sizingup
Inflation
By Steve Nadis
in january 1980, a young Stanford
physicist named Alan Guth unveiled
a brilliant idea that had just one
drawback: it didn’t work. At the time,
Guth (now a professor at MIT) was
fully aware of this shortcoming, yet
he was convinced of the idea’s importance nevertheless. History shows his
faith to have been well placed.
Unlike most 25-year-old ideas that
don’t quite work, this one, which
Guth called “inflation,” was not discarded long ago. Instead, the notion
of a fleeting yet explosive growth
spurt in the universe’s earliest moments has become a cornerstone of
modern cosmology. University of
Chicago astrophysicist Michael Turner
goes further, calling inflation “the
most important idea in cosmology
since the Big Bang.”
32 November 2005 Sky & Telescope
©2005 Sky Publishing Corp. All rights reserved.
What put the bang in the Big Bang?
A physical force whose nature
remains cloaked in mystery.
S&T illustration by Casey B. Reed
©2005 Sky Publishing Corp. All rights reserved.
Sky & Telescope November 2005 33
psizing up inflation
When Guth first conceived of inflation, he doubted that
the idea would be rigorously tested within his lifetime. But
inflation has already passed numerous observational hurdles with flying colors. Now, with the age of “precision cosmology” upon them, astronomers hope to see whether this
powerful idea holds up to even closer scrutiny.
Inflation stands at a critical threshold, claims MIT cosmologist Max Tegmark. “For the first time, inflation theory
is bumping against data. We’re finally getting to the point
where we can kill off a lot of models.” But the cup is only
half full, as the saying goes. Even if the idea withstands the
challenges posed by ever more stringent measurements,
theorists still have to explain exactly how inflation works.
Birth of an Idea
Guth, of course, had no idea what he was getting into when,
in the late 1970s, he embarked on the path that led to inflation. In fact, he knew little about cosmology at the time.
The initial problem he took on, with help from Cornell
University physicist Henry Tye, related to magnetic monopoles
— hypothetical particles that carry lone north or south
poles. Guth and Tye’s calculations suggested that fantastically large numbers of these particles should have been
produced in the Big Bang. Yet none has ever been detected.
Guth and Tye showed that monopole production would
be suppressed if a phase transition in the early universe
Inflation
period
Present
day
1020
1
na
flatio
In
dar
Stan
eory
ry th
ory
d the
Standard
cosmology 1 mm
10–20
1026m
(10–3 m)
Inflationary
cosmology
10–40
3 x 10–27m
1026m
10–60
10–40
10–30
10–20
10–10
1
1010
SOURCE: ALAN GUTH; INSET: JOSEPH SILK, A SHORT HISTORY OF THE UNIVERSE
Radius of universe observable today (meters)
10 40
Time (seconds)
Before inflation entered the picture, most cosmologists believed that today’s observable universe — the region within which light has had time
to reach us — was about 1 millimeter across when it was 10–35 second old.
Although small, this mm-wide region was far vaster than the distance that
light or heat could have traveled since the Big Bang. By contrast, inflation
posits that space expanded exponentially during the universe’s first
10–35 second (or thereabouts), allowing regions that once were in thermal contact to temporarily be taken out of each other’s view. This graph
shows how the region of space that we can see today has grown in both
conventional and inflationary cosmologies. Note that the graph is logarithmic: moving horizontally by 11 mm corresponds to multiplying the
unit of time by a factor of 1010 (10 billion), while 61/2 mm on the vertical
axis corresponds to a 10-billionfold increase in size.
34 November 2005 Sky & Telescope
were delayed by “supercooling,” so that it occurred at a lower
temperature than otherwise would have been the case (just
as supercooled water turns to ice well below its normal
freezing point). Late one night in December 1979, Guth
discovered another consequence of supercooling: it would
propel the universe into a state of exponential growth.
Inflation was thus born.
The accelerated growth Guth proposed didn’t just dilute
magnetic monopoles to unobservably low densities. It also
solved numerous cosmological puzzles, explaining why the
universe is flat, as observed; why it’s so smooth; and even
why it produced the small deviations from complete blandness that eventually generated galaxies and galaxy clusters.
How does inflation accomplish these feats? Before answering that question, let’s first review some of the theory’s
basics. Before the universe was a tiny fraction of a second
old, the theory holds, it already had completed a rapid
burst of exponential expansion lasting perhaps only 10–35
second, during which time its volume increased by a factor
of 1090 or more. Fueling this outlandish growth was an
exotic energy field — the inflaton (not inflation) field — that
turned gravity on its head. During the brief inflationary
epoch, the cosmos was filled with this invisible fog, which
pushed space apart and stretched it out.
This inflation-driving substance had another unusual
property: it was hard to dilute, maintaining a constant or
nearly constant density even as the volume of space it
inhabited expanded like mad. Fortunately for life as we
know it, inflation’s gravity-defying energy field was unstable,
and it eventually decayed into matter and the radiation
now seen as the cosmic microwave background (CMB). It
was this transition that allowed the universe to follow a far
more leisurely expansion over the last 131/2 billion years.
Inflation made the observable universe geometrically
“flat” in the same way that inflating a balloon flattens a small
patch on the balloon’s surface. It also explains why today’s
universe is so remarkably smooth, yet not too smooth to
form stars, galaxies, and galaxy clusters. The uniformity
results from blowing up a tiny region — one small enough
to have achieved thermodynamic equilibrium — into a vast
region encompassing the visible realm. (This addresses the
so-called horizon problem that arises in an inflation-free cosmos, where energy would have had to travel 100 times
faster than the speed of light in order to bring disparate
regions into thermal equilibrium.)
Conversely, the seeds of today’s cosmic structures originated when quantum fluctuations created lumps in the
otherwise uniform tapestry of space-time and inflation
then blew them up to macroscopic proportions. Since these
random, short-lived enhancements of mass and energy were
continuously produced while space stretched outward,
inflation generated fluctuations of roughly the same strength
across a broad range of spatial scales, leading to a so-called
“scale-invariant” spectrum — precisely what cosmologists
observe today.
An Evolving Theory
Although Guth’s original inflation explained many mysterious aspects of our universe, the idea was terminally flawed
— as he noted himself in 1981, when he wrote his first paper
©2005 Sky Publishing Corp. All rights reserved.
Edge
of
A
visi
ble
un
ive
rse
on the subject. How so? Bubbles generated randomly during the transition to a post-inflationary state would have
destroyed the uniformity that inflation had established,
producing a universe far more inhomogeneous than the
one we see today.
“New inflation” — conceived in 1982 by Andrei Linde
(now at Stanford University) and independently by Paul
Steinhardt and Andreas Albrecht (now at Princeton University and the University of California, Davis, respectively) —
solved that problem by modifying the primordial phase
transition. Bubbles still formed, but they grew to such
gigantic proportions that one would be
enough to encompass the entire observB
able universe.
In 1983 Alexander Vilenkin (Tufts University) pointed out that new inflation
and, indeed, almost all inflation models
Milky Way
are “eternal,” meaning that once the
process starts, it never ends. Inflation,
Co
d
says Vilenkin, is like a chain reaction,
sm
un
ic
gro
stopping in one part of space only to
r a d m icro wa v e b a c k o n s
t
i a ti o n
(CM BR) pho
continue in another. By churning out an
Diagrams are
endless number of isolated bubble uninot to scale
verses, he adds, “eternal inflation totally
changes the way we view the large-scale structure of space,
C
beyond our horizon.” As some cosmologists, Linde includStandard Cosmology
ed, see things, eternal inflation also may provide a physical
basis for the anthropic principle, since different “bubbles”
can assume very different properties, with only a few being
favorable to life (S&T: March 2004, page 42).
The Horizon Problem
(A) Shown here in false color, this map of the
cosmic microwave background (CMB) from the
WMAP satellite dramatizes what actually are
tiny (parts per hundred thousand) deviations
from the microwave sky’s overall temperature
of 2.7° Kelvin. If the Earth were as smooth as
the microwave sky, its highest mountains
would be no taller than New York City’s skyscrapers. (B) The radiation emanated about
131/2 billion years ago from the plasma that
filled the early universe, and it has streamed
toward the Milky Way ever since. (C) Early
observations hinting at the CMB’s smoothness
surprised astronomers, since pre-inflationary
cosmology didn’t allow regions now seen on
opposite sides of our sky to ever have been in
thermal contact. (D) Inflation’s temporary exponential growth spurt made it possible for all
the parcels of cosmic real estate covering our
skies to have reached thermal equilibrium
before being pulled out of one another’s reach.
Milky Way
D
Inflationary Cosmology
Milky Way
S&T: CASEY B. REED; PANEL A: WMAP TEAM
Inflation’s First Tests
If eternal inflation sounds metaphysical to you, you’re not
alone. Even Vilenkin admits that the idea will not be subject to empirical scrutiny anytime soon. Fortunately,
though, many of inflation’s predictions are testable, and
they have been tested with exquisite precision. Just where
does the theory stand today in light of current data? “So
far, the results are in beautiful agreement with inflation,”
says Steinhardt, an inflation pioneer and occasional critic.
Inflation predicts that space should appear flat because
any initial curvature in the region of the universe now visible from Earth would have been stretched taut by the universe’s rapid-fire expansion. This solved a problem nagging
cosmologists in the 1970s. Preliminary data suggested
that the universe was nearly flat — but not quite. Yet preinflation theory mandated that the slightest curvature would
cause it to curl up like a ball (a “closed” geometry) or warp
like a saddle (an “open” one). Consequently, cosmologists
reasoned, the universe had to be flat, or ours would be an
inexplicably unusual time in cosmic history.
At the time, this vaguely Copernican argument was the
best evidence in favor of a flat cosmos. But data from
NASA’s Wilkinson Microwave Anisotropy Probe (WMAP)
satellite and other CMB measurements now show the universe to be flat with a precision of about 1 percent, according to Tegmark. (The European Space Agency’s Planck
spacecraft, scheduled to fly in 2007, should improve upon
that accuracy tenfold.)
Inflation also predicts that the universe should be homo-
COSMOLOGICAL PUZZLE NO. 1
©2005 Sky Publishing Corp. All rights reserved.
psizing up inflation
genous on the largest observable scales. Data from WMAP,
NASA’s earlier Cosmic Background Explorer, and various
ground-based instruments all have borne this out, showing
that the CMB’s temperature varies across the entire sky by
only 1 part in 100,000. These measurements, says Guth,
“are every bit as precise as data we get out of particle
physics experiments, and everything seems to be agreeing
with simple inflation.”
Yet another of inflation’s predictions is scale invariance — the idea that the early universe had no
preferred scale. In such a cosmos, the relative
numbers and sizes of unusually dense or rarefied
regions should look roughly the same no matter
how closely you zoom into the cosmic tapestry. A
number called the spectral index characterizes the
distribution of these density differences, with a
value of 1 implying perfect scale invariance.
Cosmologists expect a slight departure from 1,
explains Tegmark, because if the universe were to
remain perfectly scale-invariant, the density would
never change and inflation would go on forever. But we
know inflation ended because stars and planets would
never have formed in an ever-inflating universe. So far,
WMAP and galaxy maps from the Sloan Digital Sky Survey
(SDSS) yield a spectral index of 0.97 plus or minus 0.03,
which is encouraging, says Tegmark. If the index stays just
below 1 after all the data from SDSS, WMAP, and Planck
are in, that would be a “great triumph” for inflation. A
value of exactly 1, on the other hand, would spell trouble,
as would persuasive evidence (perhaps from Planck) that
the universe is not flat after all.
Variations on a Theme
As observers design ever more exacting tests, theorists are
grappling with their own set of challenges — the principal
one being that inflationary theory is not really a theory at
all. As many see it, inflation is a collection of scenarios
rather than one compelling picture. “There are thousands
of models,” claims Turner, few of which have champions —
“apart from the authors and their mothers.”
“For the first time, inflation
theory is bumping against data.
We’re finally getting to the point
where we can kill off a lot of
models.”
— Max Tegmark, MIT
The abundance of models points to some remaining leeway in the data as well as an incomplete understanding.
“Inflation is still a vague idea that’s based on a vague inflaton field,” concedes Guth. “What are the detailed dynamics
of this field? Right now we’re making them up.”
Physicists use the term scalar field to describe the gravitycountering substance that drives inflation, much as they
describe photons (light “particles”) in terms of electromagnetic fields. Inflation’s scalar field, the inflaton field, is
simply a number at every point in space, and that number
should take on the same value everywhere to spur cosmic
COSMOLOGICAL PUZZLE NO. 2
The Flatness Problem
Below: The observable universe’s geometry depends on Ω, the density of
all of the matter and energy it contains divided by a critical value. As it
turns out, if Ω differed even slightly from 1 in the universe’s infancy, it
would quickly take on extremely high or low values. Since 1980s-era
censuses of stars, galaxies, and other forms of matter suggested that Ω
was somewhere between 0.1 and 1 in today’s era, cosmologists reasoned
that it had to be exactly 1 to avoid implausible fine-tuning. Facing page
(four panels): Inflation naturally explains why the observable universe
appears flat, just as a small patch on a balloon that expands trillions of
times over will look flat to an ant on its surface.
Universe closed
1,000
Closed geometry (Ω > 1)
10
Ω
Universe open
Ω (1 second) = 1.01
100
1.001
High density of mass/energy
Triangle corners add up to > 180°
1.0001
1.0000...
1
0.9999
0.1
0.999
Open geometry (Ω < 1)
0.01
Flat geometry (Ω = 1)
Ω (1 second) = 0.99
Low density of mass/energy
Triangle corners add up to < 180°
Critical density of
mass/energy
Triangle corners = 180°
0.001
1
1 second
102
1 minute
Time (seconds)
104
1 hour
SOURCE, ABOVE: 21ST CENTURY ASTRONOMY, JEFF HESTER ET AL.; SOURCE, FACING PAGE (FOUR PANELS): ALAN GUTH & DAVID KAISER / SCIENCE
36 November 2005 Sky & Telescope
©2005 Sky Publishing Corp. All rights reserved.
106
1 day
1 week
Temperature (degrees Kelvin)
10 32
10 27
10 15
Strong
Grand-unified-theory
(GUT) force
Planck
era
Inf latio n
expansion — though it must change with time so that inflation eventually can end.
According to the theory’s architects, the inflationary
process occurs when the universe is dominated by the scalar
field’s potential energy. Called a “false vacuum” by cosmologists, this physical state is often compared to a ball perched
on a gentle hill. As the ball rolls downhill it picks up speed.
Potential energy becomes kinetic energy, and accelerated
expansion ceases. Researchers can concoct different inflationary scenarios by altering the slope of the potentialenergy curve (the shape of the “hill”).
The whole notion of inflation is predicated on the existence of the hard-to-dilute stuff described by the inflaton
field, says Tegmark. “Nobody knows what that stuff is,
though it’s allowed by the laws of physics.” Indeed, the
“dark energy” now thought to dominate our universe shows
that gravity can act repulsively — except that dark energy
is expected to last a long time, maybe forever, rather than
decaying after a mere 10–35 second, and it is more than 10100
times weaker than inflation (S&T: March 2005, page 32).
Guth believes that “quantum gravity” — a theory that
unites the physics of the large (general relativity) and small
(quantum mechanics) — may be needed for all these ideas
to make sense, with string theory being the leading candidate. “The answer may indeed lie in a new kind of physics
we haven’t yet developed,” agrees
University of Chicago physicist
Robert Wald. But quantum gravity, he says, might revise the picture so radically that the universe
no longer goes through an early
nuclear fo
rce
nuclear
Weak
force
E le c
trowe
ak
force
E le ct
r o m a g n e tic
fo r ce
G r a v it
10–43
10–35
ational fo
rce
10–12
Age of universe (second)
The physics underlying inflation remain mysterious, but most cosmologists agree that the phenomenon occurred when the fabric of space-time
underwent a phase transition — an abrupt change vaguely akin to that
experienced by water freezing. In some theories, inflation occurred when
the strong force (which binds atomic nuclei) differentiated itself from
the electroweak force (which comprises electromagnetism and the weak
force governing nuclear decay). Adapted fom Michael Seeds, Astronomy:
The Solar System and Beyond, 2nd ed.
SOURCE: MAX TEGMARK / SCIENTIFIC AMERICAN
Temperature fluctuations (microdegrees Kelvin)
period of exponential expansion.
Even if the explanation for inflation resides in new
physics like string theory, Guth counters, the problems inflation solves still have to be addressed. “We still need a
mechanism that makes a universe with 1090 particles,” the
approximate number within the visible cosmos, he says. “For that, you
almost certainly need exponential
80
growth. So I’m pretty well convinced
Predicted
Predicted
peak
if
peak
if
that any solution to those problems
70
universe
universe
will look a lot like inflation.”
is open
is closed
What’s more, Guth adds, “recent
60
Actual
advances in string theory make the
data
whole enterprise appear much more
50
plausible.” In 1999, for example, Tye
and New York University physicist Gia
Flat
40
geometry
Dvali showed how inflation might
arise through the gravitational attrac30
tion of membranes, or “branes,”
which, along with strings, serve as
Open geometry
20
Closed geometry
fundamental units of space-time
(S&T: June 2003, page 38). In Tye and
10
Dvali’s model, inflation proceeds
when two stacks of three-dimensional
0
branes drift toward each other within
20 5 2 1
0.5
0.2
higher-dimensional space under the
Angular scale (degrees)
tug of gravity. Inflation is driven by
the gravitational potential energy of
Above: Measured only recently, the CMB power spectrum tells
the separated branes, say Tye and
cosmologists the prevalence on the microwave sky of spots with
Dvali; it stops when the branes collide
various angular sizes. Many observations show that the microand melt, unleashing the energy of
wave sky is blobbiest on angular scales of about 1/2°. This corthe hot Big Bang.
responds precisely to a flat cosmos, with the three angles of a
This geometric picture, which relies
hypothetical intergalactic triangle adding up to 180°.
on the relative motion of branes to
©2005 Sky Publishing Corp. All rights reserved.
Sky & Telescope November 2005 37
psizing up inflation
COSMOLOGICAL PUZZLE NO. 3
Today’s Structured Cosmos
Right: This supercomputer simulation shows particles of matter attracting
one another gravitationally while the universe expands. The lacy structures
formed this way resemble those seen in three-dimensional maps of the
present era’s galaxy distribution (below). To form such a structured cosmos
today, the universe must have started out with some degree of small-scale
irregularity in its infancy. Inflation provides the requisite seeds of largescale structure by inflating microscopic quantum-mechanical fluctuations
to macroscopic proportions.
redshift=18.3
redshift=5.7
redshift=1.4
redshift=0
13.4 billion
years ago
12.6 billion
years ago
9.1 billion
years ago
Present era
ABOVE: VIRGO CONSORTIUM / VOLKER SPRINGEL (MAX PLANCK INSTITUTE FOR ASTROPHYSICS); LEFT: MICHAEL A. STRAUSS / SDSS
1b
lig illion
htyea
rs
Milky Way
drive inflation, is now central to string-theory models. But
brane inflation cannot work without some mechanism for
keeping the six extra spatial dimensions of string theory,
which are normally curled up in tight bundles, from unwrapping during the process and spoiling everything. A
breakthrough came in 2003, when Linde and three coauthors showed how to keep the extra dimensions clenched
tight. The approach has been utilized in almost every
string inflation model advanced since.
Yet Steinhardt, among others, finds string inflation unappealing because the theory predicts an enormous number
of possible universes (10500 or more), each shaped by different physical parameters and different brands of inflation.
“We had hoped string theory would come in and tell us
Insofar as inflation predicts an essentially scale-free spectrum of primordial
fluctuations and a visible universe that
looks flat today, CMBR observations
and galaxy-redshift maps from these
instruments and others all support the
theory while ruling out several alternatives. However, they fall short of
probing the physics of the inflationary
era, when the universe was less than
10–35 second old. This achievement
awaits progress in gravitational-wave
astronomy, CMBR polarization, and
high-energy particle physics.
what the inflaton is and clarify the whole story,” Steinhardt
says. “Instead we’re told that what we see is part of a much
more complicated ‘landscape’ that may have an unbounded
number of versions of inflation.”
With inflation models growing increasingly “baroque”
and “bizarre,” Steinhardt has turned to the “cyclic universe”
— a competing paradigm he is developing with Neil Turok
(Cambridge University). Steinhardt and Turok’s scenario is
like brane inflation without inflation. Instead of two branes
coming together and fusing, they bounce off each other,
periodically moving apart and drawing together. Matter
and radiation get smoothed out during expansion phases,
while density fluctuations are created during contractions.
Inflation never enters the picture.
Linde, for one, doubts that fluctuations could survive the
cyclic universe’s bounce — a so-called “singularity” during
which matter and energy get squeezed to infinite densities
and conventional physics breaks down. In 2004 Matias Zaldarriaga (Harvard-Smithsonian Center for Astrophysics)
and his colleagues found that the density perturbations
produced in the cyclic model are not scale-invariant and
thus are incompatible with observations. But Steinhardt
maintains that the cyclic universe fits the data every bit as
well as inflation does.
Will Inflation Survive?
While Steinhardt and Turok refine their calculations, some
cosmologists see no real alternative to inflation at present.
Boomerang
Sloan Digital Sky Survey
BOOMERANG TEAM
38 November 2005 Sky & Telescope
REIDAR HAND / FERMILAB
©2005 Sky Publishing Corp. All rights reserved.
But it’s too early for a “victory dance,” Turner cautions. Although inflation has withstood every attempt to disprove it,
the idea has not yet been tested fully. Without some unequivocal experimental validation, Turner adds, inflation
“will remain just a convenient explanation for the observations we see.”
There is, however, a smoking gun on the horizon: gravitational waves emitted during the same violent phase transition that spawned inflation. The largest of these primordial
space-time ripples cannot be observed directly because
their wavelengths now span the entire visible universe. But
they would leave a mark in the microwave background.
While this signal would be hard to extract from CMB
temperature maps, say theorists, gravitational waves would
create a distinctive pattern in maps of the
CMB’s polarization.
Although there is certain to be a gravitational-wave imprint in the CMB, says
Tegmark, it may be too feeble to detect.
For “classic inflation,” WMAP will probably not be sensitive enough to see signs
of gravitational waves, he says. “Planck,
which will be an order of magnitude better, might be able to see it.” If not, hopes
will turn to the proposed Beyond Einstein Inflation Probe, which, if built, will
probe the CMB’s polarization with even
greater resolution than Planck’s.
Finding a gravitational-wave signature
on the CMB would be a monumental
breakthrough for inflation, cosmologists agree. The amplitude of the waves would reveal inflation’s energy scale — the
universe’s temperature during the exponential growth phase
— thereby imposing tight constraints upon inflationary theory. But it’s anyone’s guess as to what will actually turn up.
Some of the simplest inflation models yield abundant,
large-amplitude gravitational waves that could be spotted
within a decade. Failure to detect those waves would rule
out a large class of models. But the overall notion of inflation would remain standing. Indeed, the gravitational
waves produced in most string-theory models would be
“unobservably small,” even with the best foreseeable technology, according to theorist Juan Maldacena (Institute for
Advanced Study, Princeton).
Turner agrees that detecting inflation-era gravitational
waves is not guaranteed. If Planck fails to see them, inflation’s ultimate corroboration may have to wait for another
instrument and another decade. Meanwhile, the status of
this promising idea will remain up in the air until the next
make-or-break test comes along.
Regardless of the final verdict, Guth was justified in affirming inflation’s importance from the very outset, Turner
maintains. “An idea doesn’t have to be right to be important,
so long as it gets people thinking in a new way.” By that
standard alone, inflation has been a tremendous success.
Guth, for his part, takes pride in how well inflation has
held up over the decades, though he appreciates its limitations. “Never have we had a model of the early universe that
“Never have we had a model of the
early universe that worked so well
in terms of fitting observations.
But we are just as clueless as ever
about how to describe the universe
in terms of fundamental physics.”
— Alan Guth, MIT
worked so well in terms of fitting observations,” he claimed
in a Santa Barbara, California, presentation last October.
“But we are just as clueless as ever about how to describe
the universe in terms of fundamental physics.”
Devising a full-fledged inflation theory will represent a big
step toward that end, Guth says, though other mysteries
remain. Linde agrees. “Inflation is part of our past,” he says.
“It shapes the universe and forms the galaxies, but it doesn’t
tell us about the nature of dark matter or dark energy.
Although inflation is an important part of the story, and a
part I hope will stay with us, it’s not the whole story.” †
Science writer Steve Nadis covers cosmology and related fields
from his Cambridge, Massachusetts, home office.
Cosmic Background Imager
CBI / CALTECH / NSF
ACBAR
ACBAR TEAM
©2005 Sky Publishing Corp. All rights reserved.
Sky & Telescope November 2005 39
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.