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Cosmic inflation

2007 Schools Wikipedia Selection. Related subjects: Space (Astronomy)

          Physical cosmology

     * Age of the universe
     * Big Bang
     * Comoving distance
     * Cosmic microwave background
     * Dark energy
     * Dark matter
     * FLRW metric
     * Friedmann equations
     * Galaxy formation
     * Hubble's law
     * Inflation
     * Large-scale structure
     * Lambda-CDM model
     * Metric expansion of space
     * Nucleosynthesis
     * Observable universe
     * Redshift
     * Shape of the universe
     * Structure formation
     * Timeline of the Big Bang
     * Timeline of cosmology
     * Ultimate fate of the universe
     * Universe

            Related topics
     * Astrophysics
     * General relativity
     * Particle physics
     * Quantum gravity


   In physical cosmology, cosmic inflation is the idea that the nascent
   universe passes through a phase of exponential expansion that was
   driven by a negative-pressure vacuum energy density. As a direct
   consequence of this expansion, all of the observable universe
   originated in a small causally-connected region. Inflation answers the
   classic conundrums 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, inhomogeneous 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).

   Inflation was first proposed by Alan Guth in 1981 and was given its
   modern form independently by Andrei Linde, and by Andreas Albrecht and
   Paul Steinhardt.

   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 observational tests. 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

   Inflation posits that there was a period of exponential expansion in
   the very early universe. The expansion is exponential because the
   distance between any two fixed observers is increasing exponentially,
   due to the metric expansion of space (a spacetime with this property is
   called a de Sitter space). This form of expansion is special because
   the physical conditions from one moment to the next are stable: the
   rate of expansion, called the Hubble parameter, is nearly constant, and
   the universe is consequently in a highly symmetric state. Inflation is
   often called an epoch of accelerated expansion because the distance
   between two fixed observers is increasing at an accelerating rate as
   they move apart. (However, this does not mean that the Hubble parameter
   is increasing, see deceleration parameter.)

   Cosmic 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 and the only significant
   inhomogeneities are the tiny quantum fluctuations in the inflaton.
   Another major problem solved by inflation is that it dilutes exotic
   heavy particles: most extensions to the Standard Model of particle
   physics predict very heavy particles, such as magnetic monopoles, which
   are not found in nature. However, 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.

   In an expanding universe, energy densities are falling because the
   volume of the universe is increasing. For example, in a universe filled
   with ordinary matter, such as dust, the density of matter goes as the
   inverse of the volume: when linear dimensions double, the density goes
   down by a factor of eight, and the Hubble parameter falls by roughly a
   factor of three. Similarly, in universe which is filled with radiation,
   the density and Hubble parameter diminish even more quickly: when the
   universe expands so linear dimensions are doubled, the average energy
   density of the universe is reduced by a factor of sixteen and the
   Hubble parameter falls by a factor of four. According to the standard
   big bang theory, the universe is largely filled with matter now, and
   the early universe was filled with radiation in the form of a
   primordial plasma. The densities of matter and radiation actually fall
   faster than the densities of inhomogeneities, curvature and exotic
   particles, so that the overall contribution of these is actually
   growing in the present universe. To explain why they are presently so
   small, in cosmic inflation the energy density of the inflaton and the
   Hubble parameter change only very slowly relative to the rate of
   expansion of the universe, while the other contributions disappear
   quickly, leaving an empty, symmetric universe.

   Inflation must continue long enough that the observable universe came
   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. To ensure this, it is generally thought that
   the universe has expanded by a factor of at least 10^26 during
   inflation. At the end of inflation, a process called reheating occurs,
   in which the inflaton particles decay into the radiation that starts
   the hot big bang. It is not known how long inflation lasted but it is
   usually thought to be extremely short compared to the age of the
   universe. Assuming that the energy scale of inflation is between 10^15
   and 10 ^16 GeV, as is suggested by the simplest models, the period of
   inflation responsible for the observable universe probably lasted
   roughly 10^-33 seconds.

Motivation

   Inflation resolves several problems in the Big Bang cosmology that were
   pointed out in the 1970s. These problems all suggest that the universe
   has wildly absurd initial conditions, but are resolved very nicely in
   the context of cosmic inflation.

Horizon problem

   The horizon problem is the problem of determining why the universe
   appears statistically homogeneous and isotropic in accordance with the
   cosmological principle. The gas 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 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 impossible that they
   have 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 and 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

   Another problem is the flatness problem (which is sometimes called one
   of the Dicke coincidences, with the other being the cosmological
   constant problem). It had been 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 the accuracy of a
   few percent.

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, which were
   popular in the 1970s and 1980s, 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.
   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.
   Monopoles are expected to be copiously produced in Grand Unified
   Theories at high temperature, and they should have persisted to the
   present day. To very high precision, magnetic monopoles have been shown
   not to exist in nature whereas according to the big bang theory
   (without cosmic inflation) they should have been copiously produced in
   the hot, dense early universe and since become the primary constituent
   of the universe.

History

   Inflation was proposed in 1981 by Alan Guth as a mechanism for
   resolving these problems. There were several precursors, most
   importantly the work of Willem de Sitter which demonstrated the
   existence of a highly symmetric inflating universe, called de Sitter
   space. De Sitter, however, didn't apply it to any of the cosmological
   problems that interested Guth. Contemporary with Guth, Alexei
   Starobinsky argued that quantum corrections to gravity would replace
   the initial singularity of the universe with an exponentially expanding
   state. Demosthenes Kazanas anticipated part of Guth's work by
   suggesting that exponential expansion could eliminate the particle
   horizon and perhaps solve the horizon problem, and Sato suggesting that
   an exponential expansion could eliminate domain walls (another kind of
   exotic relic). However, Guth was the first to assemble a complete
   picture of how all these initial conditions problems could be solved by
   an exponentially expanding state.
   The physical size of the Hubble radius (solid line) as a function of
   the linear expansion (scale factor) of the universe. During cosmic
   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 cosmic
   inflation before coming back inside the horizon, which grows rapidly
   during radiation domination. If cosmic inflation never happened, and
   radiation domination continued back until a gravitational singularity,
   then the mode would never been inside the horizon in the very early
   universe, at no causal mechanism could have ensured that the universe
   was homogeneous on the scale of the perturbation mode.
   Enlarge
   The physical size of the Hubble radius (solid line) as a function of
   the linear expansion (scale factor) of the universe. During cosmic
   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 cosmic
   inflation before coming back inside the horizon, which grows rapidly
   during radiation domination. If cosmic inflation never happened, and
   radiation domination continued back until a gravitational singularity,
   then the mode would never been inside the horizon in the very early
   universe, at 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. (Even
   though the bubbles are expanding at the speed of light, the bubbles are
   far enough apart that the expansion of space is causing the distance
   between them to expand much faster.)

   This problem was solved by Andrei 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.

   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. 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 James
   M. Bardeen, Steinhardt and Michael Turner.

Observational status

   Inflation is a concrete mechanism for realizing the cosmological
   principle which is the basis of our model of physical cosmology: it
   accounts for the homogeneity, 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) satellite. 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.

   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). 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 satellite and other cosmic
   microwave background experiments, and galaxy surveys, especially the
   ongoing Sloan Digital Sky Survey. These experiments have shown that the
   one part in 10,000 inhomogeneities observed have exactly the form
   predicted by theory. Moreover, the slight deviation from scale
   invariance has been measured. 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. The WMAP satellite
   has measured n[s] = 0.95 and shown that it is different from one at the
   level of two standard deviations (2σ). This is considered an important
   confirmation of the theory of inflation.

   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. 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 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.

   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. These measurements are expected to be
   performed by the Planck satellite, although it is unclear if the signal
   will be visible, or if contamination from foreground sources will
   interfere with these measurements. 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.

   As of 2006, it is unclear what relationship if any the period of cosmic
   inflation has to do with 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.

Theoretical status

   Unsolved problems in physics: Is the theory of cosmic inflation
   correct, and if so, what are the details of this epoch? What is the
   hypothetical inflaton field giving rise to inflation?

   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. It is now known that the inflaton cannot be the Higgs field.
   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 like string theory or a supersymmetric grand
   unified theory. A promising suggestion is brane inflation. At present,
   however, inflation is understood principally by its detailed
   predictions of the initial conditions for the hot early universe, and
   the particle physics is largely ad hoc modelling. As such, despite the
   stringent 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. 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 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. 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, and
   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 of inflation. 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.
   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

   Cosmic inflation is generally eternal: that is, the process continues
   forever. Although the scalar field in new inflation is classically
   rolling down the potential, quantum fluctuations occasionally bring it
   back up. These regions in which the inflaton fluctuates upwards expand
   much faster than regions in which the inflaton has a lower potential
   energy. Thus, while inflation ends in some regions, the regions in
   which it continues are growing exponentially, and thus continue to
   dominate in terms of physical volume. This steady state, which was
   first described by Alexander Vilenkin, in which inflation ends in some
   regions while quantum mechanical fluctuations keep it going in the
   majority of the universe, is called "eternal inflation". It was shown
   by Linde that inflation in any theory with an unbounded potential is
   eternal. This is usually called "chaotic eternal inflation." It is
   widely thought that this steady state cannot continue indefinitely to
   the past. Roughly speaking, 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 inevitably collapse to form a gravitational
   singularity instead of matching onto an expanding spacetime. Therefore,
   it is thought that the inflationary steady state must be supplemented
   by a theory of the initial conditions of the universe. This
   interpretation is disputed by Linde, however.

Initial conditions

   Some authors have tried to resolve this, and circumvent the failure of
   past eternal inflation, by proposing models for an eternally inflating
   universe with no beginning. These models solve the problems of eternal
   inflation by postulating a special "initial" hypersurface when the
   universe has some minimum size and from which the arrow of time
   originates.

   Other proposals attempt to describe the creation of the universe from
   nothing in quantum cosmology and the subsequent onset of inflation.
   Vilenkin proposed a scenario in which the inflationary universe is
   created from nothing. Most famously, Hartle and Hawking proposed a
   concrete theory (the no-boundary proposal) for the initial creation of
   the universe in which Hawking expects inflation to arise naturally.

   Alan Guth has 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) both the first law of thermodynamics or
   energy conservation and the second law of thermodynamics or the arrow
   of time problem. However, while it is generally agreed upon that
   inflation, once begun, solves the initial condition problem for the big
   bang, some authors have argued that inflation actually exacerbates the
   initial conditions problem: it is much less likely for inflation to
   begin in the early universe than it is for the universe to wind up in
   its present state through a quantum fluctuation. Donald N. Page
   criticised inflation on these grounds. Page emphasized that the
   thermodynamic arrow of time in a Big Bang type of theory necessarily
   requires low entropy initial conditions, which Page argued would be
   extremely improbable. According to them, rather than solving this
   problem, the inflation theory further aggravates it – the reheating or
   thermalization 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. Recently, Lisa Dyson, Matthew Kleban and Leonard Susskind
   argued using the holographic principle that spontaneous inflation is
   exceedingly improbable. 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.

   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 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.

Reheating

   The end of inflation is called reheating or thermalization because the
   large potential energy decays into particles and fills the universe
   with 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.

Other models of 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. Unlike most other models of inflation,
   many versions of hybrid inflation are not eternal.

Inflation and string theory

   The discovery of flux compactifications have opened the way to
   reconciling inflation and string theory. A new theory, called brane
   inflation suggests that inflation arises from a D-brane falling into a
   deep Klebanov-Strassler throat. This is a very different theory than
   ordinary inflation (it is governed by the Dirac-Born-Infeld action
   which is very different that the other one) and the dynamics are still
   being understood. It appears that very special conditions are necessary
   for inflation occurs in tunneling between two vacua in the string
   landscape (the process of tunneling between two vacua is a kind of old
   inflation, but new inflation must then occur by some other mechanism.

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 begs the question: why did
   four space-time dimensions become large, and the rest become
   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, 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 .

   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 Chase 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.
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