Everything about Cosmic Inflation totally explained
In
physical cosmology,
cosmic inflation is the idea that the
universe passed 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 conundrum 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 proposed in January, 1980 by
Alan Guth 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 isn't known, the basic picture makes a number of predictions that have been confirmed by observational tests. Inflation is thus now considered part of the standard hot
big bang cosmology. The hypothetical
particle or
field thought to be responsible for inflation is called the
inflaton.
Overview
Inflation suggests that there was a period of exponential expansion in the very early universe. Because in a fast expanding universe, the distance to the
cosmological horizon is constant, it isn't clear whether such a universe should be called "small" or "large". If the philosophical definition of the universe is restricted to be the
observable universe, an inflating universe is small, and only becomes large once inflation has ended and the cosmological horizon is free to expand. If the philosophical position is that the universe is mostly unobservable, then the unobservable portion is expanding exponentially.
Space expands
To say that space expands exponentially means that two
inertial observers are drawn further apart with time. Expressed in
comoving Cartesian coordinates the
proper distance is:
»
Which is just like an inside-out
black hole metric--- it has a zero in the dt component on a fixed radius sphere called the
cosmological horizon. Objects are drawn away from the observer at r=0 towards the cosmological horizon, leading them to fall in after a finite proper time. This means that any inhomogeneities are smoothed out, just as any bumps or matter on the surface of a black hole horizon are swallowed and disappear.
Since the space time metric has no explicit time dependence, once an observer has fallen onto the cosmological horizon, observers closer in take its place. This process of falling outward and replacement means that every unit of time, points closer in are steadily replacing points further out--- an exponential expansion of space-time.
This steady-state exponentially expanding spacetime is called a
de Sitter space, and to sustain it there must be a
cosmological constant, a
vaccuum energy proportional to
everywhere. The physical conditions from one moment to the next are stable: the rate of expansion, called the
Hubble parameter, is nearly constant. 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. (but
can stay approximately constant see
deceleration parameter.)
Few inhomogeneities remain
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's completely dominated by the
inflaton field, the source of the cosmological constant, and the only significant inhomogeneities are the tiny quantum fluctuations in the
inflaton. Inflation also dilutes exotic heavy particles, such as the
magnetic monopoles predicted by many extensions to the
Standard Model of
particle physics. If the universe was only hot enough to form such particles
before a period of inflation, they wouldn't be observed in nature, as they'd be so rare that it's quite likely that there are none in the
Observable universe. Together, these effects are called the inflationary "no-hair theorem" by analogy with the
no hair theorem for
black holes.
The "no-hair" theorem works essentially because the cosmological horizon is no different from a black-hole horizon except for philosophical disagreements about whats on the other side. In terms of the unobservable universe, the interpretation of the no-hair theorem is that the unobservable 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.
Key requirement
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 10
26 during inflation.
Reheating
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 isn't known how long inflation lasted but it's usually thought to be extremely short compared to the age of the universe.
Motivation
Inflation resolves
several problems in the
Big Bang cosmology that were pointed out in the 1970s.
These problems arise from the observation that to look like it does
today, the universe would have to have started from very
finely tuned, or "special" initial conditions at the Big Bang. Inflation attempts to resolve these problems by providing a dynamical mechanism that drives the universe to this special state, thus making a universe like ours much more likely in the context of the Big Bang theory.
Horizon problem
The
horizon problem is the problem of determining why the universe appears statistically homogeneous and isotropic in accordance with the
cosmological principle. For example, molecules in a canister of gas are distributed homogeneously and isotropically because they're 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 doesn't 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 can't have equilibrated because they move apart from each other faster than the
speed of light — thus have never come in to
causal contact: in the history of the universe, back to the earliest times, it hasn't been possible to send a light signal between the two regions. Because they've no interaction, it's difficult to explain why they've the same temperature (are thermally 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 couldn't 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, popular in the 1970s and 1980s, which proposed that at high temperatures (such as in the early universe) the
electromagnetic force,
strong and
weak nuclear forces are not actually fundamental forces but arise due to
spontaneous symmetry breaking from a much simpler
gauge theory. These theories predict a number of heavy, stable particles which have not yet been observed in nature. The most notorious is the magnetic monopole, a kind of stable, heavy "knot" in the magnetic field. Monopoles are expected to be copiously produced in Grand Unified Theories at high temperature, and they should have persisted to the present day. To very high precision, magnetic monopoles have been shown not to exist in nature, whereas according to the big bang theory (without cosmic inflation) they should have been copiously produced in the hot, dense early universe and since become the primary constituent of the universe.
History
Precursors
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 later interested Guth.
Guth, Starobinsky and others
Inflation was proposed in January, 1980 by
Alan Guth as a mechanism for resolving these problems.
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).
Guth
Guth was the first to assemble a complete picture of how all these initial conditions problems could be solved by an exponentially expanding state.
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 didn't reheat properly: when the bubbles nucleated, they didn't generate any radiation. Radiation could only be generated in collisions between bubble walls. But if inflation lasted long enough to solve the initial conditions problems, collisions between bubbles became exceedingly rare. In any one causal patch, it's likely that only one bubble will nucleate.
Linde, Albrecht and Steinhardt
The bubble collision problem was solved by
Andrei Linde 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,
Paul Steinhardt and
Michael Turner.
Observational status
Inflation is a concrete mechanism for realizing the
cosmological principle which is the basis of the standard 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's 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, 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 = 0.960 ± 0.014 and shown that it's different from one at the level of two
standard deviations (2σ). This is considered an important confirmation of the theory of inflation. However, the third-year data revealed that the effect was a statistical anomaly.
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 that'll also show whether the energy scale of inflation predicted by the simplest models (10
15–10
16 GeV) is correct. 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 isn't 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's 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. 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
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 hasn't 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 hasn't been completely reconciled with these theories.
Robert Brandenberger has commented on fine-tuning in another situation. The amplitude of the primordial inhomogeneities produced in inflation is directly tied to the energy scale of inflation. There are strong suggestions that this scale is around 10
16 GeV or 10
−3 times the
Planck energy. The natural scale is naïvely the Planck scale so this small value could be seen as another form of fine-tuning (called a
hierarchy problem): the energy density given by the scalar potential is down by 10
−12 compared to the
Planck density. This isn't 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's 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, is called "eternal inflation". It has been shown that any inflationary theory with an unbounded potential is eternal. It is a popular belief among physicists that this steady state can't continue forever into the past. 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's necessary to have a theory for the universe's initial conditions. Linde, however, believes inflation may be past eternal.
Initial conditions
Some physicists have tried to avoid the initial conditions problem by proposing models for an eternally inflating universe with no origin. These models propose that whilst the universe, on the largest scales, expands exponentially it's always spatially infinite and has existed, and will exist, forever.
Other proposals attempt to describe the ex nihilo creation of the universe
quantum cosmology and the following inflation. Vilenkin put forth one such scenario.
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 don't violate) both the
first law of thermodynamics or
energy conservation and the
second law of thermodynamics or the
arrow of time problem. However, while there's consensus that this solves the initial conditions problem, some have disputed this, as it's much more likely that the universe came about by a quantum fluctuation. Donald Page was an outspoken critic of inflation because of this anomaly. He stressed that the thermodynamic
arrow of time necessitates low
entropy initial conditions, which would be highly unlikely. According to them, rather than solving this problem, the inflation theory 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. Other authors have argued that, since inflation is eternal, the probability doesn't matter as long as it isn't 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.
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's 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 isn't known, this process is still poorly understood, although it's believed to take place through a
parametric resonance.
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. Unlike most other models of inflation, many versions of hybrid inflation are not eternal.
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 wouldn't affect inflation termination, while fluctuations in the latter wouldn't affect the rate of expansion. Therefore hybrid inflation isn't 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 compactifications have opened the way for reconciling inflation and string theory. A new theory, called
brane inflation suggests that inflation arises from the motion of
D-branesin 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. 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're 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 isn't 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.
Further Information
Get more info on 'Cosmic Inflation'.
|
External Link Exchanges
Do you know how hard it is to get a link from a large encyclopaedia? Well we're different and will prove it. To get a link from us just add the following HTML to your site on a relevant page:
<a href="http://cosmic_inflation.totallyexplained.com">Cosmic inflation Totally Explained</a>
Then simply click through this link from your web page. Our crawlers will verify your link, extract the title of your web page and instantly add a link back to it. If you like you can remove the words Totally Explained and embed the link in article text.
As long as your link remains in place, we'll keep our link to you right here. Please play fair - our crawlers are watching. Your site must be closely related to this one's topic. Any kind of spamming, dubious practises or removing the link will result in your link from us being dropped and, potentially, your whole site being banned. |
