Dicke coincidences (along with the
cosmological constant problem). It became
known in the 1960s 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 within a few percent.
=== Magnetic-monopole problem ===
The magnetic monopole problem, sometimes called
the exotic-relics problem, says that if the
early universe were very hot, a large number
of very heavy, stable magnetic monopoles would
have been produced. This is a problem with
Grand Unified Theories, which propose 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 single gauge theory. These
theories predict a number of heavy, stable
particles that have not been observed in nature.
The most notorious is the magnetic monopole,
a kind of stable, heavy "charge" of magnetic
field. Monopoles are predicted to be copiously
produced following Grand Unified Theories
at high temperature, and they should have
persisted to the present day, to such an extent
that they would become the primary constituent
of the Universe. Not only is that not the
case, but all searches for them have failed,
placing stringent limits on the density of
relic magnetic monopoles in the Universe.
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. Though,
as cosmologist Martin Rees has written, "Skeptics
about exotic physics might not be hugely impressed
by a theoretical argument to explain the absence
of particles that are themselves only hypothetical.
Preventive medicine can readily seem 100 percent
effective against a disease that doesn't exist!"
== History ==
=== 
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. Later,
Willem de Sitter found a highly symmetric
inflating universe, which described a universe
with a cosmological constant that is otherwise
empty. It was discovered that Einstein's universe
is unstable, and that small fluctuations cause
it to collapse or turn into a de Sitter universe.
In the early 1970s Zeldovich noticed the 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.
==== False vacuum ====
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.
==== Starobinsky inflation ====
In the Soviet Union, Alexei Starobinsky noted
that quantum corrections to general relativity
should be important for the early universe.
These generically lead to curvature-squared
corrections to the Einstein–Hilbert action
and a form of f(R) modified gravity. The solution
to Einstein's equations in the presence of
curvature squared terms, when the curvatures
are large, leads to an effective cosmological
constant. Therefore, he proposed that the
early universe went through an inflationary
de Sitter era. This resolved the cosmology
problems and led to specific predictions for
the corrections to the microwave background
radiation, corrections that were then calculated
in detail. Starobinsky used the action
S
=
1
2
∫
d
4
x
(
R
+
R
2
6
M
2
)
{\displaystyle S={\frac {1}{2}}\int d^{4}x\left(R+{\frac
{R^{2}}{6M^{2}}}\right)}
which corresponds to the potential
V
(
ϕ
)
=
Λ
4
(
1
−
e
−
2
/
3
ϕ
/
M
p
2
)
2
{\displaystyle \quad V(\phi )=\Lambda ^{4}\left(1-e^{-{\sqrt
{2/3}}\phi /M_{p}^{2}}\right)^{2}}
in the Einstein frame. This results in the
observables:
n
s
=
1
−
2
N
,
r
=
12
N
2
.
{\displaystyle n_{s}=1-{\frac {2}{N}},\quad
\quad r={\frac {12}{N^{2}}}.}
==== Monopole problem ====
In 1978, Zeldovich noted the monopole problem,
which was an unambiguous quantitative version
of the horizon problem, this time in a subfield
of particle physics, which led to several
speculative attempts to resolve it. In 1980
Alan Guth realized that false vacuum decay
in the early universe would solve the problem,
leading him to propose a scalar-driven inflation.
Starobinsky's and Guth's scenarios both predicted
an initial de Sitter phase, differing only
in mechanistic details.
=== Early inflationary models ===
Guth proposed inflation in January 1980 to
explain the nonexistence of magnetic monopoles;
it was Guth who coined the term "inflation".
At the same time, Starobinsky argued that
quantum corrections to gravity would replace
the initial singularity of the Universe with
an exponentially expanding de Sitter phase.
In October 1980, Demosthenes Kazanas suggested
that exponential expansion could eliminate
the particle horizon and perhaps solve the
horizon problem, while Sato suggested that
an exponential expansion could eliminate domain
walls (another kind of exotic relic). In 1981
Einhorn and Sato 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 likely lead to a much too granular
universe, i.e., to large density variations
resulting from bubble wall collisions.
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 would nucleate.
... Kazanas (1980) called this phase of the
early Universe "de Sitter's phase." The name
"inflation" was given by Guth (1981). ... Guth
himself did not refer to work of Kazanas until
he published a book on the subject under the
title "The inflationary universe: the quest
for a new theory of cosmic origin" (1997),
where he apologizes for not having referenced
the work of Kazanas and of others, related
to inflation.
=== Slow-roll inflation ===
The bubble collision problem was solved by
Linde and independently by Andreas Albrecht
and Paul Steinhardt 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 quantum fluctuations in the inflaton
are created. These 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 analyzing Starobinsky's similar model.
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. The fluctuations were calculated
by four groups working separately over the
course of the workshop: Stephen Hawking; Starobinsky;
Guth and So-Young Pi; and Bardeen, Steinhardt
and Turner.
== Observational status ==
Inflation is a 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 Planck spacecraft.
This analysis shows that the Universe is flat
to within 0.5 percent, and that it is homogeneous
and isotropic to one part in 100,000.
Inflation predicts that the structures visible
in the Universe today formed through the gravitational
collapse of perturbations that 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 is very specific and
has only two free parameters. One is 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).
The other free parameter is the tensor to
scalar ratio. The simplest inflation models,
those without fine-tuning, predict a tensor
to scalar ratio near 0.1.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 Planck spacecraft, WMAP spacecraft
and other cosmic microwave background (CMB)
experiments, and galaxy surveys, especially
the ongoing Sloan Digital Sky Survey. These
experiments have shown that the one part in
100,000 inhomogeneities observed have exactly
the form predicted by theory. There is evidence
for a slight deviation from scale invariance.
The spectral index, ns is one for a scale-invariant
Harrison–Zel'dovich spectrum. The simplest
inflation models predict that ns is between
0.92 and 0.98. This is the range that is possible
without fine-tuning of the parameters related
to energy. From Planck data it can be inferred
that ns=0.968 ± 0.006, and a tensor to scalar
ratio that is less than 0.11. These are considered
an important confirmation of the theory of
inflation.Various inflation theories have
been proposed that make radically different
predictions, but they generally have much
more fine tuning than should be necessary.
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.
However, the third-year data revealed that
the effect was a statistical anomaly. Another
effect remarked upon since the first cosmic
microwave background satellite, the Cosmic
Background Explorer is that the amplitude
of the quadrupole moment of the CMB 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.An experimental program
is underway to further test inflation with
more precise CMB measurements. In particular,
high precision measurements of the so-called
"B-modes" of the polarization of the background
radiation could provide evidence of the gravitational
radiation produced by inflation, and could
also show whether the energy scale of inflation
predicted by the simplest models (1015–1016
GeV) is correct. In March 2014, it was announced
that B-mode CMB polarization consistent with
that predicted from inflation had been demonstrated
by a South Pole experiment. However, on 19
June 2014, lowered confidence in confirming
the findings was reported; on 19 September
2014, a further reduction in confidence was
reported and, on 30 January 2015, even less
confidence yet was reported.Other potentially
corroborating measurements are expected from
the Planck spacecraft, although it is unclear
if the signal will be visible, or if contamination
from foreground sources will interfere. Other
forthcoming measurements, such as those of
21 centimeter radiation (radiation emitted
and absorbed from neutral hydrogen before
the first stars formed), may measure the power
spectrum with even greater resolution than
the CMB 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.
== Theoretical status ==
In Guth's early proposal, it was thought that
the inflaton was the Higgs field, the field
that explains the mass of the elementary particles.
It is now believed by some that the inflaton
cannot be the Higgs field although the recent
discovery of the Higgs boson has increased
the number of works considering the Higgs
field as inflaton. One problem of this identification
is the current tension with experimental data
at the electroweak scale, which is currently
under study at the Large Hadron Collider (LHC).
Other models of inflation relied on the properties
of Grand Unified Theories. 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
such as string theory or a supersymmetric
grand unified theory. At present, while 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, although
predictions of inflation have been consistent
with the results of observational tests, many
open questions remain.
=== Fine-tuning problem ===
One of the most severe challenges for inflation
arises from the need for fine tuning. 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. New inflation requires
the Universe to have a scalar field with an
especially flat potential and special initial
conditions. However, explanations for these
fine-tunings have been proposed. For example,
classically scale invariant field theories,
where scale invariance is broken by quantum
effects, provide an explanation of the flatness
of inflationary potentials, as long as the
theory can be studied through perturbation
theory.Linde proposed a theory known as chaotic
inflation in which he suggested that the conditions
for inflation were actually satisfied quite
generically. Inflation will occur in virtually
any universe that begins in a chaotic, high
energy state that has a scalar field with
unbounded potential energy. 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. 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. 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.
Brandenberger commented on fine-tuning in
another situation. The amplitude of the primordial
inhomogeneities produced in inflation is directly
tied to the energy scale of inflation. This
scale is suggested to be around 1016 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 ===
In many models, the inflationary phase of
the Universe's expansion lasts forever in
at least some regions of the Universe. This
occurs because inflating regions expand very
rapidly, reproducing themselves. Unless the
rate of decay to the non-inflating phase is
sufficiently fast, new inflating regions are
produced more rapidly than non-inflating regions.
In such models, most of the volume of the
Universe is continuously inflating at any
given time.
All models of eternal inflation produce an
infinite, hypothetical multiverse, typically
a fractal. The multiverse theory has created
significant dissension in the scientific community
about the viability of the inflationary model.
Paul Steinhardt, one of the original architects
of the inflationary model, introduced the
first example of eternal inflation in 1983.
He showed that the inflation could proceed
forever by producing bubbles of non-inflating
space filled with hot matter and radiation
surrounded by empty space that continues to
inflate. The bubbles could not grow fast enough
to keep up with the inflation. Later that
same year, Alexander Vilenkin showed that
eternal inflation is generic.Although new
inflation is classically rolling down the
potential, quantum fluctuations can sometimes
lift it 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. It has
been shown that any inflationary theory with
an unbounded potential is eternal. There are
well-known theorems that this steady state
cannot continue forever into the past. 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 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.
In eternal inflation, regions with inflation
have an exponentially growing volume, while
regions that are not inflating don't. This
suggests 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, even though inflation
eventually ends as seen by any single pre-inflationary
observer. Scientists disagree about how to
assign a probability distribution to this
hypothetical anthropic landscape. If the probability
of different regions is counted by volume,
one should expect that inflation will never
end or applying boundary conditions that a
local observer exists to observe it, that
inflation will end as late as possible.
Some physicists believe this paradox can be
resolved by weighting observers by their pre-inflationary
volume. Others believe that there is no resolution
to the paradox and that the multiverse is
a critical flaw in the inflationary paradigm.
Paul Steinhardt, who first introduced the
eternal inflationary model, later became one
of its most vocal critics for this reason.
=== Initial conditions ===
Some physicists have tried to avoid the initial
conditions problem by proposing models for
an eternally inflating universe with no origin.
These models propose that while 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. Hartle and Hawking
offered the no-boundary proposal for the initial
creation of the Universe in which inflation
comes about naturally.Guth described the inflationary
universe as the "ultimate free lunch": new
universes, similar to our own, are continually
produced in a vast inflating background. Gravitational
interactions, in this case, circumvent (but
do not violate) the first law of thermodynamics
(energy conservation) and 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. Don Page was an outspoken critic
of inflation because of this anomaly. 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
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. 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. However,
Albrecht and Lorenzo Sorbo argued that the
probability of an inflationary cosmos, consistent
with today's observations, emerging by a random
fluctuation from some pre-existent state is
much higher than that of a non-inflationary
cosmos. This is because the "seed" amount
of non-gravitational energy required for the
inflationary cosmos is so much less than that
for a non-inflationary alternative, which
outweighs any entropic considerations.Another
problem that has occasionally been mentioned
is the trans-Planckian problem or trans-Planckian
effects. Since the energy scale of inflation
and the Planck scale are relatively close,
some of the quantum fluctuations that 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. Some disagreement
remains about the magnitude of this effect:
about whether it is just on the threshold
of detectability or completely undetectable.
=== Hybrid 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.In hybrid inflation, one scalar
field is responsible for most of the energy
density (thus determining the rate of expansion),
while another 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.
=== Relation to dark energy ===
Dark energy is broadly similar to inflation
and is thought to be causing the expansion
of the present-day universe to accelerate.
However, the energy scale of dark energy is
much lower, 10−12 GeV, roughly 27 orders
of magnitude less than the scale of inflation.
=== Inflation and string cosmology ===
The discovery of flux compactifications opened
the way for reconciling inflation and string
theory. Brane inflation suggests that inflation
arises from the motion of D-branes in the
compactified geometry, usually towards a stack
of anti-D-branes. This theory, governed by
the Dirac-Born-Infeld action, is 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
quantized spacetime. If the energy density
is larger than can be held by the quantized
spacetime, it is thought to bounce back.
== Alternatives/adjuncts ==
Other models explain some of the observations
explained by inflation. However none of these
"alternatives" has the same breadth of explanation
and still require inflation for a more complete
fit with observation. They should therefore
be regarded as adjuncts to inflation, rather
than as alternatives.
=== Big bounce ===
The big bounce hypothesis attempts to replace
the cosmic singularity with a cosmic contraction
and bounce, thereby explaining the initial
conditions that led to the big bang. The flatness
and horizon problems are naturally solved
in the Einstein-Cartan-Sciama-Kibble theory
of gravity, without needing an exotic form
of matter or free parameters. This theory
extends general relativity by removing a constraint
of the symmetry of the affine connection and
regarding its antisymmetric part, the torsion
tensor, as a dynamical variable. The minimal
coupling between torsion and Dirac spinors
generates a spin-spin interaction that is
significant in fermionic matter at extremely
high densities. Such an interaction averts
the unphysical Big Bang singularity, replacing
it with a cusp-like bounce at a finite minimum
scale factor, before which the Universe was
contracting. The rapid expansion immediately
after the Big Bounce explains why the present
Universe at largest scales appears spatially
flat, homogeneous and isotropic. As the density
of the Universe decreases, the effects of
torsion weaken and the Universe smoothly enters
the radiation-dominated era.
=== Ekpyrotic and cyclic models ===
The ekpyrotic and cyclic models are also considered
adjuncts 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 Richard Chace Tolman's oscillatory universe;
in Tolman's model, however, 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. Ekpyrotic models avoid
the magnetic monopole problem as long as the
temperature at the Big Crunch/Big Bang transition
remains below the Grand Unified Scale, as
this is the temperature required to produce
magnetic monopoles in the first place. As
things stand, there is no evidence of any
'slowing down' of the expansion, but this
is not surprising as each cycle is expected
to last on the order of a trillion years.
=== Varying c ===
Another adjunct, the varying speed of light
model was offered by Jean-Pierre Petit in
1988, John Moffat in 1992, and the two-man
team of Andreas Albrecht and João Magueijo
in 1998. Instead of superluminal expansion
the speed of light was 60 orders of magnitude
faster than its current value solving the
horizon and homogeneity problems in the early
universe.
=== String gas cosmology ===
String theory requires that, in addition to
the three observable spatial dimensions, additional
dimensions exist 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 raised the contingent 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. 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,
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. Supporters
admit that their model "does not solve the
entropy and flatness problems of standard
cosmology ..... and we can provide no explanation
for why the current universe is so close to
being spatially flat".
== Criticisms ==
Since its introduction by Alan Guth in 1980,
the inflationary paradigm has become widely
accepted. Nevertheless, many physicists, mathematicians,
and philosophers of science have voiced criticisms,
claiming untestable predictions and a lack
of serious empirical support. In 1999, John
Earman and Jesús Mosterín published a thorough
critical review of inflationary cosmology,
concluding, "we do not think that there are,
as yet, good grounds for admitting any of
the models of inflation into the standard
core of cosmology."In order to work, and as
pointed out by Roger Penrose from 1986 on,
inflation requires extremely specific initial
conditions of its own, so that the problem
(or pseudo-problem) of initial conditions
is not solved: "There is something fundamentally
misconceived about trying to explain the uniformity
of the early universe as resulting from a
thermalization process. [...] For, if the
thermalization is actually doing anything
[...] then it represents a definite increasing
of the entropy. Thus, the universe would have
been even more special before the thermalization
than after." The problem of specific or "fine-tuned"
initial conditions would not have been solved;
it would have gotten worse. At a conference
in 2015, Penrose said that "inflation isn't
falsifiable, it's falsified. [...] BICEP did
a wonderful service by bringing all the Inflation-ists
out of their shell, and giving them a black
eye."A recurrent criticism of inflation is
that the invoked inflation field does not
correspond to any known physical field, and
that its potential energy curve seems to be
an ad hoc contrivance to accommodate almost
any data obtainable. Paul Steinhardt, one
of the founding fathers of inflationary cosmology,
has recently become one of its sharpest critics.
He calls 'bad inflation' a period of accelerated
expansion whose outcome conflicts with observations,
and 'good inflation' one compatible with them:
"Not only is bad inflation more likely than
good inflation, but no inflation is more likely
than either [...] Roger Penrose considered
all the possible configurations of the inflaton
and gravitational fields. Some of these configurations
lead to inflation [...] Other configurations
lead to a uniform, flat universe directly
– without inflation. Obtaining a flat universe
is unlikely overall. Penrose's shocking conclusion,
though, was that obtaining a flat universe
without inflation is much more likely than
with inflation – by a factor of 10 to the
googol (10 to the 100) power!" Together with
Anna Ijjas and Abraham Loeb, he wrote articles
claiming that the inflationary paradigm is
in trouble in view of the data from the Planck
satellite. Counter-arguments were presented
by Alan Guth, David Kaiser, and Yasunori Nomura
and by Andrei Linde, saying that "cosmic inflation
is on a stronger footing than ever before".
== See also ==
Brane cosmology
Conservation of angular momentum
Cosmology
Dark flow
Doughnut theory of the universe
Hubble's law
Non-minimally coupled inflation
Nonlinear optics
Varying speed of light
Warm inflation
== Notes
