Cosmic inflation

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Physical cosmology
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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.


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 1026 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 1015 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.


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.


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.
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, ns 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 ns = 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 (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. 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 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

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.


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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