By 1980 most scientists believed that the big bang theory - which holds that the
universe was created from one vast explosion and subsequent expansion - was the
most likely explanation for the origin of the universe. However, the original
big bang theory had several shortcomings. In 1981 American cosmologist Alan
Guth introduced a new theory known as the inflationary model, which presents a
more detailed explanation of what may have occurred in the first fraction of a
second of the universe's existence. Guth's ideas, developed from an area of
study known as unified field theory, were modified and elaborated on by American
theoretical physicist Paul Steinhardt and others in the early 1980s. The
inflationary model has many interesting implications, including the possibility
that our universe is only one of billions of universes and that it may have been
created out of nothing - what one cosmologist jokingly called "the ultimate free
lunch". Guth and Steinhardt explain inflationary theory in this 1984 *
Scientific American* article.

The Inflationary Universe

*A
new theory of cosmology suggests that the observable universe is embedded in
a much larger region of space that had an extraordinary growth spurt a fraction
of a second after the primordial big bang*

By Alan H. Guth and Paul J. Steinhardt

**I**n
the past few years certain flaws in the standard big-bang theory of cosmology
have led to the development of a new model of the very early history of the
universe. The model, known as the inflationary universe, agrees precisely with
the generally accepted description of the observed universe for all times after
the first 10-30 second.
For this first fraction of a second, however, the story is dramatically
different. According to the inflationary model, the universe had a brief period
of extraordinarily rapid inflation, or expansion, during which its diameter
increased by a factor perhaps 1050 times
larger than had been thought. In the course of this stupendous growth spurt all
the matter and energy in the universe could have been created from virtually
nothing. The inflationary process also has important implications for the
present universe. If the new model is correct, the observed universe is only a
very small fraction of the entire universe.

**T**he inflationary model has many features in common with the standard big-bang
model. In both models the universe began between 10 and 15 billion years ago as
a primeval fireball of extreme density and temperature, and it has been
expanding and cooling ever since. This picture has been successful in explaining
many aspects of the observed universe, including the red-shifting of the light
from distant galaxies, the cosmic microwave background radiation and the
primordial abundances of the lightest elements. All these predictions have to do
only with events that presumably took place after the first second, when the two
models coincide.

**U**ntil about five years ago there were few serious attempts to describe the
universe during its first second. The temperature in this period is thought to
have been higher than 10 billion degrees Kelvin, and little was known about the
properties of matter under such conditions. Relying on recent developments in
the physics of elementary particles, however, cosmologists are now attempting to
understand the history of the universe back to 10-45 second
after its beginning. (At even earlier times the energy density would have been
so great that Einstein's general theory of relativity would have to be replaced
by a quantum theory of gravity, which so far does not exist.) When the standard
big-bang model is extended to these earlier times, various problems arise.
First, it becomes clear that the model requires a number of stringent,
unexplained assumptions about the initial conditions of the universe. In
addition most of the new theories of elementary particles imply that the
standard model would lead to a tremendous overproduction of the exotic particles
called magnetic monopoles (each of which corresponds to an isolated north or
south magnetic pole).

**T**he inflationary universe [theory] was invented to overcome these problems. The
equations that describe the period of inflation have a very attractive feature:
from almost any initial conditions the universe evolves to precisely the state
that had to be assumed as the initial one in the standard model. Moreover, the
predicted density of magnetic monopoles becomes small enough to be consistent
with observations. In the context of the recent developments in
elementary-particle theory the inflationary model seems to be a natural solution
to many of the problems of the standard big-bang picture.

**T**he standard big-bang model is based on several assumptions. First, it is
assumed that the fundamental laws of physics do not change with time and that
the effects of gravitation are correctly described by Einstein's general theory
of relativity. It is also assumed that the early universe was filled with an
almost perfectly uniform, expanding, intensely hot gas of elementary particles
in thermal equilibrium. The gas filled all of space, and the gas and space
expanded together at the same rate. When they are averaged over large regions,
the densities of matter and energy have remained nearly uniform from place to
place as the universe has evolved. It is further assumed that any changes in the
state of the matter and the radiation have been so smooth that they have had a
negligible effect on the thermodynamic history of the universe. The violation of
the last assumption is a key to the inflationary-universe model.

**T**he big-bang model leads to three important, experimentally testable
predictions. First, the model predicts that as the universe expands, galaxies
recede from one another with a velocity proportional to the distance between
them. In the 1920's Edwin P. Hubble inferred just such an expansion law from his
study of the red shifts of distant galaxies. Second, the big-bang model predicts
that there should be a background of microwave radiation bathing the universe as
a remnant of the intense heat of its origin. The universe became transparent to
this radiation several hundred thousand years after the big bang. Ever since
then the matter has been clumping into stars, galaxies, and the like, but the
radiation has simply continued to expand and red-shift, and in effect to cool.
In 1964 Arno A. Penzias and Robert W. Wilson of the Bell Telephone Laboratories
discovered a background of microwave radiation received uniformly from all
directions with an effective temperature of about three degrees K. Third, the
model leads to successful predictions of the formation of light atomic nuclei
from protons and neutrons during the first minutes after the big bang.
Successful predictions can be obtained in this way for the abundance of helium
4, deuterium, helium 3, and lithium 7. (Heavier nuclei are thought to have been
produced much later in the interior of stars.)

**U**nlike the successes of the big-bang model, all of which pertain to events a
second or more after the big bang, the problems all concern times when the
universe was much less than a second old. One set of problems has to do with the
special conditions the model requires as the universe emerged from the big bang.

**T**he first problem is the difficulty of explaining the large-scale uniformity of
the observed universe. The large-scale uniformity is most evident in the
microwave background radiation, which is known to be uniform in temperature to
about one part in 10,000. In the standard model the universe evolves much too
quickly to allow this uniformity to be achieved by the usual processes whereby a
system approaches thermal equilibrium. The reason is that no information or
physical process can propagate faster than a light signal. At any given time
there is a maximum distance, known as the horizon distance, that a light signal
could have traveled since the beginning of the universe. In the standard model
the sources of the microwave background radiation observed from opposite
directions in the sky were separated from each other by more than 90 times the
horizon distance when the radiation was emitted. Since the regions could not
have communicated, it is difficult to see how they could have evolved conditions
so nearly identical.

**T**he puzzle of explaining why the universe appears to be uniform over distances
that are large compared with the horizon distance is known as the horizon
problem. It is not a genuine inconsistency of the standard model; if the
uniformity is assumed in the initial conditions, the universe will evolve
uniformly. The problem is that one of the most salient features of the observed
universeâits large-scale uniformityâcannot be explained by the standard model;
it must be assumed as an initial condition.

**E**ven with the assumption of large-scale uniformity, the standard big-bang model
requires yet another assumption to explain the nonuniformity observed on smaller
scales. To account for the clumping of matter into galaxies, clusters of
galaxies, superclusters of clusters, and so on, a spectrum of primordial
inhomogeneities must be assumed as part of the initial conditions. The fact that
the spectrum of inhomogeneities has no explanation is a drawback in itself, but
the problem becomes even more pronounced when the model is extended back to 10-45 second
after the big bang. The incipient clumps of matter develop rapidly with time as
a result of their gravitational self-attraction, and so a model that begins at a
very early time must begin with very small inhomogeneities. To begin at 10-45 second
the matter must start in a peculiar state of extraordinary but not quite perfect
uniformity. A normal gas in thermal equilibrium would be far too inhomogeneous,
owing to the random motion of particles. This peculiarity of the initial state
of matter required by the standard model is called the smoothness problem.

**A**nother subtle problem of the standard model concerns the energy density of the
universe. According to general relativity, the space of the universe can in
principle be curved, and the nature of the curvature depends on the energy
density. If the energy density exceeds a certain critical value, which depends
on the expansion rate, the universe is said to be closed: space curves back on
itself to form a finite volume with no boundary. (A familiar analogy is the
surface of a sphere, which is finite in area and has no boundary.) If the energy
density is less than the critical density, the universe is open: space curves
but does not turn back on itself, and the volume is infinite. If the energy
density is just equal to the critical density, the universe is flat: space is
described by the familiar Euclidean geometry (again with infinite volume).

**T**he ratio of the energy density of the universe to the critical density is a
quantity cosmologists designate by the Greek letter Ù (omega). The value Ù = 1
(corresponding to a flat universe) represents a state of unstable equilibrium.
If Ù was ever exactly equal to 1, it would remain exactly equal to 1 forever. If
Ù differed slightly from 1 an instant after the big bang, however, the deviation
from 1 would grow rapidly with time. Given this instability, it is surprising
that Ù is measured today as being between .1 and 2. (Cosmologists are still not
sure whether the universe is open, closed, or flat.) In order for Ù to be in
this rather narrow range today, its value a second after the big bang had to
equal 1 to within one part in 1015.
The standard model offers no explanation of why Ù began so close to 1 but merely
assumes the fact as an initial condition. This shortcoming of the standard
model, called the flatness problem, was first pointed out in 1979 by Robert H.
Dicke and P. James E. Peebles of Princeton University.

**T**he successes and drawbacks of the big-bang model we have considered so far
involve cosmology, astrophysics, and nuclear physics. As the big-bang model is
traced backward in time, however, one reaches an epoch for which these branches
of physics are no longer adequate. In this epoch all matter is decomposed into
its elementary-particle constituents. In an attempt to understand this epoch
cosmologists have made use of recent progress in the theory of elementary
particles. Indeed, one of the important developments of the past decade has been
the fusing of interests in particle physics, astrophysics and cosmology. The
result for the big-bang model appears to be at least one more success and at
least one more failure.

**P**erhaps the most important development in the theory of elementary particles
over the past decade has been the notion of grand unified theories, the
prototype of which was proposed in 1974 by Howard M. Georgi and Sheldon Lee
Glashow of Harvard University. The theories are difficult to verify
experimentally because their most distinctive predictions apply to energies far
higher than those that can be reached with particle accelerators. Nevertheless,
the theories have some experimental support, and they unify the understanding of
elementary-particle interactions so elegantly that many physicists find them
extremely attractive.

**T**he basic idea of a grand unified theory is that what were perceived to be three
independent forcesâthe strong, the weak, and the electromagneticâare actually
parts of a single unified force. In the theory a symmetry relates one force to
another. Since experimentally the forces are very different in strength and
character, the theory is constructed so that the symmetry is spontaneously
broken in the present universe.

**
A**
spontaneously broken symmetry is one that is present in the underlying theory
describing a system but is hidden in the equilibrium state of the system. For
example, a liquid described by physical laws that are rotationally symmetric is
itself rotationally symmetric: the distribution of molecules looks the same no
matter how the liquid is turned. When the liquid freezes into a crystal,
however, the atoms arrange themselves along crystallographic axes and the
rotational symmetry is broken. One would expect that if the temperature of a
system in a broken-symmetry state were raised, it could undergo a kind of phase
transition to a state in which the symmetry is restored, just as a crystal can
melt into a liquid. Grand unified theories predict such a transition at a
critical temperature of roughly
1027 degrees.

**O**ne novel property of the grand unified theories has to do with the particles
called baryons, a class whose most important members are the proton and the
neutron. In all physical processes observed up to now the number of baryons
minus the number of antibaryons does not change; in the language of particle
physics the total baryon number of the system is said to be conserved. A
consequence of such a conservation law is that the proton must be absolutely
stable; because it is the lightest baryon, it cannot decay into another particle
without changing the total baryon number. Experimentally the lifetime of the
proton is known to exceed 1031 years.

**G**rand unified theories imply that baryon number is not exactly conserved. At low
temperature, in the broken-symmetry phase, the conservation law is an excellent
approximation, and the observed limit on the proton lifetime is consistent with
at least many versions of grand unified theories. At high temperature, however,
processes that change the baryon number of a system of particles are expected to
be quite common.

**O**ne direct result of combining the big-bang model with grand unified theories is
the successful prediction of the asymmetry of matter and antimatter in the
universe. It is thought that all the stars, galaxies, and dust observed in the
universe are in the form of matter rather than antimatter; their nuclear
particles are baryons rather than antibaryons. It follows that the total baryon
number of the observed universe is about 1078.
Before the advent of grand unified theories, when baryon number was thought to
be conserved, this net baryon number had to be postulated as yet another initial
condition of the universe. When grand unified theories and the big-bang picture
are combined, however, the observed excess of matter over antimatter can be
produced naturally by elementary-particle interactions at temperatures just
below the critical temperature of the phase transition. Calculations in the
grand unified theories depend on too many arbitrary parameters for a
quantitative prediction, but the observed matter-antimatter asymmetry can be
produced with a reasonable choice of values for the parameters.

**
A**
serious problem that results from combining grand unified theories with the
big-bang picture is that a large number of defects are generally formed during
the transition from the symmetric phase to the broken-symmetry phase. The
defects are created when regions of symmetric phase undergo a transition to
different broken-symmetry states. In an analogous situation, when a liquid
crystallizes, different regions may begin to crystallize with different
orientations of the crystallographic axes. The domains of different crystal
orientation grow and coalesce, and it is energetically favorable for them to
smooth the misalignment along their boundaries. The smoothing is often
imperfect, however, and localized defects remain.

**
I**n
the grand unified theories there are serious cosmological problems associated
with pointlike defects, which correspond to magnetic monopoles, and surfacelike
defects, called domain walls. Both are expected to be extremely stable and
extremely massive. (The monopole can be shown to be about 1016 times
as heavy as the proton.) A domain of correlated broken-symmetry phase cannot be
much larger than the horizon distance at that time, and so the minimum number of
defects created during the transition can be estimated. The result is that there
would be so many defects after the transition that their mass would dominate the
energy density of the universe and thereby speed up its subsequent evolution.
The microwave background radiation would reach its present temperature of three
degrees K. only 30,000 years after the big bang instead of 10 billion years, and
all the successful predictions of the big-bang model would be lost. Thus any
successful union of grand unified theories and the big-bang picture must
incorporate some mechanism to drastically suppress the production of magnetic
monopoles and domain walls.

**T**he inflationary-universe model appears to provide a satisfactory solution to
these problems. Before the model can be described, however, we must first
explain a few more of the details of symmetry breaking and phase transitions in
grand unified theories.

**A**ll modern particle theories, including the grand unified theories, are examples
of quantum field theories. The best-known field theory is the one that describes
electromagnetism. According to the classical (nonquantum) theory of
electromagnetism developed by James Clerk Maxwell in the 1860's, electric and
magnetic fields have a well-defined value at every point in space, and their
variation with time is described by a definite set of equations. Maxwell's
theory was modified early in the 20th century in order to achieve consistency
with the quantum theory. In the classical theory it is possible to increase the
energy of an electromagnetic field by any amount, but in the quantum theory the
increases in energy can come only in discrete lumps, the quanta, which in this
case are called photons. The photons have both wavelike and particlelike
properties, but in the lexicon of modern physics they are usually called
particles. In general the formulation of a quantum field theory begins with a
classical theory of fields, and it becomes a theory of particles when the rules
of the quantum theory are applied.

**
A**s
we have already mentioned, an essential ingredient of grand unified theories is
the phenomenon of spontaneous symmetry breaking. The detailed mechanism of
spontaneous symmetry breaking in grand unified theories is simpler in many ways
than the analogous mechanism in crystals. In a grand unified theory spontaneous
symmetry breaking is accomplished by including in the formulation of the theory
a special set of fields known as Higgs fields (after Peter W. Higgs of the
University of Edinburgh). The symmetry is unbroken when all the Higgs fields
have a value of zero, but it is spontaneously broken whenever at least one of
the Higgs fields acquires a nonzero value. Furthermore, it is possible to
formulate the theory in such a way that a Higgs field has a nonzero value in the
state of lowest energy density, which in this context is known as the true
vacuum. At temperatures greater than about 1027 degrees
thermal fluctuations drive the equilibrium value of the Higgs field to zero,
resulting in a transition to the symmetric phase.

**
W**e
have now assembled enough background information to describe the inflationary
model of the universe, beginning with the form in which it was first proposed by
one of us (Guth) in 1980. Any cosmological model must begin with some
assumptions about the initial conditions, but for the inflationary model the
initial conditions can be rather arbitrary. One must assume, however, that the
early universe included at least some regions of gas that were hot compared with
the critical temperature of the phase transition and that were also expanding.
In such a hot region the Higgs field would have a value of zero. As the
expansion caused the temperature to fall it would become thermodynamically
favorable for the Higgs field to acquire a nonzero value, bringing the system to
its broken-symmetry phase.

**F**or some values of the unknown parameters of the grand unified theories this
phase transition would occur very slowly compared with the cooling rate. As a
result the system could cool to well below 1027 degrees
with the value of the Higgs field remaining at zero. This phenomenon, known as
supercooling, is quite common in condensed-matter physics; water, for example,
can be supercooled to more than 20 degrees below its freezing point, and glasses
are formed by rapidly supercooling a liquid to a temperature well below its
freezing point.

**
A**s
the region of gas continued to supercool, it would approach a peculiar state of
matter known as a false vacuum. This state of matter has never been observed,
but it has properties that are unambiguously predicted by quantum field theory.
The temperature, and hence the thermal component of the energy density, would
rapidly decrease and the energy density of the state would be concentrated
entirely in the Higgs field. A zero value for the Higgs field implies a large
energy density for the false vacuum. In the classical form of the theory such a
state would be absolutely stable, even though it would not be the state of
lowest energy density. States with a lower energy density would be separated
from the false vacuum by an intervening energy barrier, and there would be no
energy available to take the Higgs field over the barrier.

**
I**n
the quantum version of the model the false vacuum is not absolutely stable.
Under the rules of the quantum theory all the fields would be continually
fluctuating. As was first described by Sidney R. Coleman of Harvard, a quantum
fluctuation would occasionally cause the Higgs field in a small region of space
to âtunnelâ through the energy barrier, nucleating a âbubbleâ of the
broken-symmetry phase. The bubble would then start to grow at a speed that would
rapidly approach the speed of light, converting the false vacuum into the
broken-symmetry phase. The rate at which bubbles form depends sensitively on the
unknown parameters of the grand unified theory; in the inflationary model it is
assumed that the rate would be extremely low.

**T**he most peculiar property of the false vacuum is probably its pressure, which
is both large and negative. To understand why, consider again the process by
which a bubble of true vacuum would grow into a region of false vacuum. The
growth is favored energetically because the true vacuum has a lower energy
density than the false vacuum. The growth also indicates, however, that the
pressure of the true vacuum must be higher than the pressure of the false
vacuum, forcing the bubble wall to grow outward. Because the pressure of the
true vacuum is zero, the pressure of the false vacuum must be negative. A more
detailed argument shows that the pressure of the false vacuum is equal to the
negative value of its energy density (when the two quantities are measured in
the same units).

**T**he negative pressure would not result in mechanical forces within the false
vacuum, because mechanical forces arise only from differences in pressure.
Nevertheless, there would be gravitational effects. Under ordinary circumstances
the expansion of the region of gas would be slowed by the mutual gravitational
attraction of the matter within it. In Newtonian physics this attraction is
proportional to the mass density, which in relativistic theories is equal to the
energy density divided by the square of the speed of light. According to general
relativity, the pressure also contributes to the attraction; to be specific, the
gravitational force is proportional to the energy density plus three times the
pressure. For the false vacuum the contribution made by the pressure would
overwhelm the energy-density contribution and would have the opposite sign.
Hence the bizarre notion of negative pressure leads to the even more bizarre
effect of a gravitational force that is effectively repulsive. As a result the
expansion of the region would be accelerated and the region would grow
exponentially, doubling in diameter during each interval of about 10-34 second.

**T**his period of accelerated expansion is called the inflationary era, and it is
the key element of the inflationary model of the universe. According to the
model, the inflationary era continued for 10-32 second
or longer, and during this period the diameter of the universe increased by a
factor of 1050 or
more. It is assumed that after this colossal expansion the transition to the
broken-symmetry phase finally took place. The energy density of the false vacuum
was then released, resulting in a tremendous amount of particle production. The
region was reheated to a temperature of almost 1027 degrees.
(In the language of thermodynamics the energy released is called the latent
heat; it is analogous to the energy released when water freezes.) From this
point on the region would continue to expand and cool at the rate described by
the standard big-bang model. A volume the size of the observable universe would
lie well within such a region.

**T**he horizon problem is avoided in a straightforward way. In the inflationary
model the observed universe evolves from a region that is much smaller in
diameter (by a factor of 1050 or
more) than the corresponding region in the standard model. Before inflation
begins the region is much smaller than the horizon distance, and it has time to
homogenize and reach thermal equilibrium. This small homogeneous region is then
inflated to become large enough to encompass the observed universe. Thus the
sources of the microwave background radiation arriving today from all directions
in the sky were once in close contact; they had time to reach a common
temperature before the inflationary era began.

**T**he flatness problem is also evaded in a simple and natural way. The equations
describing the evolution of the universe during the inflationary era are
different from those for the standard model, and it turns out that the ratio Ù
is driven rapidly toward 1, no matter what value it had before inflation. This
behavior is most easily understood by recalling that a value of Ù = 1
corresponds to a space that is geometrically flat. The rapid expansion causes
the space to become flatter just as the surface of a balloon becomes flatter
when it is inflated. The mechanism driving Ù toward 1 is so effective that one
is led to an almost rigorous prediction: The value of Ù today should be very
accurately equal to 1. Many astronomers (although not all) think a value of 1 is
consistent with current observations, but a more reliable determination of Ù
would provide a crucial test of the inflationary model.

**
I**n
the form in which the inflationary model was originally proposed it had a
crucial flaw: under the circumstances described, the phase transition itself
would create inhomogeneities much more extreme than those observed today. As we
have already described, the phase transition would take place by the random
nucleation of bubbles of the new phase. It can be shown that the bubbles would
always remain in finite clusters disconnected from one another, and that each
cluster would be dominated by a single largest bubble. Almost all the energy in
the cluster would be initially concentrated in the surface of the largest
bubble, and there is no apparent mechanism to redistribute energy uniformly.
Such a configuration bears no resemblance to the observed universe.

**F**or almost two years after the invention of the inflationary-universe model it
remained a tantalizing but clearly imperfect solution to a number of important
cosmological problems. Near the end of 1981, however, a new approach was
developed by A. D. Linde of the P. N. Lebedev Physical Institute in Moscow and
independently by Andreas Albrecht and one of us (Steinhardt) of the University
of Pennsylvania. This approach, known as the new inflationary universe, avoids
all the problems of the original model while maintaining all its successes.

**T**he key to the new approach is to consider a special form of the energy-density
function that describes the Higgs field. Quantum field theories with
energy-density functions of this type were first studied by Coleman, working in
collaboration with Erick J. Weinberg of Columbia University. In contrast to the
more typical caseâ¦, there is no energy barrier separating the false vacuum from
the true vacuum; instead the false vacuum lies at the top of a rather flat
plateau. In the context of grand unified theories such an energy-density
function is achieved by a special choice of parameters. As we shall explain
below, this energy-density function leads to a special type of phase transition
that is sometimes called a slow-rollover transition.

**T**he scenario begins just as it does in the original inflationary model. Again
one must assume the early universe had regions that were hotter than about 1027 degrees
and were also expanding. In these regions thermal fluctuations would drive the
equilibrium value of the Higgs fields to zero and the symmetry would be
unbroken. As the temperature fell it would become thermodynamically favorable
for the system to undergo a phase transition in which at least one of the Higgs
fields acquired a nonzero value, resulting in a broken-symmetry phase. As in the
previous case, however, the rate of this phase transition would be extremely low
compared with the rate of cooling. The system would supercool to a negligible
temperature with the Higgs field remaining at zero, and the resulting state
would again be considered a false vacuum.

**T**he important difference in the new approach is the way in which the phase
transition would take place. Quantum fluctuations or small residual thermal
fluctuations would cause the Higgs field to deviate from zero. In the absence of
an energy barrier the value of the Higgs field would begin to increase steadily;
the rate of increase would be much like that of a ball rolling down a hill of
the same shape as the curve of the energy-density function, under the influence
of a frictional drag force. Since the energy-density curve is almost flat near
the point where the Higgs field vanishes, the early stage of the evolution would
be very slow. As long as the Higgs field remained close to zero, the energy
density would be almost the same as it is in the false vacuum. As in the
original scenario, the region would undergo accelerated expansion, doubling in
diameter every 10-34 second
or so. Now, however, the expansion would cease to accelerate when the value of
the Higgs field reached the steeper part of the curve. By computing the time
required for the Higgs field to evolve, the amount of inflation can be
determined. An expansion factor of 1050 or
more is quite plausible, but the actual factor depends on the details of the
particle theory one adopts.

**
S**o
far the description of the phase transition has been slightly oversimplified.
There are actually many different broken-symmetry states, just as there are many
possible orientations for the axes of a crystal. There are a number of Higgs
fields, and the various broken-symmetry states are distinguished by the
combination of Higgs fields that acquire nonzero values. Since the fluctuations
that drive the Higgs fields from zero are random, different regions of the
primordial universe would be driven toward different broken-symmetry states,
each region forming a domain with an initial radius of roughly the horizon
distance. At the start of the phase transition the horizon distance would be
about 10-24 centimeter.
Once the domain formed, with the Higgs fields deviating slightly from zero in a
definite combination, it would evolve toward one of the stable broken-symmetry
states and would inflate by a factor of 1050 or
more. The size of the domain after inflation would then be greater than 1026 centimeters.
The entire observable universe, which at that time would be only about 10
centimeters across, would be able to fit deep inside a single domain.

**
I**n
the course of this enormous inflation any density of particles that might have
been present initially would be diluted to virtually zero. The energy content of
the region would then consist entirely of the energy stored in the Higgs field.
How could this energy be released? Once the Higgs field evolved away from the
flat part of the energy-density curve, it would start to oscillate rapidly about
the true-vacuum value. Drawing on the relation between particles and fields
implied by quantum field theory, this situation can also be described as a state
with a high density of Higgs particles. The Higgs particles would be unstable,
however: they would rapidly decay to lighter particles, which would interact
with one another and possibly undergo subsequent decays. The system would
quickly become a hot gas of elementary particles in thermal equilibrium, just as
was assumed in the initial conditions for the standard model. The reheating
temperature is calculable and is typically a factor of between two and 10 below
the critical temperature of the phase transition. From this point on, the
scenario coincides with that of the standard big-bang model, and so all the
successes of the standard model are retained.

**N**ote that the crucial flaw of the original inflationary model is deftly avoided.
Roughly speaking, the isolated bubbles that were discussed in the original model
are replaced here by the domains. The domains of the slow-rollover transition
would be surrounded by other domains rather than by false vacuum, and they would
tend not to be spherical. The term âbubbleâ is therefore avoided. The key
difference is that in the new inflationary model each domain inflates in the
course of its formation, producing a vast essentially homogeneous region within
which the observable universe can fit.

**S**ince the reheating temperature is near the critical temperature of the
grand-unified-theory phase transition, the matter-antimatter asymmetry could be
produced by particle interactions just after the phase transition. The
production mechanism is the same as the one predicted by grand unified theories
for the standard big-bang model. In contrast to the standard model, however, the
inflationary model does not allow the possibility of assuming the observed net
baryon number of the universe as an initial condition; the subsequent inflation
would dilute any initial baryon-number density to an imperceptible level. Thus
the viability of the inflationary model depends crucially on the viability of
particle theories, such as the grand unified theories, in which baryon number is
not conserved.

**O**ne can now grasp the solutions to the cosmological problems discussed above.
The horizon and flatness problems are resolved by the same mechanisms as in the
original inflationary-universe model. In the new inflationary scenario the
problem of monopoles and domain walls can also be solved. Such defects would
form along the boundaries separating domains, but the domains would have been
inflated to such an enormous size that the defects would lie far beyond any
observable distance. (A few defects might be generated by thermal effects after
the transition, but they are expected to be negligible in number.)

**T**hus with a few simple ideas the improved inflationary model of the universe
leads to a successful resolution of several major problems that plague the
standard big-bang picture: the horizon, flatness, magnetic-monopole, and
domain-wall problems. Unfortunately the necessary slow-rollover transition
requires the fine tuning of parameters; calculations yield reasonable
predictions only if the parameters are assigned values in a narrow range. Most
theorists (including both of us) regard such fine tuning as implausible. The
consequences of the scenario are so successful, however, that we are encouraged
to go on in the hope we may discover realistic versions of grand unified
theories in which such a slow-rollover transition occurs without fine tuning.

**T**he successes already discussed offer persuasive evidence in favor of the new
inflationary model. Moreover, it was recently discovered that the model may also
resolve an additional cosmological problem not even considered at the time the
model was developed: the smoothness problem. The generation of density
inhomogeneities in the new inflationary universe was addressed in the summer of
1982 at the Nuffield Workshop on the Very Early Universe by a number of
theorists, including James M. Bardeen of the University of Washington, Stephen
W. Hawking of the University of Cambridge, So-Young Pi of Boston University,
Michael S. Turner of the University of Chicago, A. A. Starobinsky of the L. D.
Landau Institute of Theoretical Physics in Moscow and the two of us. It was
found that the new inflationary model, unlike any previous cosmological model,
leads to a definite prediction for the spectrum of inhomogeneities. Basically
the process of inflation first smoothes out any primordial inhomogeneities that
might have been present in the initial conditions. Then in the course of the
phase transition inhomogeneities are generated by the quantum fluctuations of
the Higgs field in a way that is completely determined by the underlying
physics. The inhomogeneities are created on a very small scale of length, where
quantum phenomena are important, and they are then enlarged to an astronomical
scale by the process of inflation.

**T**he predicted shape for the spectrum of inhomogeneities is essentially
scale-invariant; that is, the magnitude of the inhomogeneities is approximately
equal on all length scales of astrophysical significance. This prediction is
comparatively insensitive to the details of the underlying grand unified theory.
It turns out that a spectrum of precisely this shape was proposed in the early
1970's as a phenomenological model for galaxy formation by Edward R. Harrison of
the University of Massachusetts at Amherst and Yakov B. Zel'dovich of the
Institute of Physical Problems in Moscow, working independently. The details of
galaxy formation are complex and are still not well understood, but many
cosmologists think a scale-invariant spectrum of inhomogeneities is precisely
what is needed to explain how the present structure of galaxies and galactic
clusters evolved.

**T**he new inflationary model also predicts the magnitude of the density
inhomogeneities, but the prediction is quite sensitive to the details of the
underlying particle theory. Unfortunately the magnitude that results from the
simplest grand unified theory is far too large to be consistent with the
observed uniformity of the cosmic microwave background. This inconsistency
represents a problem, but it is not yet known whether the simplest grand unified
theory is the correct one. In particular the simplest grand unified theory
predicts a lifetime for the proton that appears to be lower than present
experimental limits. On the other hand, one can construct more complicated grand
unified theories that result in density inhomogeneities of the desired
magnitude. Many investigators imagine that with the development of the correct
particle theory the new inflationary model will add the resolution of the
smoothness problem to its list of successes.

**O**ne promising line of research involves a class of quantum field theories with a
new kind of symmetry called supersymmetry. Supersymmetry relates the properties
of particles with integer angular momentum to those of particles with
half-integer angular momentum; it thereby highly constrains the form of the
theory. Many theorists think supersymmetry might be necessary to construct a
consistent quantum theory of gravity, and to eventually unify gravity with the
strong, the weak and the electromagnetic forces. A tantalizing property of
models incorporating supersymmetry is that many of them give slow-rollover phase
transitions without any fine tuning of parameters. The search is on to find a
supersymmetry model that is realistic as far as particle physics is concerned
and that also gives rise to inflation and to the correct magnitude for the
density inhomogeneities.

**
I**n
short, the inflationary model of the universe is an economical theory that
accounts for many features of the observable universe lacking an explanation in
the standard big-bang model. The beauty of the inflationary model is that the
evolution of the universe becomes almost independent of the details of the
initial conditions, about which little if anything is known. It follows,
however, that if the inflationary model is correct, it will be difficult for
anyone to ever discover observable consequences of the conditions existing
before the inflationary phase transition. Similarly, the vast distance scales
created by inflation would make it essentially impossible to observe the
structure of the universe as a whole. Nevertheless, one can still discuss these
issues, and a number of remarkable scenarios seem possible.

**T**he simplest possibility for the very early universe is that it actually began
with a big bang, expanded rather uniformly until it cooled to the critical
temperature of the phase transition and then proceeded according to the
inflationary scenario. Extrapolating the big-bang model back to zero time brings
the universe to a cosmological singularity, a condition of infinite temperature
and density in which the known laws of physics do not apply. The instant of
creation remains unexplained. A second possibility is that the universe began
(again without explanation) in a random, chaotic state. The matter and
temperature distributions would be nonuniform, with some parts expanding and
other parts contracting. In this scenario certain small regions that were hot
and expanding would undergo inflation, evolving into huge regions easily capable
of encompassing the observable universe. Outside these regions there would
remain chaos, gradually creeping into the regions that had inflated.

**R**ecently there has been some serious speculation that the actual creation of the
universe is describable by physical laws. In this view the universe would
originate as a quantum fluctuation, starting from absolutely nothing. The idea
was first proposed by Edward P. Tryon of Hunter College of the City University
of New York in 1973, and it was put forward again in the context of the
inflationary model by Alexander Vilenkin of Tufts University in 1982. In this
context ânothingâ; might refer to empty space, but Vilenkin uses it to describe
a state devoid of space, time and matter. Quantum fluctuations of the structure
of space-time can be discussed only in the context of quantum gravity, and so
these ideas must be considered highly speculative until a working theory of
quantum gravity is formulated. Nevertheless, it is fascinating to contemplate
that physical laws may determine not only the evolution of a given state of the
universe but also the initial conditions of the observable universe.

**
A**s
for the structure of the universe as a whole, the inflationary model allows for
several possibilities. (In all cases the observable universe is a very small
fraction of the universe as a whole; the edge of our domain is likely to lie 1035 or
more light-years away.) The first possibility is that the domains meet one
another and fill all space. The domains are then separated by domain walls, and
in the interior of each wall is the symmetric phase of the grand unified theory.
Protons or neutrons passing through such a wall would decay instantly. Domain
walls would tend to straighten with time. After 1035 years
or more smaller domains (possibly even our own) would disappear and larger
domains would grow.

**A**lternatively, some versions of grand unified theories do not allow for the
formation of sharp domain walls. In these theories it is possible for different
broken-symmetry states in two neighboring domains to merge smoothly into each
other. At the interface of two domains one would find discontinuities in the
density and velocity of matter, and one would also find an occasional magnetic
monopole.

**
A**
quite different possibility would result if the energy density of the Higgs
fields were described by a [different type of] curveâ¦ As in the other two cases,
regions of space would supercool into the false-vacuum state and undergo
accelerated expansion. As in the original inflationary model, the false-vacuum
state would decay by the mechanism of random bubble formation: quantum
fluctuations would cause at least one of the Higgs fields in a small region of
space to tunnel through the energy barrierâ¦ In contrast to the original
inflationary scenario, the Higgs field would then evolve very slowlyâ¦to its
true-vacuum value. The accelerated expansion would continue, and the single
bubble would become large enough to encompass the observed universe. If the rate
of bubble formation were low, bubble collisions would be rare. The fraction of
space filled with bubbles would become closer to 1 as the system evolved, but
space would be expanding so fast that the volume remaining in the false-vacuum
state would increase with time. Bubble universes would continue to form forever,
and there would be no way of knowing how much time had elapsed before our bubble
was formed. This picture is much like the old steady-state cosmological model on
the very large scale, and yet the interior of each bubble would evolve according
to the big-bang model, improved by inflation.

**F**rom a historical point of view probably the most revolutionary aspect of the
inflationary model is the notion that all the matter and energy in the
observable universe may have emerged from almost nothing. This claim stands in
marked contrast to centuries of scientific tradition in which it was believed
that something cannot come from nothing. The tradition, dating back at least as
far as the Greek philosopher Parmenides in the fifth century B.C., has manifested itself in modern times in the
formulation of a number of conservation laws, which state that certain physical
quantities cannot be changed by any physical process. A decade or so ago the
list of quantities thought to be conserved included energy, linear momentum,
angular momentum, electric charge, and baryon number.

**S**ince the observed universe apparently has a huge baryon number and a huge
energy, the idea of creation from nothing has seemed totally untenable to all
but a few theorists. (The other conservation laws mentioned above present no
such problems: the total electric charge and the angular momentum of the
observed universe have values consistent with zero, whereas the total linear
momentum depends on the velocity of the observer and so cannot be defined in
absolute terms.) With the advent of grand unified theories, however, it now
appears quite plausible that baryon number is not conserved. Hence only the
conservation of energy needs further consideration.

**T**he total energy of any system can be divided into a gravitational part and a nongravitational part. The gravitational part (that is, the energy of the
gravitational field itself) is negligible under laboratory conditions, but
cosmologically it can be quite important. The nongravitational part is not by
itself conserved; in the standard big-bang model it decreases drastically as the
early universe expands, and the rate of energy loss is proportional to the
pressure of the hot gas. During the era of inflation, on the other hand, the
region of interest is filled with a false vacuum that has a large negative
pressure. In this case the nongravitational energy increases drastically.
Essentially all the nongravitational energy of the universe is created as the
false vacuum undergoes its accelerated expansion. This energy is released when
the phase transition takes place, and it eventually evolves to become stars,
planets, human beings, and so forth. Accordingly, the inflationary model offers
what is apparently the first plausible scientific explanation for the creation
of essentially all the matter and energy in the observable universe.

**U**nder these circumstances the gravitational part of the energy is somewhat
ill-defined, but crudely speaking one can say that the gravitational energy is
negative, and that it precisely cancels the nongravitational energy. The total
energy is then zero and is consistent with the evolution of the universe from
nothing.

**
I**f
grand unified theories are correct in their prediction that baryon number is not
conserved, there is no known conservation law that prevents the observed
universe from evolving out of nothing. The inflationary model of the universe
provides a possible mechanism by which the observed universe could have evolved
from an infinitesimal region. It is then tempting to go one step further and
speculate that the entire universe evolved from literally nothing.