A simple model with only six parameters
(the age of the universe, the density of atoms, the density of matter,
the amplitude
of the initial fluctuations, the scale
dependence of this amplitude, and the epoch of first star formation)
fits all of our
cosmological data . Although simple, this
standard model is strange. The model implies that most of the matter in
our Galaxy
is in the form of “dark matter,” a new type of
particle not yet detected in the laboratory, and most of the energy in
the
universe is in the form of “dark energy,” energy
associated with empty space. Both dark matter and dark energy require
extensions
to our current understanding of particle physics
or point toward a breakdown of general relativity on cosmological
scales.
John Archibald Wheeler, my academic great-grandfather, succintly summarized “geometrodynamics,” his preferred name for the
theory of general relativity (1): “Spacetime tells matter how to move; matter tells spacetime how to curve.”
Cosmologists observe the motion of atoms
(either in the form of gas or stars) or follow the paths taken by light
propagating
across the universe and use these observations to
infer the curvature of spacetime. They then use these measurements of
the
curvature of spacetime to infer the distribution of
matter and energy in the universe. Throughout this Review I will
discuss
a variety of observational techniques, but
ultimately they all use general relativity to interpret the observations
and they
all lead to the conclusion that atoms, stuff that
we understand, make up only 5% of the matter and energy density of the
universe.
Standard cosmological model fits, but at a price
Observations of the large-scale distribution of galaxies and quasars show that the universe is nearly uniform on its largest
scales (2) and that the velocity of a distant galaxy depends on its distance (3).
General relativity then implies that we live in an expanding universe
that started in a big bang. Because the universe
expands, light is “redshifted,” so that light
from a distant galaxy appears redder when it reaches us. Hubble’s
observations
that found a linear relationship between galaxy
redshift and distance established the basic model in the 1920s.
Our current cosmological standard model
assumes that general relativity and the standard model of particle
physics have been
a good description of the basic physics of the
universe throughout its history. It assumes that the large-scale
geometry of
the universe is flat: The total energy of the
universe is zero. This implies that Euclidean geometry, the mathematics
taught
to most of us in middle school, is valid on the
scale of the universe. Although the geometry of the universe is simple,
its
composition is strange: The universe is composed
not just of atoms (mostly hydrogen and helium), but also dark matter
and
dark energy.
The currently most popular cosmological
model posits that soon after the big bang, the universe underwent a
period of very
rapid expansion. During this inflationary epoch,
our visible universe expanded in volume by at least 180 e-foldings.
The cosmic background radiation is the leftover heat from this rapid
expansion. This inflationary expansion also
amplifies tiny quantum fluctuations into
variations in density. The inflationary model predicts that these
fluctuations are
“nearly scale-invariant”: The fluctuations have
nearly the same amplitude on all scales.
These density variations set off sound
waves that propagate through the universe and leave an imprint in the
microwave sky
and the large-scale distribution of galaxies.
Our observations of the microwave background are a window into the
universe
380,000 years after the big bang. During this
epoch, electron and protons combined to form hydrogen. Once the universe
became
neutral, microwave background photons could
propagate freely, so the sound waves imprint a characteristic scale, the
distance
that they can propagate in 380,000 years. This
characteristic scale, the “baryon acoustic scale,” serves as a cosmic
ruler
for measuring the geometry of space, thus
determining the density of the universe.
Observations of the temperature and polarization fluctuations in the cosmic microwave background, both from space (4–6) and from ground-based telescopes (7, 8),
test this standard cosmological model and determine its basic
parameters. Remarkably, a model with only six independent
parameters—the age of the universe, the density
of atoms, the density of matter, the amplitude of the density
fluctuations,
their scale dependence, and the epoch of first
star formation—provides a detailed fit to all of the statistical
properties
of the current microwave background
measurements. The same model also fits observations of the large-scale
distribution of
galaxies (9), measurements of the Hubble constant, and the expansion rate of the universe (10, 11), as well as distance determinations from supernovae (12).
The success comes at a price: Atoms make up less than 5% of our
universe; the standard model posits that dark matter dominates
the mass of galaxies and that dark energy,
energy associated with empty space, makes up most of the energy density
of the
universe (see Fig. 1).
Fig. 1
The multiple components that compose our universe.
Dark energy
comprises 69% of the mass energy density of the universe, dark matter
comprises 25%, and “ordinary” atomic matter
makes up 5%. There are other observable
subdominant components: Three different types of neutrinos comprise at
least 0.1%,
the cosmic background radiation makes up
0.01%, and black holes comprise at least 0.005%.
Astronomical observations and cosmological theory suggest that the composition of the universe is remarkably rich and complex.
As Fig. 1 shows, the current best estimates of the universe’s composition (5–8)
suggest that dark energy, dark matter, atoms, three different types of
neutrinos, and photons all make an observable contribution
to the energy density of the universe. Although
black holes are an unlikely candidate for the dark matter (13), their contribution to the mass density of the universe is roughly 0.5% of the stellar density (14).
Astronomical evidence for dark matter
The evidence for dark matter long
predates our observations of the microwave background, supernova
observations, and measurements
of large-scale structure. In a prescient article
published in 1933, Fritz Zwicky (15)
showed that the velocities of galaxies in the Coma cluster were much
higher than expected from previous estimates of galaxy
masses, thus implying that there was a great
deal of additional mass in the cluster. In the 1950s, Kahn and Woltjer (16) argued that the Local Group of galaxies could be dynamically stable only if it contained appreciable amounts of unseen matter.
By the 1970s, astronomers argued that mass in both clusters (17) and galaxies (18) increased with radius and did not trace light. Theoretical arguments that showed that disk stability required dark matter
halos (19) buttressed these arguments. Astronomers studying the motion of gas in the outer regions of galaxies found evidence in an
ever-increasing number of systems for the existence of massive halos (20–24). By the 1980s, dark matter had become an accepted part of the cosmological paradigm.
What do we know about dark matter from astronomical observations today?
Microwave background and large-scale structure observations imply that dark matter is five times more abundant than ordinary
atoms (4–8).
The observations also imply that the dark matter has very weak (or no)
interactions with photons, electrons, and protons.
If the dark matter was made of atoms today, then
in the early universe, it would have been made of ions and electrons
and
would have left a clear imprint on the microwave
sky. Thus, dark matter must be nonbaryonic and “dark.”
Observations of large-scale structure
and simulations of galaxy formation imply that the dark matter must also
be “cold”:
The dark matter particles must be able to
cluster on small scales. Simulations of structure formation with cold
dark matter
(and dark energy) are generally successful at
reproducing the observations of the large-scale distribution of galaxies
(25). When combined with hydrodynamical simulations that model the effects of cooling and star formation, the simulations can
reproduce the basic observed properties of galaxies (26, 27).
Supermassive clusters are important
laboratories for studying dark matter properties. These clusters are
thought to be “fair
samples” of the universe, as the ratio of dark
matter to ordinary matter observed in the clusters is very close to the
cosmological
value (28). X-ray observations directly trace the distribution of ordinary (“baryonic”) matter as most of the atoms in the cluster
gas have been ionized. As Zwicky (29)
first discussed, observations of gravitational lensing of background
galaxies directly trace the total distribution of matter
in the clusters. Today, over 75 years after
Zwicky’s suggestion, astronomers use large-format cameras on the Hubble
Space
Telescope to make detailed maps of the cluster
dark matter distribution (30). These observations reveal considerable amounts of dark matter substructure in the clusters, generally consistent with the
predictions of numerical simulations (31).
At much smaller scales, dwarf galaxies
are another important astronomical testing ground for theories of dark
matter. The
gravitational potential wells of these dark
matter–dominated systems are quite shallow, so the predicted properties
of dwarf
galaxy halos are quite sensitive to dark matter
properties. Several groups (32, 33)
have argued that the observed properties of dwarf galaxies do not match
the predictions of numerical simulations. Although
some astrophysicists argue that improved models
of star-formation feedback can reconcile this discrepancy (34), others suggest that dark matter self-interactions are needed to match simulations to observations (35).
All of the astronomical arguments for the existence of dark matter assume that general relativity is valid on galactic scales.
Alternative gravity theories, such as modified Newtonian dynamics (MOND) (36), obviate the need for dark matter by changing the physics of gravity. Although these models have some phenomenological success
on the galaxy scale (37), they have great difficulties fitting the microwave background fluctuation observations (4–8, 38) and observations of clusters, particularly the bullet cluster (39). Most theorists also consider these alternative models as lacking motivation from fundamental physics.
What is the dark matter?
The existence of nonbaryonic dark
matter implies that there must be new physics beyond the standard model
of particle physics.
Particle physicists have suggested a wealth of
possibilities, some motivated by ideas in fundamental physics and others
by
a desire to explain astronomical phenomena (40).
The early universe was an incredibly
powerful particle accelerator. At the high temperatures and densities of
the early moments
of the big bang, the cosmic background radiation
created an enormous number of particles. Cosmic microwave background
experiments
(5–8) have detected the observational signatures of the copious number of neutrinos produced in the early first moments of the
universe. These early moments could have also created the dark matter particles.
Supersymmetry, the most studied
extension of our current understanding of particle physics, provides
potential candidates
for dark matter. Particles can be divided into
two types: fermions and bosons. Fermions obey the Pauli exclusion
principle:
Only one particle can be found in each state.
Multiple bosons can be found in the same quantum state. Electrons are
fermions,
while photons are bosons. Supersymmetry would be
a new symmetry of nature that links each boson to a fermionic partner
and
vice versa. This symmetry implies a plethora of
new particles: The photon would have a fermionic partner, the photino,
and
the electron would have a bosonic partner, the
selectron. One of the goals of the Large Hadron Collider (LHC) is to
search
for these yet undiscovered supersymmetric
particles.
The lightest supersymmetric particle
(LSP) can be stable. These particles would have been produced copiously
in the first
moments after the big bang. For certain
parameters in the supersymmetric model, the abundance of the LSP is just
what is needed
to explain the observed abundance of dark
matter. This success is an example of the “WIMP miracle” of cosmology: A
weakly
interacting massive particle (WIMP), a particle
that interacts through exchanging particle with masses comparable to the
Higgs
mass, has the needed properties to be the dark
matter.
Particle physics suggests other well-motivated dark matter candidates, including the axion (41) and “asymmetric dark matter” (42), particles whose abundances are not set by their cross section but by an asymmetry between particles and antiparticles.
If WIMPs are the dark matter, then they could be detected through several different routes: Dark matter could be created at
an accelerator or seen either in deep underground experiments or through astronomical observations (40, 43).
These possibilities have led to an active program of searching for dark
matter. This search has had many exciting moments.
There are currently a number of intriguing
signals that might turn out to be the first detection of dark matter:
1) The Gran Sasso Dark Matter (DAMA) experiment has seen an annual modulation in the event rate in its detector (44) with just the theoretical predicted form (45). The interpretation of this result is controversial, as other experiments have failed to detect dark matter and seem to
be in contradiction with this detection claim (46, 47).
2) There have been multiple claims of excess gamma-ray signals coming from the center of our Galaxy at a range of potential
dark matter masses (48, 49).
Because of the high dark matter density in the galactic center, it is
potentially the brightest source of high-energy photons
produced through dark matter self-annihilation.
However, the galactic center also contains a wealth of astrophysical
sources
that emit high-energy photons. Searches in
external galaxies have also suggested the existence of dark matter with
yet a different
mass (50). This claim is also controversial (51). Cosmologists hope that observations of nearby dwarfs could provide a less ambiguous signal (52).
3) Dark matter annihilation in our Galaxy could potentially produce positrons. Cosmic-ray experiments have been searching
for these signals (53). The challenge for these experiments is to separate this signal from astrophysical sources of cosmic rays, such as pulsars
and production from secondary collisions.
Hopefully, future experiments will verify one of these results.
The discovery of the dark matter
particle would resolve a long-standing mystery in astronomy, provide
insights into dark matter’s
role in galaxy formation and structure, and be
the first signature of new physics beyond the Higgs.
Dark energy
When Einstein introduced his theory of
general relativity, he added a cosmological constant term. This term
generated a repulsive
force that countered the pull of gravity and
kept the universe static and stable. In the 1920s, Hubble’s discoveries
showed
that the universe was expanding, and physicists
dropped the cosmological constant term.
Motivated by observational evidence favoring a low-density universe and theoretical prejudice that favored a flat universe,
enthusiasm for a cosmological constant revived in the 1970s and 1980s in the astronomy community (54–56). Physicists recognized that the value of the cosmological constant was a profound problem in fundamental physics (57).
A universe dominated by a cosmological
constant is a strange place to live. We think of gravity as an
attractive force. If
you throw a ball upwards, gravity slows its
climb out of the Earth’s gravitational well. Similarly, gravity (in the
absence
of a cosmological constant) slows the expansion
rate of the universe. Imagine your surprise if you threw a ball upwards
and
it started to accelerate! This is the effect
that a cosmological constant has on the universe’s rate of expansion.
Supernova observations provided critical evidence for the universe’s acceleration. Supernovae are bright stellar explosions
of nearly uniform peak luminosities (58).
Thus, they serve as beacons that can be used to determine the
light-travel distance to their host galaxies. By determining
distance as a function of galaxy redshift, the
supernova observations measure the expansion rate of the universe as a
function
of time. In the late 1990s, supernova observers
reported the surprising result that the expansion rate of the universe
is
accelerating (59, 60).
Over the past 15 years, the observational evidence for cosmic acceleration has continued to grow. Measurements of the baryon
acoustic scale, both in the microwave background (3–8) and in the galaxy distribution (9) as a function of redshift, traced the scale of the universe back to a redshift of 1100. Measurements of the growth rate
of structure as a function of redshift also reinforced the case for cosmic acceleration.
Why is the universe accelerating? The
most studied possibility is that the cosmological constant (or
equivalently, the vacuum
energy of empty space) is driving cosmic
acceleration. Another possibility is that there is an evolving scalar
field that
fills space (like the Higgs field or the
inflaton field that drove the rapid early expansion of the universe) (61).
Both of these possibilities are lumped together in “dark energy.”
Because all of the evidence for dark energy uses the
equations of general relativity to interpret our
observations of the universe’s expansion and evolution, an alternative
conclusion
is that a new theory of gravity is needed to
explain the observations (38). Possibilities include modified gravity theories with extra dimensions (62).
Future observations can determine the
source of cosmic acceleration and determine the nature of dark energy.
Our observations
can measure two different effects: the
relationship between distance and redshift and the growth rate of
structure (63). If general relativity is valid on cosmological scales, then these two measurements should be consistent. These measurements
will also determine the basic properties of the dark energy.
Astrophysicists are currently
operating several ambitious experiments that aim to use measurements of
galaxy clustering and
supernova observations to measure distance and
gravitational lensing observations to measure the growth rate of
structure
(64, 65, 66). These are complemented by microwave background observations (67, 68, 69)
that will provide independent measurements of gravitational lensing and
more precise measurements of cosmic structure. In
the next decade, even more powerful observations
will map the large-scale structure of the universe over the past 10
billion
years and trace the distribution of matter over
much of the observable sky background (70, 71, 72). These observations will provide deeper insights into the source of cosmic acceleration.
Conclusions
Although general relativity is now a
hundred-year-old theory, it remains a powerful, and controversial, idea
in cosmology.
It is one of the basic assumptions behind our
current cosmological model: a model that is both very successful in
matching
observations, but implies the existence of both
dark matter and dark energy. These signify that our understanding of
physics
is incomplete. We will likely need a new idea as
profound as general relativity to explain these mysteries and require
more
powerful observations and experiments to light
the path toward our new insights.
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