According to inflationary cosmology
[1,
2,
3],
the universe expanded exponentially quickly for a fraction of a
second very early in its history - growing from a patch as
small as 10^{-26} m, one hundred billion times smaller than a
proton, to macroscopic scales on the order of a meter, all within
about 10^{-35} s - before slowing down to the more
stately rate of expansion that has characterized the universe's
behavior ever since. The driving force behind this dramatic
growth, strangely enough, was gravity. [For technical
introductions to inflationary cosmology, see
[4,
5,
6];
a more popular description may be found in
[7].]
Although this might sound like hopeless (or, depending on one's
inclinations, interesting) speculation, in fact inflationary cosmology
leads to several quantitative predictions about the present behavior of
our universe - predictions that are being tested to
unprecedented accuracy by a new generation of observational
techniques. So far the agreement has been excellent.

How could gravity drive the universal repulsion during inflation?
The key to this rapid expansion is that in Einstein's general
relativity (physicists' reigning description of gravity), the
gravitational field couples both to mass-energy (where mass and
energy are interchangeable thanks to Einstein's *E* =
*mc*^{2}) and
to pressure, rather than to mass alone. In the simplest
scenario, in which at least the observable portion of our
universe can be approximated as being homogeneous and isotropic
- that is, having no preferred locations or directions -
Einstein's gravitational equations give a particularly simple
result. The expansion of the universe may be described by
introducing a time-dependent "scale factor," *a*(*t*), with the
separation between any two objects in the universe being
proportional to *a*(*t*). Einstein's equations prescribe how this
scale factor will evolve over time, *t*. The rate of
acceleration is proportional to the density of mass-energy in the
universe, ,
plus three times its pressure, *p*:
*d*^{2} *a* / *dt*^{2} =
- 4
*G*( +
3*p*) *a* / 3, where *G* is Newton's
gravitational constant (and we use units for which the speed of
light *c* = 1). The minus sign is important: ordinary matter under
ordinary circumstances has both positive mass-energy density and
positive (or zero) pressure, so that
( +3*p*)
> 0. In this
case, gravity acts as we would expect it to: All of the matter in
the universe tends to attract all of the other matter, causing
the expansion of the universe as a whole to slow down.

The crucial idea behind inflation is that matter can behave
rather differently from this familiar pattern. Ideas from
particle physics suggest that the universe is permeated by scalar
fields, such as the Higgs field of the standard model of particle
physics, or its more exotic generalizations. (A scalar field
takes exactly one value at every point in space and time. For
example, one could measure the temperature at every position in a
room and repeat the measurements over time, and represent the
measurements by a scalar field, *T*, of temperature. Electric
and magnetic fields are vector fields, which carry three distinct
components at every point in space and time: the field in the *x*
direction, in the *y* direction, and in the *z* direction.
Scalar fields are introduced in particle physics to describe
certain kinds of particles, just as photons are described in
quantum field theories in terms of electromagnetic fields.) These
scalar fields can exist in a special state, having a high energy
density that cannot be rapidly lowered, such as the arrangement
labeled (a) in Fig. 1. Such a state is called a
"false vacuum." Particle physicists use the word "vacuum" to denote
the state of lowest energy. "False vacua" are only metastable,
not the true states of lowest possible energy.

In the early universe, a scalar field in such a false vacuum
state can dominate all the contributions to the total mass-energy
density, . During this period,
remains nearly
constant, even as the volume of the universe expands rapidly:
_{f} =
constant. This is quite different
from the density of ordinary matter, which decreases when the
volume of its container increases. Moreover, the first law of
thermodynamics, in the context of general relativity, implies
that if
_{f}
while the universe expands, then the
equation of state for this special state of matter must be
*p* -
_{f}, a
negative pressure. This yields
*d*^{2} *a* / *dt*^{2} =
8 *G*
_{f}
*a* / 3: Rather than slowing down, the cosmic
expansion rate will grow rapidly, driven by the negative pressure
created by this special state of matter. Under these
circumstances, the scale factor grows as
*a*
*e*^{Ht}, where the Hubble parameter,
*H*
*a*^{-1} *da* / *dt*, which
measures the universe's rate of expansion, assumes the constant
value, *H*
[8 *G*
_{f} /
3]^{1/2}. The universe expands
exponentially until the scalar field rolls to near the bottom of
the hill in the potential energy diagram.

What supplies the energy for this gigantic expansion? The answer,
surprisingly, is that no energy is needed
[7].
Physicists have known since the 1930s
[8]
that the gravitational field carries *negative* potential energy
density. As vast quantities of matter are produced during
inflation, a vast amount of negative potential energy
materializes in the gravitational field that fills the
ever-enlarging region of space. The total energy remains
constant, and very small, and possibly exactly equal to zero.

There are now dozens of models that lead to this generic
inflationary behavior, featuring an equation of state,
*p* -
, during the
early universe
[4,
9].
This entire family of models, moreover, leads to several main
predictions about today's universe. First, our observable
universe should be spatially flat. Einstein's general relativity
allows for all kinds of curved (or "non-Euclidean") spacetimes.
Homogeneous and isotropic spacetimes fall into three classes
(Fig. 2), depending on the value of the
mass-energy density,
. If
>
_{c},
where
_{c}
3*H*^{2} /
(8 *G*), then Einstein's
equations imply that the spacetime will be
positively curved, or closed (akin to the two-dimensional surface
of a sphere); parallel lines will intersect, and the interior
angles of a triangle will always add up to more than 180°.
If <
_{c},
the spacetime will be negatively curved, or
open (akin to the two-dimensional surface of a saddle); parallel
lines will diverge and triangles will sum to less than
180°. Only if
=
_{c}
will spacetime be spatially
flat (akin to an ordinary two-dimensional flat surface); in this
case, all of the usual rules of Euclidean geometry apply.
Cosmologists use the letter
to designate the
ratio of the actual mass-energy density in the universe to this critical
value:
/
_{c}.
Although general relativity allows any value for this ratio, inflation
predicts that
= 1 within our
observable universe to extremely
high accuracy. Until recently, uncertainties in the measurement
of allowed any
value in the wide range,
0.1
2, with many observations
seeming to favor
0.3. A new generation of
detectors, however, has dramatically
changed the situation. The latest observations, combining data
from the Wilkinson Microwave Anisotropy Probe (WMAP), the Sloan
Digital Sky Survey (SDSS), and observations of type Ia
supernovae, have measured
=
1.012_{-0.022}^{+0.018}
[10]
- an amazing match between prediction and observation.

In fact, inflation offers a simple explanation for why the
universe should be so flat today. In the standard big bang
cosmology (without inflation),
= 1 is an
*unstable*
solution: if were
ever-so-slightly less than 1 at an
early time, then it would rapidly slide toward 0. For example,
if were 0.9 at 1 s
after the big bang, it would be only 10^{-14} today. If
were 1.1 at
*t* = 1 s,
then it would have grown so quickly that the universe would have
recollapsed just 45 s later. In inflationary models, on
the other hand, any original curvature of the early universe
would have been stretched out to near-flatness as the universe
underwent its rapid expansion (Fig. 3).
Quantitatively, | -1|
1 /
(*aH*)^{2}, so that while
*H* constant
and *a*
*e*^{Ht} during the inflationary epoch,
gets driven rapidly to 1.

The second main prediction of inflation is that the presently
observed universe should be remarkably smooth and homogeneous on
the largest astronomical scales. This, too, has been measured to
extraordinary accuracy during the past decades. Starting in the
1960s, Earth-bound, balloon-borne, and now satellite detectors
have measured the cosmic microwave background (CMB) radiation, a
thermal bath of photons that fills the sky. The photons today
have a frequency that corresponds to a temperature of 2.728 K
[11].
These photons were released
~ 400,000 years after the inflationary epoch, when the
universe had cooled to a low enough temperature that would allow
stable (and electrically neutral) atoms to form. Before that
time, the ambient temperature of matter in the universe was so
high that would-be atoms were broken up by high-energy photons as
soon as they formed, so that the photons were effectively
trapped, constantly colliding into electrically charged matter.
Since stable atoms formed, however, the CMB photons have been
streaming freely. Their temperature today is terrifically
uniform: After adjusting for the Earth's motion, CMB photons
measured from any direction in the sky have the same temperature
to one part in 10^{5}
[12].

Without inflation, this large-scale smoothness appears quite
puzzling. According to ordinary (noninflationary) big bang
cosmology, these photons should never have had a chance to come
to thermal equilibrium: The regions in the sky from which they
were released would have been about 100 times farther apart than
even light could have traveled between the time of the big bang
and the time of the photons' release
[1,
4,
5,
6]. Much
like the flatness problem, inflation provides a simple and
generic reason for the observed homogeneity of the CMB: Today's
observable universe originated from a *much* smaller region
than that in the noninflationary scenarios. This much-smaller
patch could easily have become smooth before inflation began.
Inflation would then stretch this small homogeneous region to
encompass the entire observable universe.

A third major prediction of inflationary cosmology is that there
should be tiny departures from this strict large-scale
smoothness, and that these ripples (or "perturbations") should
have a characteristic spectrum. Today these ripples can be seen
directly as fluctuations in the CMB. Although the ripples
are believed to be responsible for the grandest structures of the
universe - galaxies, superclusters, and giant voids - in
inflationary models they arise from quantum fluctuations, usually
important only on atomic scales or smaller. The field
that drives inflation, like all quantum fields, undergoes quantum
fluctuations in accord with the Heisenberg uncertainty principle.
During inflation these quantum fluctuations are stretched
proportionally to *a*(*t*), rapidly growing to macroscopic
scales. The result: a set of nearly scale-invariant perturbations
extending over a huge range of wavelengths
[13].
Cosmologists parameterize the spectrum of primordial
perturbations by a spectral index, *n*_{s}. A scale-invariant
spectrum would have
*n*_{s} = 1.00; inflationary models generically
predict *n*_{s} = 1 to within ~ 10%. The latest measurements
of these perturbations by WMAP and SDSS reveal
*n*_{s} = 0.977_{-0.025}^{+0.039}
[10].

Until recently, astronomers were aware of several cosmological
models that were consistent with the known data: an open
universe, with
0.3; an inflationary
universe with considerable dark energy
(); an
inflationary universe
without ; and a
universe in which the primordial
perturbations arose from topological defects such as cosmic
strings. Dark energy
[14]
is a form of matter with
negative pressure that is currently believed to contribute more
than 70% of the total energy of the observed universe. Cosmic
strings are long, narrow filaments hypothesized to be scattered
throughout space, remnants of a symmetry-breaking phase
transition in the early universe
[15,
16].
[Cosmic strings are topologically nontrivial configurations of fields
which should not be confused with the fundamental strings of
superstring theory. The latter are usually believed to have
lengths on the order of 10^{-35} m, although for some
compactifications these strings might also have astronomical lengths
[17].]
Each of these models leads to a
distinctive pattern of resonant oscillations in the early
universe, which can be probed today through its imprint on the
CMB. As can be seen in Fig. 4
[18],
three of the models are now definitively ruled out. The full class of
inflationary models can make a variety of predictions, but the
prediction of the simplest inflationary models with large
, shown on the
graph, fits the data beautifully.