"Inflation model" and "Inflation theory" redirect here. For a general rise in the price level, seeInflation. For other uses, seeInflation (disambiguation).
Inphysical cosmology,cosmic inflation,cosmological inflation, or justinflation, is a theory of exponentialexpansion of space in the very earlyuniverse. Following the inflationary period, the universe continued to expand, but at a slower rate. The re-acceleration of this slowing expansion due todark energy began after the universe was already over 7.7 billion years old (5.4 billion years ago).[1]
The detailedparticle physics mechanism responsible for inflation is unknown. A number of inflation model predictions have been confirmed by observation; for example temperature anisotropies observed by the COBE satellite in 1992 exhibit nearly scale-invariant spectra as predicted by the inflationary paradigm andWMAP results also show strong evidence for inflation.[4] However, some scientists dissent from this position.[5][6][7] The hypotheticalfield thought to be responsible for inflation is called theinflaton.[8]
Around 1930,Edwin Hubble discovered that light from remote galaxies wasredshifted; the more remote, the more shifted. This implies that the galaxies are receding from the Earth, with more distant galaxies receding more rapidly, such that galaxies also recede from each other. Thisexpansion of the universe was previously predicted byAlexander Friedmann andGeorges Lemaître from the theory ofgeneral relativity. It can be understood as a consequence of an initial impulse, which sent the contents of the universe flying apart at such a rate that their mutual gravitational attraction has not reversed their increasing separation.
Inflation may have provided this initial impulse. According to theFriedmann equations that describe the dynamics of an expanding universe, afluid with sufficiently negative pressure exerts gravitational repulsion in the cosmological context. Afield in a positive-energyfalse vacuum state could represent such a fluid, and the resulting repulsion would set the universe into exponential expansion. Thisinflation phase was originally proposed byAlan Guth in 1979 because the exponential expansion could dilute exotic relics, such asmagnetic monopoles, that were predicted bygrand unified theories at the time. This would explain why such relics were not seen. It was quickly realized that such accelerated expansion would resolve thehorizon problem and theflatness problem. These problems arise from the notion that to look like it doestoday, the Universe must have started from veryfinely tuned, or "special", initial conditions at the Big Bang.
An expanding universe generally has acosmological horizon, which, by analogy with the more familiarhorizon caused by the curvature ofEarth's surface, marks the boundary of the part of the Universe that an observer can see. Light (or other radiation) emitted by objects beyond the cosmological horizon in anaccelerating universe never reaches the observer, because the space in between the observer and the object is expanding too rapidly.
Theobservable universe is onecausal patch of a much larger unobservable universe; other parts of the Universe cannot communicate with Earth yet. These parts of the Universe are outside our current cosmological horizon, which is believed to be 46 billion light years in all directions from Earth.[14] In the standard hot big bang model, without inflation, the cosmological horizon moves out, bringing new regions into view.[15] Yet as a local observer sees such a region for the first time, it looks no different from any other region of space the local observer has already seen: Its background radiation is at nearly the same temperature as the background radiation of other regions, and its space-time curvature is evolving lock-step with the others. This presents a mystery: how did these new regions know what temperature and curvature they were supposed to have? They could not have learned it by getting signals, because they were not previously in communication with our pastlight cone.[16][17]
Inflation answers this question by postulating that all the regions come from an earlier era with a big vacuum energy, orcosmological constant. A space with a cosmological constant is qualitatively different: instead of moving outward, the cosmological horizon stays put. For any one observer, the distance to thecosmological horizon is constant. With exponentially expanding space, two nearby observers are separated very quickly; so much so, that the distance between them quickly exceeds the limits of communication. The spatial slices are expanding very fast to cover huge volumes. Things are constantly moving beyond the cosmological horizon, which is a fixed distance away, and everything becomes homogeneous.
As the inflationary field slowly relaxes to the vacuum, the cosmological constant goes to zero and space begins to expand normally. The new regions that come into view during the normal expansion phase are exactly the same regions that were pushed out of the horizon during inflation, and so they are at nearly the same temperature and curvature, because they come from the same originally small patch of space.
The theory of inflation thus explains why the temperatures and curvatures of different regions are so nearly equal. It also predicts that the total curvature of a space-slice at constant global time is zero. This prediction implies that the total ordinary matter,dark matter and residualvacuum energy in the Universe have to add up to thecritical density, and the evidence supports this. More strikingly, inflation allows physicists to calculate the minute differences in temperature of different regions from quantum fluctuations during the inflationary era, and many of these quantitative predictions have been confirmed.[18][19]
In a space that expands exponentially (or nearly exponentially) with time, any pair of free-floating objects that are initially at rest will move apart from each other at an accelerating rate, at least as long as they are not bound together by any force. From the point of view of one such object, the spacetime is something like an inside-outSchwarzschild black hole—each object is surrounded by a spherical event horizon. Once the other object has fallen through this horizon it can never return, and even light signals it sends will never reach the first object (at least so long as the space continues to expand exponentially).
In the approximation that the expansion is exactly exponential, the horizon is static and remains a fixed physical distance away. This patch of an inflating universe can be described by the followingmetric:[20][21]
This exponentially expanding spacetime is called ade Sitter space, and to sustain it there must be acosmological constant, avacuum energy density that is constant in space and time and proportional to Λ in the above metric. For the case of exactly exponential expansion, the vacuum energy has a negative pressurep equal in magnitude to its energy densityρ; theequation of state isp=−ρ.
Inflation is typically not an exactly exponential expansion, but rather quasi- or near-exponential. In such a universe the horizon will slowly grow with time as the vacuum energy density gradually decreases.
Because the accelerating expansion of space stretches out any initial variations in density or temperature to very large length scales, an essential feature of inflation is that it smooths outinhomogeneities andanisotropies, and reduces thecurvature of space. This pushes the Universe into a very simple state in which it is completely dominated by theinflaton field and the only significant inhomogeneities are tinyquantum fluctuations. Inflation also dilutes exotic heavy particles, such as themagnetic monopoles predicted by many extensions to theStandard Model ofparticle physics. If the Universe was only hot enough to form such particlesbefore 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 theobservable universe. Together, these effects are called the inflationary "no-hair theorem"[22] by analogy with theno hair theorem forblack holes.
The "no-hair" theorem works essentially because the cosmological horizon is no different from a black-hole horizon, except for not testable disagreements about what is on the other side. The interpretation of the no-hair theorem is that the Universe (observable and unobservable) expands by an enormous factor during inflation. In an expanding universe,energy densities generally fall, or get diluted, as the volume of the Universe increases. For example, the density of ordinary "cold" matter (dust) declines as the inverse of the volume: when linear dimensions double, the energy density declines by a factor of eight; the radiation energy density declines even more rapidly as the Universe expands since the wavelength of eachphoton is stretched (redshifted), in addition to the photons being dispersed by the expansion. When linear dimensions are doubled, the energy density in radiation falls by a factor of sixteen (seethe solution of the energy density continuity equation for an ultra-relativistic fluid). During inflation, the energy density in the inflaton field is roughly constant. However, the energy density in everything else, including inhomogeneities, curvature, anisotropies, exotic particles, and standard-model particles is falling, and through sufficient inflation these all become negligible. This leaves the Universe flat and symmetric, and (apart from the homogeneous inflaton field) mostly empty, at the moment inflation ends and reheating begins.[a]
Inflation is a period of supercooled expansion, when the temperature drops by a factor of 100,000 or so. (The exact drop is model-dependent, but in the first models it was typically from 1027 K down to 1022 K.[24]) This relatively low temperature is maintained during the inflationary phase. When inflation ends, the temperature returns to the pre-inflationary temperature; this is calledreheating or thermalization because the large potential energy of the inflaton field decays into particles and fills the Universe withStandard Model particles, includingelectromagnetic radiation, starting theradiation dominated phase of the Universe. Because the nature of the inflaton field is not known, this process is still poorly understood, although it is believed to take place through aparametric resonance.[25][26]
Inflation tries to resolveseveral problems inBig Bang cosmology that were discovered in the 1970s.[27] Inflation was first proposed by Alan Guth in 1979 while investigating the problem of why nomagnetic monopoles are seen today; he found that a positive-energyfalse vacuum would, according togeneral relativity, generate an exponential expansion of space. It was quickly realised that such an expansion would resolve many other long-standing problems. These problems arise from the observation that to look like it doestoday, the Universe would have to have started from veryfinely tuned, or "special" initial conditions at the Big Bang. Inflation attempts to resolve these problems by providing a dynamical mechanism that drives the Universe to this special state, thus making a universe like ours much more likely in the context of the Big Bang theory.
Thehorizon problem is the problem of determining why the universe appears statistically homogeneous and isotropic in accordance with thecosmological principle.[28][29][30] For example, molecules in a canister of gas are distributed homogeneously and isotropically because they are in thermal equilibrium: gas throughout the canister has had enough time to interact to dissipate inhomogeneities and anisotropies. The situation is quite different in the big bang model without inflation, because gravitational expansion does not give the early universe enough time to equilibrate. In a big bang with only thematter andradiation known in the Standard Model, two widely separated regions of the observable universe cannot have equilibrated because they move apart from each other faster than thespeed of light and thus have never come intocausal contact. In the early Universe, it was not possible to send a light signal between the two regions. Because they have had no interaction, it is difficult to explain why they have the same temperature (are thermally equilibrated). Historically, proposed solutions included thePhoenix universe of Georges Lemaître,[31] the relatedoscillatory universe ofRichard Chase Tolman,[32] and theMixmaster universe ofCharles 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 ofentropy over several cycles. Misner made the (ultimately incorrect) conjecture that the Mixmaster mechanism, which made the Universemore chaotic, could lead to statistical homogeneity and isotropy.[29][33]
Therefore, regardless of theshape 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 curvatureredshifts away more slowly than matter and radiation. Extrapolated into the past, this presents afine-tuning problem because the contribution of curvature to the Universe must be exponentially small (sixteen orders of magnitude less than the density of radiation atBig Bang nucleosynthesis, for example). Observations of the cosmic microwave background have demonstrated that the Universe is flat to within a few percent.[37]
Stable magnetic monopoles are a problem forGrand Unified Theories, which propose that at high temperatures (such as in the early universe), theelectromagnetic force,strong, andweaknuclear forces are not actually fundamental forces but arise due tospontaneous symmetry breaking from a singlegauge theory. These theories predict a number of heavy, stable particles that have not been observed in nature. The most notorious is the magnetic monopole, a kind of stable, heavy "charge" of magnetic field.[38][39]
Monopoles are predicted to be copiously produced following Grand Unified Theories at high temperature,[40][41] and they should have persisted to the present day, to such an extent that they would become the primary constituent of the Universe.[42][43] Not only is that not the case, but all searches for them have failed, placing stringent limits on the density of relic magnetic monopoles in the Universe.[44]
A period of inflation that occurs below the temperature where magnetic monopoles can be produced would offer a possible resolution of this problem: Monopoles would be separated from each other as the Universe around them expands, potentially lowering their observed density by many orders of magnitude. Though, as cosmologistMartin Rees has written,
"Skeptics about exotic physics might not be hugely impressed by a theoretical argument to explain the absence of particles that are themselves only hypothetical. Preventive medicine can readily seem 100 percent effective against a disease that doesn't exist!"[45]
In the early days ofgeneral relativity,Albert Einstein introduced thecosmological constant to allow astatic solution, which was athree-dimensional sphere with a uniform density of matter. Later,Willem de Sitter found a highly symmetric inflating universe, which described a universe with a cosmological constant that is otherwise empty.[46] It was discovered that Einstein's universe is unstable, and that small fluctuations cause it to collapse or turn into a de Sitter universe.
In 1965, Erast Gliner proposed a unique assumption regarding the early Universe's pressure in the context of the Einstein–Friedmann equations. According to his idea, the pressure was negatively proportional to the energy density. This relationship between pressure and energy density served as the initial theoretical prediction of dark energy.[citation needed]
In the early 1970s,Yakov Zeldovich noticed the flatness and horizon problems of Big Bang cosmology; before his work, cosmology was presumed to be symmetrical on purely philosophical grounds.[6] In the Soviet Union, this and other considerations ledVladimir Belinski andIsaak Khalatnikov to analyze the chaoticBKL singularity in general relativity.[citation needed] Misner'sMixmaster universe attempted to use this chaotic behavior to solve the cosmological problems, with limited success.[citation needed]
In the late 1970s,Sidney Coleman applied theinstanton techniques developed byAlexander Polyakov and collaborators to study the fate of thefalse vacuum inquantum field theory. Like a metastable phase instatistical mechanics—water below the freezing temperature or above the boiling point—a quantum field would need to nucleate a large enough bubble of the new vacuum, the new phase, in order to make a transition. Coleman found the most likely decay pathway for vacuum decay and calculated the inverse lifetime per unit volume. He eventually noted that gravitational effects would be significant, but he did not calculate these effects and did not apply the results to cosmology.
The universe could have been spontaneously created from nothing (nospace,time, normatter) byquantum fluctuations of metastable false vacuum causing an expanding bubble of true vacuum.[47]
In 1978 and 1979,Robert Brout,François Englert and Edgard Gunzig suggested that the universe could originate from a fluctuation of Minkowski space which would be followed by a period in which the geometry would resemble De Sitter space.This initial period would then evolve into the standard expanding universe. They noted that their proposal makes the universe causal, as there are neither particle nor event horizons in their model.[48]
In the Soviet Union,Alexei Starobinsky noted that quantum corrections to general relativity should be important for the early universe. These generically lead to curvature-squared corrections to theEinstein–Hilbert action and a form off(R) modified gravity. The solution to Einstein's equations in the presence of curvature squared terms, when the curvatures are large, leads to an effective cosmological constant. Therefore, he proposed that the early universe went through an inflationary de Sitter era.[49] This resolved the cosmology problems and led to specific predictions for the corrections to the microwave background radiation, corrections that were then calculated in detail. Starobinsky used the action
which corresponds to the potential
in the Einstein frame. This results in the observables:[50]
In 1978, Zeldovich noted the magnetic monopole problem, which was an unambiguous quantitative version of the horizon problem, this time in a subfield of particle physics, which led to several speculative attempts to resolve it. In 1980, Alan Guth realized that false vacuum decay in the early universe would solve the problem, leading him to propose a scalar-driven inflation. Starobinsky's and Guth's scenarios both predicted an initial de Sitter phase, differing only in mechanistic details.
The physical size of theHubble radius (solid line) as a function of the linear expansion (scale factor) of the universe. During cosmological inflation, the Hubble radius is constant. The physical wavelength of a perturbation mode (dashed line) is also shown. The plot illustrates how the perturbation mode grows larger than the horizon during cosmological inflation before coming back inside the horizon, which grows rapidly during radiation domination. If cosmological inflation had never happened, and radiation domination continued back until agravitational singularity, then the mode would never have been inside the horizon in the very early universe, and nocausal mechanism could have ensured that the universe was homogeneous on the scale of the perturbation mode.
Guth proposed inflation in January 1981 to explain the nonexistence of magnetic monopoles;[51][52] it was Guth who coined the term "inflation".[53] At the same time, Starobinsky argued that quantum corrections to gravity would replace the supposed initial singularity of the Universe with an exponentially expanding de Sitter phase.[54] In October 1980, Demosthenes Kazanas suggested that exponential expansion could eliminate theparticle horizon and perhaps solve the horizon problem,[55][56] whileKatsuhiko Sato suggested that an exponential expansion could eliminatedomain walls (another kind of exotic relic).[57] In 1981, Einhorn and Sato[58] published a model similar to Guth's and showed that it would resolve the puzzle of themagnetic monopole abundance in Grand Unified Theories. Like Guth, they concluded that such a model not only required fine tuning of the cosmological constant, but also would likely lead to a much too granular universe, i.e., to large density variations resulting from bubble wall collisions.
Guth proposed that as the early universe cooled, it was trapped in a false vacuum with a high energy density, which is much like a cosmological constant. As the very early universe cooled it was trapped in ametastable state (it was supercooled), which it could only decay out of through the process ofbubble nucleation viaquantum tunneling. Bubbles oftrue vacuum spontaneously form in the sea of false vacuum and rapidly begin expanding at thespeed of light. Guth recognized that this model was problematic because the model did not reheat properly: when the bubbles nucleated, they did not generate radiation. Radiation could only be generated in collisions between bubble walls. But if inflation lasted long enough to solve the initial conditions problems, collisions between bubbles became exceedingly rare. In any one causal patch it is likely that only one bubble would nucleate.
...Kazanas (1980) called this phase of the early Universe "de Sitter's phase". The name "inflation" was given byGuth (1981). ... Guth himself did not refer to work of Kazanas until he published a book on the subject, under the titleThe Inflationary Universe: The quest for a new theory of cosmic origin (1997),[59] where he apologizes for not having referenced the work of Kazanas and of others, related to inflation.[60]
The bubble collision problem was solved byAndrei Linde[61] and independently byAndreas Albrecht andPaul Steinhardt[62] in a model namednew inflation orslow-roll inflation (Guth's model then became known asold inflation). In this model, instead of tunneling out of a false vacuum state, inflation occurred by ascalar 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 quantum fluctuations in the inflaton are created. These fluctuations form the primordial seeds for all structure created in the later universe.[63] These fluctuations were first calculated byViatcheslav Mukhanov and G. V. Chibisov in analyzing Starobinsky's similar model.[64][65][66] 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 atCambridge University.[67] The fluctuations were calculated by four groups working separately over the course of the workshop:Stephen Hawking;[68] Starobinsky;[69]Alan Guth andSo-Young Pi;[70] andJames Bardeen,Paul Steinhardt andMichael Turner.[71]
Inflation is a mechanism for realizing thecosmological principle, which is the basis of the standard model of physical cosmology: it accounts for the homogeneity and isotropy of the observable universe. In addition, it accounts for the observed flatness and absence of magnetic monopoles. Since Guth's early work, each of these observations has received further confirmation, most impressively by the detailed observations of thecosmic microwave background made by thePlanck spacecraft.[72] This analysis shows that the Universe is flat to within 1 /2 percent, and that it is homogeneous and isotropic to one part in 100,000.
Inflation predicts that the structures visible in the Universe today formed through thegravitational collapse of perturbations that were formed as quantum mechanical fluctuations in the inflationary epoch. The detailed form of the spectrum of perturbations, called anearly-scale-invariantGaussian random field is very specific and has only two free parameters. One is the amplitude of the spectrum and thespectral index, which measures the slight deviation from scale invariance predicted by inflation (perfect scale invariance corresponds to the idealizedde Sitter universe).[b]The other free parameter is the tensor to scalar ratio. The simplest inflation models, those withoutfine-tuning, predict atensor to scalar ratio near 0.1 .[73]
Inflation predicts that the observed perturbations should be inthermal equilibrium with each other (these are calledadiabatic orisentropic perturbations). This structure for the perturbations has been confirmed by thePlanck spacecraft,WMAP spacecraft and other cosmic microwave background (CMB) experiments, andgalaxy surveys, especially the ongoingSloan Digital Sky Survey.[74] These experiments have shown that the one part in 100,000 inhomogeneities observed have exactly the form predicted by theory. There is evidence for a slight deviation from scale invariance. Thespectral index,ns is one for a scale-invariant Harrison–Zel'dovich spectrum. The simplest inflation models predict thatns is between 0.92 and 0.98 .[75][73][76][c] This is the range that is possible withoutfine-tuning of the parameters related to energy.[76] From Planck data it can be inferred thatns=0.968 ± 0.006,[72][77] and atensor to scalar ratio that is less than 0.11 . These are considered an important confirmation of the theory of inflation.[18]
Various inflation theories have been proposed that make radically different predictions, but they generally have much morefine-tuning than should be necessary.[75][73] 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-yearWMAP data suggested that the spectrum might not be nearly scale-invariant, but might instead have a slight curvature.[78] However, the third-year data revealed that the effect was a statistical anomaly.[18] Another effect remarked upon since the first cosmic microwave background satellite, theCosmic Background Explorer is that the amplitude of thequadrupole moment of the CMB is unexpectedly low and the other low multipoles appear to be preferentially aligned with theecliptic plane. Some have claimed that this is a signature ofnon-Gaussianity and thus contradicts the simplest models of inflation. Others have suggested that the effect may be due to quantum corrections or new physics, foreground contamination, or evenpublication bias.[79]
An experimental program is underway to further test inflation with more precise CMB measurements. In particular, high precision measurements of the so-called "B-modes" of thepolarization of the background radiation could provide evidence of thegravitational radiation produced by inflation, and could also show whether the energy scale of inflation predicted by the simplest models (1015~1016GeV) is correct.[73][76] In March 2014, theBICEP2 team announced B-mode CMB polarization confirming inflation had been demonstrated. The team announced the tensor-to-scalar power ratior was between 0.15 and 0.27 (rejecting thenull hypothesis;r is expected to be 0 in the absence of inflation).[80] However, on 19 June 2014, lowered confidence in confirming the findings was reported;[81][82][83] on 19 September 2014, a further reduction in confidence was reported[84][85] and, on 30 January 2015, even less confidence yet was reported.[86][87] By 2018, additional data suggested, with 95% confidence, that is 0.06 or lower: Consistent with the null hypothesis, but still also consistent with many remaining models of inflation.[80]
Other potentially corroborating measurements are expected from thePlanck spacecraft, although it is unclear if the signal will be visible, or if contamination from foreground sources will interfere.[88]Other forthcoming measurements, such as those of21 centimeter radiation (radiation emitted and absorbed from neutral hydrogen before thefirst stars formed), may measure the power spectrum with even greater resolution than the CMB and galaxy surveys, although it is not known if these measurements will be possible or if interference withradio sources on Earth and in the galaxy will be too great.[89]
Is the theory of cosmological inflation correct, and if so, what are the details of this epoch? What is the hypothetical inflaton field giving rise to inflation?
In Guth's early proposal, it was thought that theinflaton was theHiggs field, the field that explains the mass of the elementary particles.[52] It is now believed by some that the inflaton cannot be the Higgs field.[59] One problem of this identification is the current tension with experimental data at theelectroweak scale,.[90] Other models of inflation relied on the properties ofGrand Unified Theories.[62]
One of the most severe challenges for inflation arises from the need forfine tuning. In new inflation, theslow-roll conditions must be satisfied for inflation to occur. The slow-roll conditions say that the inflatonpotential must be flat (compared to the large vacuum energy) and that the inflaton particles must have a small mass.[clarification needed][d]New inflation requires the Universe to have a scalar field with an especially flat potential and special initial conditions. However, explanations for these fine-tunings have been proposed. For example, classically scale invariant field theories, where scale invariance is broken by quantum effects, provide an explanation of the flatness of inflationary potentials, as long as the theory can be studied throughperturbation theory.[92]
Linde proposed a theory known aschaotic inflation in which he suggested that the conditions for inflation were actually satisfied quite generically. Inflation will occur in virtuallyany universe that begins in a chaotic, high energy state that has a scalar field with unbounded potential energy.[93]However, in his model, the inflaton field necessarily takes values larger than onePlanck unit: For this reason, these are often calledlarge field models and the competing new inflation models are calledsmall field models. In this situation, the predictions ofeffective field theory are thought to be invalid, asrenormalization should cause large corrections that could prevent inflation.[e]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.[95]While inflation depends on quantum field theory (and thesemiclassical approximation toquantum gravity) in an important way, it has not been completely reconciled with these theories.
Brandenberger commented on fine-tuning in another situation.[96]The amplitude of the primordial inhomogeneities produced in inflation is directly tied to the energy scale of inflation. This scale is suggested to be around 1016GeV or 10−3 times thePlanck energy. The natural scale is naïvely the Planck scale so this small value could be seen as another form of fine-tuning (called ahierarchy problem): The energy density given by the scalar potential is down by 10−12 compared to thePlanck 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.
In many models, the inflationary phase of the Universe's expansion lasts forever in at least some regions of the Universe. This occurs because inflating regions expand very rapidly, reproducing themselves. Unless the rate of decay to the non-inflating phase is sufficiently fast, new inflating regions are produced more rapidly than non-inflating regions. In such models, most of the volume of the Universe is continuously inflating at any given time.
All models of eternal inflation produce an infinite, hypothetical multiverse, typically a fractal. The multiverse theory has created significant dissension in the scientific community about the viability of the inflationary model.
Paul Steinhardt, one of the original architects of the inflationary model, introduced the first example of eternal inflation in 1983.[97] He showed that the inflation could proceed forever by producing bubbles of non-inflating space filled with hot matter and radiation surrounded by empty space that continues to inflate. The bubbles could not grow fast enough to keep up with the inflation. Later that same year,Alexander Vilenkin showed that eternal inflation is generic.[98]
Although new inflation is classically rolling down the potential, quantum fluctuations can sometimes lift it to previous levels. These regions in which the inflaton fluctuates upwards, expand much faster than regions in which the inflaton has a lower potential energy, and tend to dominate in terms of physical volume. It has been shown that any inflationary theory with an unbounded potential is eternal. There are well-known theorems that this steady state cannot continue forever into the past. Inflationary spacetime, which is similar to de Sitter space, is incomplete without a contracting region. However, unlike de Sitter space, fluctuations in a contracting inflationary space collapse to form a gravitational singularity, a point where densities become infinite. Therefore, it is necessary to have a theory for the Universe's initial conditions.
In eternal inflation, regions with inflation have an exponentially growing volume, while regions that are not inflating do not. This suggests that the volume of the inflating part of the Universe in the global picture is always unimaginably larger than the part that has stopped inflating, even though inflation eventually ends as seen by any single pre-inflationary observer. Scientists disagree about how to assign a probability distribution to this hypothetical anthropic landscape. If the probability of different regions is counted by volume, one should expect that inflation will never end or applying boundary conditions that a local observer exists to observe it, that inflation will end as late as possible.
Some physicists believe this paradox can be resolved by weighting observers by their pre-inflationary volume. Others believe that there is no resolution to the paradox and that themultiverse is a critical flaw in the inflationary paradigm. Paul Steinhardt, who first introduced the eternal inflationary model,[97] later became one of its most vocal critics for this reason.[99][100][101]
Some physicists have tried to avoid the initial conditions problem by proposing models for an eternally inflating universe with no origin.[102][103][104] These models propose that while the Universe, on the largest scales, expands exponentially it was, is and always will be, spatially infinite and has existed, and will exist, forever.
Other proposals attempt to describe the ex nihilo creation of the Universe based onquantum cosmology and the following inflation. Vilenkin put forth one such scenario.[98]Hartle and Hawking offered theno-boundary proposal for the initial creation of the Universe in which inflation comes about naturally.[105][106][107]
Guth described the inflationary universe as the "ultimate free lunch":[108][109] new universes, similar to our own, are continually produced in a vast inflating background. Gravitational interactions, in this case, circumvent (but do not violate) thefirst law of thermodynamics (energy conservation) and thesecond law of thermodynamics (entropy and thearrow of time problem). However, while there is consensus that this solves the initial conditions problem, some have disputed this, as it is much more likely that the Universe came about by aquantum fluctuation.Don Page was an outspoken critic of inflation because of this anomaly.[110] He stressed that the thermodynamicarrow of time necessitates lowentropy initial conditions, which would be highly unlikely. According to them, rather than solving this problem, the inflation theory aggravates it – the reheating at the end of the inflation era increases entropy, making it necessary for the initial state of the Universe to be even more orderly than in other Big Bang theories with no inflation phase.
Hawking and Page later found ambiguous results when they attempted to compute the probability of inflation in the Hartle–Hawking initial state.[111] 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.[5][112]: 223–225 However, Albrecht and Lorenzo Sorbo argued that the probability of an inflationary cosmos, consistent with today's observations, emerging by a random fluctuation from some pre-existent state is much higher than that of a non-inflationary cosmos. This is because the "seed" amount of non-gravitational energy required for the inflationary cosmos is so much less than that for a non-inflationary alternative, which outweighs any entropic considerations.[113]
Another problem that has occasionally been mentioned is the trans-Planckian problem or trans-Planckian effects.[114] Since the energy scale of inflation and the Planck scale are relatively close, some of the quantum fluctuations that have made up the structure in our universe were smaller than the Planck length before inflation. Therefore, there ought to be corrections from Planck-scale physics, in particular the unknown quantum theory of gravity. Some disagreement remains about the magnitude of this effect: about whether it is just on the threshold of detectability or completely undetectable.[115]
Another kind of inflation, calledhybrid 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.[116]
In hybrid inflation, one scalar field is responsible for most of the energy density (thus determining the rate of expansion), while another is responsible for the slow roll (thus determining the period of inflation and its termination). Thus fluctuations in the former inflaton would not affect inflation termination, while fluctuations in the latter would not affect the rate of expansion. Therefore, hybrid inflation is not eternal.[117][118] When the second (slow-rolling) inflaton reaches the bottom of its potential, it changes the location of the minimum of the first inflaton's potential, which leads to a fast roll of the inflaton down its potential, leading to termination of inflation.
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 27orders of magnitude less than the scale of inflation.
The discovery offlux compactifications opened the way for reconciling inflation and string theory.[119]Brane inflation suggests that inflation arises from the motion ofD-branes[120] in the compactified geometry, usually towards a stack of anti-D-branes. This theory, governed by theDirac–Born–Infeld action, is different from ordinary inflation. The dynamics are not completely understood. It appears that special conditions are necessary since inflation occurs in tunneling between two vacua in thestring landscape. The process of tunneling between two vacua is a form of old inflation, but new inflation must then occur by some other mechanism.
When investigating the effects the theory ofloop quantum gravity would have on cosmology, aloop quantum cosmology model has evolved that provides a possible mechanism for cosmological inflation. Loop quantum gravity assumes a quantized spacetime. If the energy density is larger than can be held by the quantized spacetime, it is thought to bounce back.[121]
The big bounce hypothesis attempts to replace the cosmic singularity with a cosmic contraction and bounce, thereby explaining the initial conditions that led to the big bang. The flatness and horizon problems are naturally solved in theEinstein–Cartan–Sciama–Kibble theory of gravity, without needing an exotic form of matter or free parameters.[122][123] This theory extends general relativity by removing a constraint of the symmetry of the affine connection and regarding its antisymmetric part, thetorsion tensor, as a dynamical variable. The minimal coupling between torsion andDirac spinors generates a spin-spin interaction that is significant in fermionic matter at extremely high densities. Such an interaction averts the unphysical Big Bang singularity, replacing it with a cusp-like bounce at a finite minimum scale factor, before which the Universe was contracting. The rapid expansion immediately after theBig Bounce explains why the present Universe at largest scales appears spatially flat, homogeneous and isotropic. As the density of the Universe decreases, the effects of torsion weaken and the Universe smoothly enters the radiation-dominated era.
Theekpyrotic andcyclic models are also considered adjuncts to inflation. These models solve thehorizon problem through an expanding epoch wellbefore the Big Bang, and then generate the required spectrum of primordial density perturbations during a contracting phase leading to aBig Crunch. The Universe passes through the Big Crunch and emerges in a hotBig Bang phase. In this sense they are reminiscent ofRichard Chace Tolman'soscillatory universe; in Tolman's model, however, the total age of the Universe is necessarily finite, while in these models this is not necessarily so. Whether the correct spectrum of density fluctuations can be produced, and whether the Universe can successfully navigate the Big Bang/Big Crunch transition, remains a topic of controversy and current research. Ekpyrotic models avoid themagnetic monopole problem as long as the temperature at the Big Crunch/Big Bang transition remains below the Grand Unified Scale, as this is the temperature required to produce magnetic monopoles in the first place. As things stand, there is no evidence of any 'slowing down' of the expansion, but this is not surprising as each cycle is expected to last on the order of a trillion years.[124]
String theory requires that, in addition to the three observable spatial dimensions, additional dimensions exist that are curled up orcompactified (see alsoKaluza–Klein theory). Extra dimensions appear as a frequent component ofsupergravity models and other approaches toquantum gravity. This raised the contingent question of why four space-time dimensions became large and the rest became unobservably small. An attempt to address this question, calledstring gas cosmology, was proposed byRobert Brandenberger andCumrun Vafa.[125] This model focuses on the dynamics of the early universe considered as a hot gas of strings. Brandenberger and Vafa show that a dimension ofspacetime can only expand if the strings that wind around it can efficiently annihilate each other, which became known asBrandenberger–Vafa mechanism. Each string is a one-dimensional object, and the largest number of dimensions in which two strings willgenerically intersect (and, presumably, annihilate) is three. Therefore, the most likely number of non-compact (large) spatial dimensions is three. Current work on this model centers on whether it can succeed in stabilizing the size of the compactified dimensions and produce the correct spectrum of primordial density perturbations.[126] The original model did not "solve the entropy and flatness problems of standard cosmology",[127] although Brandenburger and coauthors later argued that these problems can be eliminated by implementing string gas cosmology in the context of a bouncing-universe scenario.[128][129]
Cosmological models employing avariable speed of light have been proposed to resolve the horizon problem of and provide an alternative to cosmic inflation. In the VSL models, the fundamental constantc, denoting thespeed of light in vacuum, is greater in theearly universe than its present value, effectively increasing theparticle horizon at the time of decoupling sufficiently to account for the observed isotropy of the CMB.
Since its introduction by Alan Guth in 1980, the inflationary paradigm has become widely accepted. Nevertheless, many physicists, mathematicians, and philosophers of science have voiced criticisms, claiming untestable predictions and a lack of serious empirical support.[5] In 1999, John Earman and Jesús Mosterín published a thorough critical review of inflationary cosmology, concluding,
"we do not think that there are, as yet, good grounds for admitting any of the models of inflation into the standard core of cosmology."[6]
As pointed out byRoger Penrose from 1986 on, in order to work, inflation requires extremely specific initial conditions of its own, so that the problem (or pseudo-problem) of initial conditions is not solved:
"There is something fundamentally misconceived about trying to explain the uniformity of the early universe as resulting from a thermalization process. ... For, if the thermalization is actually doing anything ... then it represents a definite increasing of the entropy. Thus, the universe would have been even more special before the thermalization than after."[130]
The problem of specific or "fine-tuned" initial conditions would not have been solved; it would have gotten worse. At a conference in 2015, Penrose said that
"inflation isn't falsifiable, it's falsified. ...BICEP did a wonderful service by bringing all the inflation-ists out of their shell, and giving them a black eye."[7]
A recurrent criticism of inflation is that the invoked inflaton field does not correspond to any known physical field, and that itspotential energy curve seems to be an ad hoc contrivance to accommodate almost any data obtainable.Paul Steinhardt, one of the founding fathers of inflationary cosmology, calls 'bad inflation' a period of accelerated expansion whose outcome conflicts with observations, and 'good inflation' one compatible with them:
"Not only is bad inflation more likely than good inflation, but no inflation is more likely than either ... Roger Penrose considered all the possible configurations of the inflaton and gravitational fields. Some of these configurations lead to inflation ... Other configurations lead to a uniform, flat universe directly – without inflation. Obtaining a flat universe is unlikely overall. Penrose's shocking conclusion, though, was that obtaining a flat universe without inflation is much more likely than with inflation – by a factor of10 to the googol[f] power!"[5][112]
Together with Anna Ijjas andAbraham Loeb, he wrote articles claiming that the inflationary paradigm is in trouble in view of the data from thePlanck satellite.[131][132]
^Not only is inflation very effective at driving down the number density of magnetic monopoles, it is also effective at driving down the number density of every other type of particle, including photons.[23](p 202–207)
^Perturbations can be represented byFourier modes of awavelength. Each Fourier mode isnormally 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 ofpower to the spectrum of perturbations. Since the Fourier transform is in three dimensions, this means that the variance of a mode goes as 1/k3 to compensate for the fact that within any volume, the number of modes with a given wavenumberk goes ask3.
^This is known as a "red" spectrum, in analogy toredshift, because the spectrum has more power at longer wavelengths.
^Technically, these conditions are that thelogarithmic derivative of the potential, and second derivative are both small, where is the potential, and the equations are written inreduced Planck units.[91]
^Technically, this is because the inflaton potential is expressed as a Taylor series in where is the inflaton and is thePlanck mass. While for a single term, such as the mass term the slow roll conditions can be satisfied for much greater than this is precisely the situation in effective field theory in which higher order terms would be expected to contribute and destroy the conditions for inflation. The absence of these higher order corrections can be seen as another sort of fine tuning.[94]
^A googol is 10100, hence Steinhardt[5] is claiming the probability ratio is 1010100.
^abHložek, Renée (10–12 June 2015).CMB@50 day three. Cosmic Microwave Background @50. Princeton, NJ. Archived fromthe original on 19 December 2017. Retrieved15 July 2015. — collated remarks from the third day of the conference.
^Barbara Sue Ryden (2003).Introduction to cosmology. Addison-Wesley.ISBN978-0-8053-8912-8.
^Guth, Alan (21 June – 9 July 1982) [1st ed. 1983]. Gibbons, G.W.;Hawking, S.; Siklos, S.T.C. (eds.).Phase transitions in the very early universe. The Very Early Universe: Proceedings of the Nuffield Workshop,Cambridge (illustrated, reprint ed.). Cambridge, UK:Cambridge U.P. (published 29 March 1985).ISBN9780521316774.OCLC14137101.ISBN0-521-31677-4
^abMisner, Charles; Thorne, Kip S. & Wheeler, John Archibald (1973).Gravitation. San Francisco: W. H. Freeman. pp. 489–490,525–526.ISBN978-0-7167-0344-0.
^Lemaître, Georges (1933). "The expanding universe".Annales de la Société Scientifique de Bruxelles.47A: 49., English inGen. Rel. Grav.29:641–680, 1997.
^Dicke, Robert H. (1970).Gravitation and the Universe. Philadelphia, PA: American Philosophical Society.
^Dicke, Robert H.; Peebles, P.J.E. (1979). "The big bang cosmology – enigmas and nostrums". In Hawking, S.W.; Israel, W. (eds.).General Relativity: An Einstein centenary survey. Cambridge University Press.
^Lightman, Alan P. (1 January 1993).Ancient Light: Our Changing View of the Universe. Harvard University Press.ISBN978-0-674-03363-4.
^SeeGuth (1997) for a popular description of the workshop, orThe Very Early Universe, eds Gibbon, Hawking, & Siklos,ISBN0-521-31677-4, for a more detailed report.
^Rosset, C.; et al. (PLANCK-HFI collaboration) (2005). "Systematic effects in CMB polarization measurements".Exploring the Universe: Contents and structures of the universe. XXXIXth Rencontres de Moriond.arXiv:astro-ph/0502188.
^abGibbons, Gary W.; Hawking, Stephen W.; Siklos, S.T.C., eds. (1983)."Natural Inflation," in The Very Early Universe. Cambridge University Press. pp. 251–66.ISBN978-0-521-31677-4.
^Steinhardt, Paul J. (2011)."The Cyclic Theory of the Universe"(PDF). In Vaas, Rudy (ed.).Beyond the Big Bang: Competing Scenarios For An Eternal Universe (Unpublished manuscript). The Frontiers Collectuion. Springer.Archived(PDF) from the original on 9 October 2022.[better source needed]
^Linde, Andrei (8 July – 2 August 2013).Inflationary cosmology after Planck 2013. Post-Planck Cosmology: École de physique des Houches. Oxford, UK: Ecole d'été de physique théorique / Oxford University Press (published 2015). session C.ISBN978-0-19-872885-6.
Smeenk, Chris (2005). Kox, A.J.; Eisenstaedt, Jean (eds.).False Vacuum: Early Universe Cosmology and the Development of Inflation. In: The Universe of General Relativity (Einstein Studies, Book 11). Birkhäuser Boston. pp. 223–257.ISBN978-0817643805.
