Clouding of consciousness, also called brain fog or mental fog, occurs when a person is slightly less wakeful or aware than normal. They are not as aware of time or their surroundings and find it difficult to pay attention. People describe this subjective sensation as their mind being "foggy".
Background
The term clouding of consciousness has always denoted the main pathogenetic feature of delirium since physician Georg Greiner pioneered the term (Verdunkelung des Bewusstseins) in 1817. The Diagnostic and Statistical Manual of Mental Disorders (DSM) has historically used the term in its definition of delirium. However, the DSM-III-R and the DSM-IV replaced "clouding of consciousness" with "disturbance of consciousness" to make it easier to operationalize, but it is still fundamentally the same thing. Clouding of consciousness may be less severe than delirium on a spectrum of abnormal consciousness. Clouding of consciousness may be synonymous with subsyndromal delirium.
Subsyndromal delirium differs from normal delirium by being
overall less severe, lacking acuteness in onset and duration, having a
relatively stable sleep-wake cycle, and having relatively stable motor
alterations.
The significant clinical features of subsyndromal delirium are
inattention, thought process abnormalities, comprehension abnormalities,
and language abnormalities. The full clinical manifestations of delirium may never be reached.
Among intensive care unit patients, subsyndromal subjects were as
likely to survive as patients with a Delirium Screening Checklist score
of 0, but required extended care at rates greater than 0-scoring
patients (although lower rates than those with full delirium)
or have a decreased post-discharge level of functional independence vs.
the general population but still more independence than full delirium.
In clinical practice, there is no standard test that is exclusive and specific; therefore, the diagnosis depends on the subjective impression of the physician. The DSM-IV-TR instructs clinicians to code subsyndromal delirium presentations under the miscellaneous category of "cognitive disorder not otherwise specified".
Psychopathology
The conceptual model of clouding of consciousness is that of a part of the brain regulating the "overall level" of the consciousness part of the brain, which is responsible for awareness of oneself and of the environment. Various etiologies disturb this regulating part of the brain, which in turn disturbs the "overall level" of consciousness. This system of a sort of general activation of consciousness is referred to as "arousal" or "wakefulness".
It is not necessarily accompanied by drowsiness, however. Patients may be awake (not sleepy) yet still have a clouded consciousness (disorder of wakefulness). Paradoxically, affected individuals say that they are "awake but, in another way, not".
Lipowski points out that decreased "wakefulness" as used here is not
exactly synonymous with drowsiness. One is a stage on the way to coma, the other on the way to sleep which is very different.
The affected person experiences a subjective sensation of mental clouding described in the patient's own words as feeling "foggy". One patient described it as "I thought it became like misty, in some way... the outlines were sort of fuzzy". Others may describe a "spaced out" feeling. Affected individuals compare their overall experience to that of a dream because, as in a dream, consciousness, attention, orientation to time and place, perceptions, and awareness are disturbed.
Barbara Schildkrout, MD, a board-certified psychiatrist and clinical
instructor in psychiatry at the Harvard Medical School, described her
subjective experience of clouding of consciousness, or what she also
called "mental fog", after taking a single dose of chlorpheniramine (an antihistamine for her allergy to cottonwood)
while on a cross-country road trip. She described feeling "out of it"
and being in a "dreamy state". She described a sense of not trusting her
own judgment and a dulled awareness, not knowing how long time went by. Clouding of consciousness is not the same thing as depersonalization
even though people affected by both compare their experience to that of
a dream. Psychometric tests produce little evidence of a relationship
between clouding of consciousness and depersonalization.
This may affect performance on virtually any cognitive task. As one author put it, "It should be apparent that cognition is not possible without a reasonable degree of arousal." Cognition includes perception, memory, learning, executive functions, language,
constructive abilities, voluntary motor control, attention, and mental
speed. The most significant clinical features of brain fog, however, are
inattention, thought process abnormalities, comprehension
abnormalities, and language abnormalities.
The extent of the impairment is variable because inattention may impair
several cognitive functions. Affected individuals may complain of
forgetfulness, being "confused", or being "unable to think straight". Despite the similarities, subsyndromal delirium is not the same thing as mild cognitive impairment; the fundamental difference is that mild cognitive impairment is a dementia-like impairment, which does not involve a disturbance in arousal (wakefulness).
In diseases
The
term "brain fog" is used to represent a subjective condition of
perceived cognitive impairment. It is defined as “a phenomenon of
fluctuating states of perceived cognitive dysfunction that could have
implications in the functional application of cognitive skills in
people’s participation in daily activities”. Brain fog is a common symptom in many illnesses where chronic pain is a major component. Brain fog affects 15% to 40% of those with chronic pain as their major illness. In such illnesses, pain processing may use up resources and therefore decrease the brain's ability to think effectively.
Many people with fibromyalgia experience cognitive problems (known as "fibrofog" or "brainfog"), which may involve impaired concentration, problems with short and long-term memory, short-term memory consolidation, working memory, impaired speed of performance, inability to multi-task, cognitive overload, and diminished attention span. About 75% of fibromyalgia patients report significant problems with concentration, memory, and multitasking. A 2018 meta-analysis found that the largest differences between fibromyalgia patients and healthy subjects were for inhibitory control, memory, and processing speed. Many of these are also common symptoms of ADHD
(attention deficit hyperactivity disorder), and the two conditions have
been linked via studies, to the point that a diagnosis of fibromyalgia
has been proposed as an indication to also screen for ADHD. It is alternatively hypothesized that the increased pain compromises attention systems, resulting in cognitive problems.
Problems with thinking and memory (cognitive dysfunction, sometimes described as "brain fog")
While standing or sitting upright; lightheadedness, dizziness, weakness, fainting or vision changes may occur (orthostatic intolerance)
Lyme disease's
neurologic syndrome, called Lyme encephalopathy, is associated with
subtle memory and cognitive difficulties, among other issues. Lyme can cause a chronic encephalomyelitis that resembles multiple sclerosis. It may be progressive and can involve cognitive impairment, migraines, balance issues, and extensive other issues.
The emerging concept of sluggish cognitive tempo has also been implicated in the expression of 'brain fog' symptoms.
Brain fog and other neurological symptoms may also result from mold exposure. This may be due to mycotoxin exposure and consequent innate immune system activation and inflammation, including in the central nervous system.
However, adverse neurological health effects of mold exposure are
controversial due to inadequate research and data, and more research is
needed in this area.
In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch is believed to have lasted from 10−36 seconds to between 10−33 and 10−32 seconds after the Big Bang.
Following the inflationary period, the universe continued to expand,
but at a slower rate. The acceleration of this expansion due to dark energy began after the universe was already over 7.7 billion years old (5.4 billion years ago).
The detailed particle physics
mechanism responsible for inflation is unknown. The basic inflationary
paradigm is accepted by most physicists, as a number of inflation model
predictions have been confirmed by observation; however, a substantial minority of scientists dissent from this position. The hypothetical field thought to be responsible for inflation is called the inflaton.
Around 1930, Edwin Hubble discovered that light from remote galaxies was redshifted;
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. This expansion of the universe was previously predicted by Alexander Friedmann and Georges Lemaître from the theory of general 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 separation.
Inflation may provide this initial impulse. According to the Friedmann equations that describe the dynamics of an expanding universe, a fluid with sufficiently negative pressure exerts gravitational repulsion in the cosmological context. A field in a positive-energy false vacuum state could represent such a fluid, and the resulting repulsion would set the universe into exponential expansion. This inflation phase was originally proposed by Alan Guth in 1979 because the exponential expansion could dilute exotic relics, such as magnetic monopoles, that were predicted by grand unified theories
at the time. This would explain why such relics were not seen. It was
quickly realized that such accelerated expansion would resolve the horizon problem and the flatness problem. These problems arise from the notion that to look like it does today, the Universe must have started from very finely tuned, or "special", initial conditions at the Big Bang.
An expanding universe generally has a cosmological horizon, which, by analogy with the more familiar horizon caused by the curvature of Earth'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 an accelerating universe never reaches the observer, because the space in between the observer and the object is expanding too rapidly.
The observable universe is one causal 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. In the standard hot big bang
model, without inflation, the cosmological horizon moves out, bringing
new regions into view.
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 couldn't have learned it by getting
signals, because they were not previously in communication with our past
light cone.
Inflation answers this question by postulating that all the regions come from an earlier era with a big vacuum energy, or cosmological 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 the cosmological 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 communications. 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 residual vacuum energy in the Universe have to add up to the critical 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.
Space expands
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-out Schwarzschild
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 following metric:
This exponentially expanding spacetime is called a de Sitter space, and to sustain it there must be a cosmological constant, a vacuum 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 pressure p equal in magnitude to its energy density ρ; the equation of state is p=−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.
Few inhomogeneities remain
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 out inhomogeneities and anisotropies, and reduces 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 tiny quantum fluctuations. 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 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.
The "no-hair" theorem works essentially because the cosmological
horizon is no different from a black-hole horizon, except for
philosophical 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)
goes down as the inverse of the volume: when linear dimensions double,
the energy density goes down by a factor of eight; the radiation energy
density goes down even more rapidly as the Universe expands since the
wavelength of each photon 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 (see the 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.
Duration
A key
requirement is that inflation must continue long enough to produce the
present observable universe from a single, small inflationary Hubble volume.
This is necessary to ensure that the Universe appears flat, homogeneous
and isotropic at the largest observable scales. This requirement is
generally thought to be satisfied if the Universe expanded by a factor
of at least 1026 during inflation.
Reheating
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.)
This relatively low temperature is maintained during the inflationary
phase. When inflation ends the temperature returns to the
pre-inflationary temperature; this is called reheating or thermalization because the large potential energy of the inflaton field decays into particles and fills the Universe with Standard Model particles, including electromagnetic radiation, starting the radiation 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 a parametric resonance.
Motivations
Inflation resolves several problems in Big Bang cosmology that were discovered in the 1970s. Inflation was first proposed by Alan Guth in 1979 while investigating the problem of why no magnetic monopoles are seen today; he found that a positive-energy false vacuum would, according to general relativity,
generate an exponential expansion of space. It was very quickly
realised that such an expansion would resolve many other long-standing
problems. 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.
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 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 move apart
from each other faster than the speed of light and thus have never come into causal 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 the Phoenix universe of Georges Lemaître, 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.
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 within a few percent.
Magnetic-monopole problem
The magnetic monopole problem,
sometimes called "the exotic-relics problem", says that if the early
universe were very hot, a large number of very heavy, stable magnetic monopoles would have been produced.
Stable magnetic monopoles are a problem for Grand Unified Theories, which propose that at high temperatures (such as in the early universe) the electromagnetic force, strong, and weaknuclear forces are not actually fundamental forces but arise due to spontaneous symmetry breaking from a single gauge 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.
Monopoles are predicted to be copiously produced following Grand Unified Theories at high temperature,
and they should have persisted to the present day, to such an extent
that they would become the primary constituent of the Universe.
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.
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 cosmologist Martin 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!"
History
Precursors
In the early days of General Relativity, Albert Einstein introduced the cosmological constant to allow a static solution, which was a three-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.
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 the early 1970s Zeldovich
noticed the flatness and horizon problems of Big Bang cosmology; before
his work, cosmology was presumed to be symmetrical on purely
philosophical grounds. In the Soviet Union, this and other considerations led Belinski and Khalatnikov to analyze the chaotic BKL singularity in General Relativity. Misner's Mixmaster universe attempted to use this chaotic behavior to solve the cosmological problems, with limited success.
In the late 1970s, Sidney Coleman applied the instanton techniques developed by Alexander Polyakov and collaborators to study the fate of the false vacuum in quantum field theory. Like a metastable phase in statistical 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 (no space, time, nor matter) by quantum fluctuations of metastable false vacuum causing an expanding bubble of true vacuum.
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 the Einstein–Hilbert action and a form of f(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.
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:
Monopole problem
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.
Early inflationary models
The physical size of the Hubble 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 a gravitational singularity, then the mode would never have been inside the horizon in the very early universe, and no causal 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;it was Guth who coined the term "inflation".
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.
In October 1980, Demosthenes Kazanas suggested that exponential expansion could eliminate the particle horizon and perhaps solve the horizon problem,
while Sato suggested that an exponential expansion could eliminate domain walls (another kind of exotic relic). In 1981 Einhorn and Sato published a model similar to Guth's and showed that it would resolve the puzzle of the magnetic 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 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.
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 by Guth (1981). ... Guth
himself did not refer to work of Kazanas until he published a book on
the subject under the title The Inflationary Universe: The quest for a new theory of cosmic origin (1997), where he apologizes for not having referenced the work of Kazanas and of others, related to inflation.
Slow-roll inflation
The bubble collision problem was solved by 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 quantum fluctuations in the
inflaton are created. These 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 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 Bardeen, Steinhardt and Turner.
Observational status
Inflation is a mechanism for realizing the cosmological 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 the cosmic microwave background made by the Planck spacecraft. 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 the gravitational collapse
of perturbations that were formed as quantum mechanical fluctuations in
the inflationary epoch. The detailed form of the spectrum of
perturbations, called a nearly-scale-invariantGaussian random field is very specific and has only two free parameters. One is 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).
The other free parameter is the tensor to scalar ratio. The simplest inflation models, those without fine-tuning, predict a tensor to scalar ratio near 0.1 .
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 Planck spacecraft, WMAP spacecraft and other cosmic microwave background (CMB) experiments, and galaxy surveys, especially the ongoing Sloan Digital Sky Survey.
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. The spectral index, ns is one for a scale-invariant Harrison–Zel'dovich spectrum. The simplest inflation models predict that ns is between 0.92 and 0.98 . This is the range that is possible without fine-tuning of the parameters related to energy. From Planck data it can be inferred that ns=0.968 ± 0.006, and a tensor to scalar ratio that is less than 0.11 . These are considered an important confirmation of the theory of inflation.
Various inflation theories have been proposed that make radically different predictions, but they generally have much more fine-tuning than should be 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 remarked upon since the first cosmic microwave background satellite, the Cosmic Background Explorer is that the amplitude of the quadrupole moment of the CMB 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 CMB measurements. In particular, high precision
measurements of the so-called "B-modes" of the polarization of the background radiation could provide evidence of the gravitational radiation produced by inflation, and could also show whether the energy scale of inflation predicted by the simplest models (1015~1016GeV) is correct. In March 2014, the BICEP2
team announced B-mode CMB polarization confirming inflation had been
demonstrated. The team announced the tensor-to-scalar power ratio r was between 0.15 and 0.27 (rejecting the null hypothesis; r is expected to be 0 in the absence of inflation). However, on 19 June 2014, lowered confidence in confirming the findings was reported; on 19 September 2014, a further reduction in confidence was reported and, on 30 January 2015, even less confidence yet was reported. 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.
Other potentially corroborating measurements are expected from the Planck spacecraft, although it is unclear if the signal will be visible, or if contamination from foreground sources will interfere. Other forthcoming measurements, such as those of 21 centimeter radiation (radiation emitted and absorbed from neutral hydrogen before the first 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 with radio sources on Earth and in the galaxy will be too great.
Theoretical status
Unsolved problem in physics:
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 the inflaton was the Higgs field, the field that explains the mass of the elementary particles. It is now believed by some that the inflaton cannot be the Higgs field
although the recent discovery of the Higgs boson has increased the number of works considering the Higgs field as inflaton.
One problem of this identification is the current tension with experimental data at the electroweak scale,
which is currently under study at the Large Hadron Collider (LHC).
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 such as string theory
or a supersymmetric grand unified theory. At present, while inflation
is understood principally by its detailed predictions of the initial conditions for the hot early universe, the particle physics is largely ad hoc
modelling. As such, although predictions of inflation have been
consistent with the results of observational tests, many open questions
remain.
Fine-tuning problem
One of the most severe challenges for inflation arises from the need for fine tuning. 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.
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 through perturbation theory.
Linde proposed a theory known as chaotic inflation
in which he suggested that the conditions for inflation were actually
satisfied quite generically. Inflation will occur in virtually any universe that begins in a chaotic, high energy state that 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, as 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. 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.
Brandenberger 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. This scale is
suggested to be around 1016GeV 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.
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.
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.
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
don't. 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 the multiverse is a critical
flaw in the inflationary paradigm. Paul Steinhardt, who first introduced
the eternal inflationary model, later became one of its most vocal critics for this reason.
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 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 on quantum cosmology and the following inflation. Vilenkin put forth one such scenario. Hartle and Hawking offered the no-boundary proposal for the initial creation of the Universe in which inflation comes about naturally.
Guth 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) the first law of thermodynamics (energy conservation) and the second law of thermodynamics (entropy and the arrow 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 a quantum fluctuation. Don 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 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 is not precisely zero: once it
starts, inflation perpetuates itself and quickly dominates the Universe.
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.
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 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.
Hybrid 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.
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.
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.
Relation to 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.
Inflation and string cosmology
The discovery of flux compactifications opened the way for reconciling inflation and string theory. Brane inflation suggests that inflation arises from the motion of D-branes in the compactified geometry, usually towards a stack of anti-D-branes. This theory, governed by the Dirac-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 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.
Inflation and loop quantum gravity
When investigating the effects the theory of loop quantum gravity would have on cosmology, a loop 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.
Alternatives and adjuncts
Other models have been advanced that are claimed to explain some or all of the observations addressed by inflation.
Big bounce
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 the Einstein-Cartan-Sciama-Kibble theory of gravity, without needing an exotic form of matter or free parameters.
This theory extends general relativity by removing a constraint of the
symmetry of the affine connection and regarding its antisymmetric part,
the torsion tensor, as a dynamical variable. The minimal coupling between torsion and Dirac 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 the Big 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.
Ekpyrotic and cyclic models
The ekpyrotic and cyclic models are also considered adjuncts 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 Richard Chace Tolman's oscillatory 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 the magnetic 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.
String gas cosmology
String theory requires that, in addition to the three observable spatial dimensions, additional dimensions exist 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 raised the contingent 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, 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. The original model did not "solve the entropy and flatness problems of standard cosmology",
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.
Cosmological models employing a variable 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
constant c, denoting the speed of light in vacuum, is greater in the early universe than its present value, effectively increasing the particle horizon at the time of decoupling sufficiently to account for the observed isotropy of the CMB.
Criticisms
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. 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."
As pointed out by Roger 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."
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."
A recurrent criticism of inflation is that the invoked inflaton field
does not correspond to any known physical field, and that its potential 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, has recently
become one of its sharpest critics. He 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 of 10 to the googol power!"
Together with Anna Ijjas and Abraham Loeb, he wrote articles claiming that the inflationary paradigm is in trouble in view of the data from the Planck satellite.
