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In , 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 Fluctuation s 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 American physicist and cosmologist and Paul Steinhardt .A. Albrecht and P. J. Steinhardt, "Cosmology For Grand Unified Theories With Radiatively Induced Symmetry Breaking," ''Phys. Rev. Lett.'' 48, 1220 (1982). 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 See Also: Metric expansion of space Inflation suggests 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 , is nearly constant, which leads to high levels of symmetry. Inflation is often called a period 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 . Inflation also dilutes exotic heavy particles, such as the Magnetic Monopole s 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"Kolb and Turner (1988). by analogy with the No Hair Theorem for Black Hole s. The "no-hair" theorem works essentially because the universe expands by an enormous factor during inflation. In an expanding universe, Energy Densities generally fall 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 energy density in radiation goes down even more rapidly as the universe expands: 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. 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.This is usually quoted as 60 ''e''-folds of expansion, where ''e''60 ≈ 1026. It is equal to the amount of expansion since reheating, which is roughly ''E''inflation/''T''0, where T0 = 2.7 K is the temperature of the cosmic microwave background today. See, ''e.g.'' Kolb and Turner (1998) or Liddle and Lyth (2000). 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 1015 and 1016 GeV , as is suggested by the simplest models, the period of inflation responsible for the observable universe probably lasted roughly 10-33 seconds.This comes from the Friedmann Equation , which, written in terms of the Hubble time is , where is Newton's constant. Inflation is expected to last at least 60 Hubble times. This is a lower bound, however. The overall epoch of inflation could have been somewhat longer. MOTIVATION Inflation resolves Several Problems in the Big Bang cosmology that were pointed out in the 1970s.Much of the historical context is explained in chapters 15–17 of Peebles (1993). 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 near 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 natural in the context of the Big Bang theory. Horizon problem See Also: horizon problem The of Charles Misner .6 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 See Also: 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 ).78 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 Redshift s 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 , popular in the 1970 s and 1980 s, which proposed that at high temperatures (such as in the early universe) the Electromagnetic Force , Strong and Weak Nuclear Force s are not actually fundamental forces but arise due to Spontaneous Symmetry Breaking from a much simpler Gauge Theory .The importance of grand unification has waned somewhat since the early 1990 s, 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 9 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.1011 Monopoles are expected to be copiously produced in Grand Unified Theories at high temperature, and they should have persisted to the present day.1213 To very high precision, magnetic monopoles have been shown not to exist in natureSee, ''e.g.'' 14, 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.15 Contemporary with Guth, Alexei Starobinsky argued that quantum corrections to gravity would replace the initial singularity of the universe with an exponentially expanding state.16 Demosthenes Kazanas anticipated part of Guth's work by suggesting that exponential expansion could eliminate the Particle Horizon and perhaps solve the horizon problem,17 and Sato suggesting that an exponential expansion could eliminate Domain Wall s (another kind of exotic relic).18 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. , 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 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 ;21 Starobinsky;22 Guth and So-Young Pi ;23 and James M. Bardeen , Paul Steinhardt and Michael Turner .24 OBSERVATIONAL STATUS Inflation is a concrete mechanism for realizing the made by the Wilkinson Microwave Anisotropy Probe (WMAP) satellite.See, ''e.g.'' 25 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).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 ''k''³. 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 Survey s, especially the ongoing Sloan Digital Sky Survey .26 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 0.98.272829This is known as a "red" spectrum, in analogy to Redshift , because the spectrum has more power at longer wavelengths. The WMAP satellite has measured ''n''s = 0.95 and shown that it is different from one at the level of two Standard Deviation s (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.30 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 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 .See Cosmic Microwave Background#Low Multipoles for details and references. 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 (1015–1016 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.31 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.32 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 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.Technically, these conditions are that the Logarithmic Derivative of the potential, and second derivative are small, where is the potential and the equations are written in Reduced Planck Units . See, ''e.g.'' Liddle and Lyth (2000). 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.33 However, in his model the to Quantum Gravity ) in an important way, it has not been completely reconciled with these theories. . 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 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,37 is called "eternal inflation". It has been shown that any inflationary theory with an unbounded potential is eternal.38 39 It is a popular belief among physicists that this steady state cannot continue forever into the past.404142 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. This interpretation is disputed by Linde, however.Linde (2005, §V). Initial conditions Some physicists have tried to avoid this problem by proposing models for an eternally inflating universe with no origin.4344Anthony Aguirre, Steven Gratton, ''Inflation without a beginning: A null boundary proposal'', Phys.Rev. D67 (2003) 083515, Aguirre, Steven Gratton, ''Steady-State Eternal Inflation'', Phys.Rev. D65 (2002) 083507, [http://arxiv.org/abs/astro-ph/0111191 These models propose a special "initial" hypersurface when the universe has some minimum size and from which time begins. Other proposals attempt to describe the ex nihilo creation of the universe Quantum Cosmology and the following inflation. Vilenkin put forth one such scenario. Hartle and Hawking proposed the No-boundary Proposal for the initial creation of the universe in which inflation comes about naturally.J. Hartle and S. W. Hawking, "Wave function of the universe", ''Phys. Rev.'' D28, 2960 (1983). See also Hawking (1998). Alan Guth has described the inflationary universe as the "ultimate free lunch":Hawking (1998), p. 129. Wikiquote 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 . 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.45 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 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.46 Another problem that has occasionally been mentioned is the trans-Planckian problem or trans-Planckian effects.47 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 .See Kolb and Turner (1988) or Mukhanov (2005).48 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.Robert H. Brandenberger, "A Status Review of Inflationary Cosmology", proceedings Journal-ref: BROWN-HET-1256 (2001), (available from v1 11 Jan 2001) Unlike most other models of inflation, many versions of hybrid inflation are not eternal. Andrei Linde, "Prospects of Inflation", ''Physica Scripta Online'' (2004) (available from ) Blanco-Pallido et al. , "Racetrack inflation", (2004) (available from ) 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 at 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 this inflaton down its potential, leading to termination of inflation. Inflation and string cosmology The discovery of Flux Compactification s have opened the way for reconciling inflation and string theory.49 A new theory, called Brane Inflation suggests that inflation arises from the motion of D-brane sG. R. Dvali, S. H. Henry Tye, ''Brane inflation,'' ''Phys.Lett.'' B450, 72-82 (1999), .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. 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 Robert H. Brandenberger and C. Vafa, ''Superstrings in the early universe,'' ''Nucl. Phys.'' B316, 391 (1989). 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 Thorsten Battefeld and Scott Watson, ''String Gas Cosmology'', ''Rev. Mod. Phys'' '''78''', 435-454 (2006)Robert H. Brandenberger, Ali Nayeri, Subodh P. Patil and Cumrun Vafa, ''String Gas Cosmology and Structure Formation'', IJMPA-D-07-00102 (2007), . The Ekpyrotic and Cyclic Model s 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. SEE ALSO NOTES REFERENCES
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