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NATURE Vol 440 27 April 2006 doi:10.1038/nature04805
The large-scale structure of the UniverseVolker Springel1, Carlos S. Frenk2 & Simon D. M. White1 Research over the past 25 years has led to the view that the rich tapestry of present-day cosmic structure
arose during the first instants of creation, where weak ripples were imposed on the otherwise uniform and
rapidly expanding primordial soup. Over 14 billion years of evolution, these ripples have been amplified
to enormous proportions by gravitational forces, producing ever-growing concentrations of dark matter
in which ordinary gases cool, condense and fragment to make galaxies. This process can be faithfully
mimicked in large computer simulations, and tested by observations that probe the history of the Universe
starting from just 400,000 years after the Big Bang.

The past two and a half decades have seen enormous advances in the and is supported by a quantitative comparison of clustering5. Here we study of cosmic structure, both in our knowledge of how it is manifest review what we can learn from this excellent match.
in the large-scale matter distribution, and in our understanding of its The early 1980s produced two audacious ideas that transformed a origin. A new generation of galaxy surveys — the 2-degree Field Galaxy speculative and notoriously uncertain subject into one of the most rap- Redshift Survey, or 2dFGRS1, and the Sloan Digital Sky Survey, or SDSS2 idly developing branches of physics. The first was the proposal that the — have quantified the distribution of galaxies in the local Universe with ubiquitous dark matter that dominates large-scale gravitational forces a level of detail and on length scales that were unthinkable just a few consists of a new (and still unidentified) weakly interacting elemen- years ago. Surveys of quasar absorption and of gravitational lensing have tary particle. Because these particles are required to have small random produced qualitatively new data on the distributions of diffuse inter- velocities at early times, they were dubbed ‘cold dark matter' or CDM. galactic gas and of dark matter. At the same time, observations of the (Hot dark matter is also possible, for example a neutrino with a mass cosmic microwave background radiation, by showing us the Universe of a few tens of electron volts. Early cosmological simulations showed, when it was only about 400,000 years old, have vindicated bold theoreti- however, that the galaxy distribution in a universe dominated by such cal ideas put forward in the 1980s regarding the contents of the Universe particles would not resemble that observed6.) The second idea is ‘cosmic and the mechanism that initially generated structure shortly after the inflation'7, the proposal that the Universe grew exponentially for many Big Bang. The critical link between the early, near-uniform Universe doubling times perhaps 10–35 seconds after the Big Bang, driven by the and the rich structure seen at more recent times has been provided vacuum energy density of an effective scalar field that rolls slowly from by direct numerical simulation. This has made use of the unremitting a false to the true vacuum. Quantum fluctuations in this ‘inflaton' field increase in the power of modern computers to create ever more realistic are blown up to macroscopic scales and converted into genuine ripples virtual universes: simulations of the growth of cosmic structure that in the cosmic energy density. These weak seed fluctuations grow under show how astrophysical processes have produced galaxies and larger the influence of gravity and eventually produce galaxies and the cosmic structures from the primordial soup. Together, these advances have led web. Simple models of inflation predict the statistical properties of these to the emergence of a ‘standard model of cosmology' which, although primordial density fluctuations: their Fourier components should have seemingly implausible, has nevertheless been singularly successful. random and independent phases and a near-scale-invariant power spec- Figure 1 strikingly illustrates how well this standard model can fit trum8. Inflation also predicts that the present Universe should have a flat nearby structure. The observational wedge plots at the top and at the geometry. With concrete proposals for the nature of the dark matter and left show subregions of the SDSS and 2dFGRS, illustrating the large for the initial fluctuation distribution, the growth of cosmic structure volume they cover in comparison to the ground-breaking Center for became, for the first time, a well-posed problem that could be tackled Astrophysics (CfA) galaxy redshift survey3 carried out during the 1980s with the standard tools of physics.
(the central small wedge). These slices through the local three-dimen- The backbone of the cosmic web is the clumpy yet filamentary dis- sional galaxy distribution reveal a tremendous richness of structure. tribution of dark matter. The presence of dark matter was first inferred Galaxies, groups and clusters are linked together in a pattern of sheets from the dynamics of galaxy clusters by Zwicky9. But it took over half a and filaments that is commonly known as the ‘cosmic web'4. A handful century for dark matter to become an integral part of our view of galaxies of particularly prominent aggregations clearly stand out in these images, and of the Universe as a whole, and for its average density to be estimated the largest containing of the order of 10,000 galaxies and extending for reliably. Today, the evidence for the pervasive presence of dark matter several hundred million light years. The corresponding wedge plots is overwhelming and includes galactic rotation curves, the structure of at the right and at the bottom show similarly constructed surveys of a galaxy groups and clusters, large-scale cosmic flows and, perhaps most virtual universe, the result of a simulation of the growth of structure and directly, gravitational lensing, a phenomenon first proposed as an astro- of the formation of galaxies in the current standard model of cosmology. nomical tool by Zwicky himself10. The distorted images of background The examples shown were chosen among a set of random ‘mock surveys' galaxies as their light travels near mass concentrations reveal the pres- to have large structures in similar positions to the real surveys. The ence of dark matter in the outer haloes of galaxies11,12, in galaxy clusters13 similarity of structure between simulation and observation is striking, and in the general mass field14.
1Max-Planck-Institute for Astrophysics, Karl-Schwarzschild-Strasse 1, 85740 Garching, Germany. 2Institute for Computational Cosmology, Department of Physics, University of Durham, South Road, Durham DH1 3LE, UK.
2006 Nature Publishing Group
Springel pagesrc.indd 1137 19/4/06 10:25:16 am 2006 Nature Publishing Group
NATURE Vol 440 27 April 2006 Figure 1 The galaxy distribution obtained from
spectroscopic redshift surveys and from mock
catalogues constructed from cosmological
simulations. The small slice at the top shows the
CfA2 ‘Great Wall'3, with the Coma cluster at the
centre. Drawn to the same scale is a small section
of the SDSS, in which an even larger ‘Sloan
Great Wall' has been identified100. This is one of
the largest observed structures in the Universe,
containing over 10,000 galaxies and stretching
over more than 1.37 billion light years. The cone
on the left shows one-half of the 2dFGRS, which
determined distances to more than 220,000
galaxies in the southern sky out to a depth of
2 billion light years. The SDSS has a similar
depth but a larger solid angle and currently
includes over 650,000 observed redshifts in the
northern sky. At the bottom and on the right,

mock galaxy surveys constructed using semi-
analytic techniques to simulate the formation
and evolution of galaxies within the evolving
dark matter distribution of the ‘Millennium'
simulation5 are shown, selected with matching
survey geometries and magnitude limits.
When expressed in units of the critical density required for a flat cos- low estimates of the mean matter density Ω are incompatible with the mic geometry, the mean density of dark matter is usually denoted by flat geometry predicted by inflation unless the Universe contains an Ω . Although a variety of dynamical tests have been used to constrain additional unclustered and dominant contribution to its energy density, Ω , in general such tests give ambiguous results because velocities are for example a cosmological constant Λ such that Ω + Ω ≈ 1. Two large- induced by the unseen dark matter and the relation of its distribution scale structure surveys carried out in the late 1980s, the APM (automated to that of the visible tracers of structure is uncertain. The notion of a photographic measuring) photographic survey23 and the QDOT redshift substantial bias in the galaxy distribution relative to that of dark matter survey of infrared galaxies24, showed that the power spectrum of the was introduced in the 1980s to account for the fact that different samples galaxy distribution, if it traces that of the mass on large scales, can be of galaxies or clusters are not directly tracing the underlying matter fitted by a simple CDM model only if the matter density is low, Ω ≈ 0.3. distribution15–17. Defined simply as the ratio of the clustering strengths, This independent confirmation of the dynamical arguments led many the ‘bias function' was also invoked to reconcile low dynamical estimates to adopt the now standard model of cosmology, ΛCDM.
for the mass-to-light ratio of clusters with the high global value required It was therefore with a mixture of amazement and déjà vu that cos- in the theoretically preferred flat, Ω = 1 universe. But because massive mologists greeted the discovery in 1998 of an accelerated cosmic expan- clusters must contain approximately the universal mix of dark matter sion25,26. Two independent teams used distant type Ia supernovae to and baryons (ordinary matter), this uncertainty is neatly bypassed by perform a classical observational test. These ‘standard candles' can be comparing the measured baryon fraction in clusters with the universal observed out to redshifts beyond 1. Those at z ≥ 0.5 are fainter than fraction under the assumption that the mean baryon density, Ω , is the expected, apparently indicating that the cosmic expansion is currently value inferred from Big Bang nucleosynthesis18. Applied to the Coma speeding up. Within the standard Friedmann cosmology, there is only cluster, this simple argument gave Ω ≤ 0.3 where the inequality arises one agent that can produce an accelerating expansion: the cosmological because some or all of the dark matter could be baryonic18. This was constant first introduced by Einstein, or its possibly time- or space- the first determination of Ω < 1 that could not be explained away by dependent generalization, ‘dark energy'. The supernova evidence is invoking bias. Subsequent measurements have confirmed the result19 consistent with Ω ≈ 0.7, just the value required for the flat universe which also agrees with recent independent estimates based, for example, predicted by inflation.
on the relatively slow evolution of the abundance of galaxy clusters20,21 or The other key prediction of inflation, a density fluctuation field con- on the detailed structure of fluctuations in the microwave background sistent with amplified quantum noise, received empirical support from the discovery by the COsmic Background Explorer (COBE) satellite in The mean baryon density implied by matching Big Bang nucle- 1992 of small fluctuations in the temperature of the cosmic microwave osynthesis to the observed abundances of the light elements is background (CMB) radiation27. These reflect primordial density fluc- only Ω h2 ≈ 0.02, where h denotes the Hubble constant in units of tuations, modified by damping processes in the early Universe which 100 km s–1 Mpc–1. Dynamical estimates, although subject to bias uncer- depend on the matter and radiation content of the Universe. More recent tainties, have long suggested that Ω = Ω + Ω ≈ 0.3, implying that the measurements of the CMB28–32 culminating with those by the WMAP dark matter cannot be baryonic. Plausibly it is made up of the hypotheti- (Wilkinson Microwave Anisotropy Probe) satellite22 have provided a cal elementary particles postulated in the 1980s, for example axions or striking confirmation of the inflationary CDM model: the measured the lowest mass supersymmetric partner of the known particles. Such temperature fluctuation spectrum is nearly scale-invariant on large 2006 Nature Publishing Group
Springel pagesrc.indd 1138 19/4/06 10:25:22 am 2006 Nature Publishing Group
NATURE Vol 440 27 April 2006 scales and has a series of ‘acoustic' peaks that reflect the coherent oscil- the pattern already present in the gaussian random field of initial fluc- lations experienced by the photon–baryon fluid before the moment tuations4. The first observable objects were probably massive stars col- when the primordial plasma recombined and the radiation escaped. lapsing in small haloes and switching on at redshifts of 50 and higher43. The fluctuation spectrum depends on the parameters that define the By a redshift of 15 these may have been sufficiently numerous for their geometry and content of the Universe and the initial fluctuation distri- radiation to re-ionize all the gas in the Universe44. So far they have not bution, so their values are constrained by the data. In practice, there are been observed directly, but it is one of the main goals of the next genera- degeneracies among the parameters, and the strongest constraints come tion of low-frequency radio telescopes to observe their effects directly in from combining the CMB data with other large-scale structure data- the strongly redshifted 21-cm transition of neutral hydrogen.
sets. Present estimates22,33–36 give a flat universe with Ω = 0.20 ± 0.020, Detailed simulations from ΛCDM initial conditions have been used Ω = 0.042 ± 0.002, Ω = 0.76 ± 0.020, h = 0.74 ± 0.02. The consistency to study the formation of the first luminous objects and the re-ionization of these values with other independent determinations and the close of the Universe, but these still await testing against observation44,45. In agreement of the CMB data with theoretical predictions formulated contrast, predictions for the structure, the ionization state and the heavy over 20 years earlier37 belong amongst the most remarkable successes element content of intergalactic gas at redshifts below 6 can be checked of modern cosmology.
in detail against absorption features observed in the spectra of distant quasars which provide, in effect, a one-dimensional topographic image The growth of large-scale structure
of the intervening large-scale structure.
The microwave background radiation provides a clear picture of the As an example, Fig. 2 shows a typical high-resolution spectrum of young Universe, where weak ripples on an otherwise uniform sea dis- a distant quasar at redshift z = 3.26. At shorter wavelengths than the play a pattern that convincingly supports our standard model for the Lyman α emission line of the quasar, there is a ‘forest' of absorption lines cosmic mass/energy budget and for the process that initially imprinted of differing strength. The modern interpretation is that these features cosmic structure. At that time there were no planets, no stars, no galax- arise from Lyman α absorption by the smoothly varying distribution of ies, none of the striking large-scale structures seen in Fig. 1. The rich- foreground intergalactic hydrogen, in effect from the filaments, sheets ness of the observed astronomical world grew later in a complex and and haloes of cosmic structure. It was a conceptual breakthrough, and highly nonlinear process driven primarily by gravity. This evolution an important success for the CDM paradigm, when hydrodynamical can be followed in detail only by direct numerical simulation. Early simulations showed that this interpretation could explain in detail simulations were able to reproduce qualitatively the structure observed the observed statistics of the absorption lines38,46. Considerable recent both in large galaxy surveys and in the intergalactic medium16,38. They advances both in the quality and in the quantity of data available have motivated the widespread adoption of the CDM model well before made it possible to measure a variety of statistics for the Lyman α forest it gained support from microwave background observations. Many as a function of redshift to high precision47–49. Comparing with appro- physical processes affect galaxy formation, however, and many aspects priately designed numerical simulations has provided strong confirma- must be treated schematically within even the largest simulations. The tion of the underlying paradigm at a level that is remarkable, given the resulting uncertainties are best estimated by exploring a wide range evidence that intergalactic gas is contaminated with galaxy ejecta in a of plausible descriptions and checking results against observations of way that the simulations do not yet adequately reproduce36,50–52. This many different types. The main contribution of early CDM galaxy for- approach has also helped to strengthen constraints on the paradigm's mation modelling was perhaps the dethroning of the ‘island universe' or parameters, in particular on the spectrum of fluctuations produced by ‘monolithic collapse' paradigm and the realization that galaxy formation inflation and on the masses of neutrinos.
is a process extending from early times to the present day, rather than At lower redshift direct and quantitative measures of large-scale struc- an event that occurred in the distant past39.
ture can be obtained from the weak, coherent distortions of the images In a ΛCDM universe, quasi-equilibrium dark matter clumps or of faint galaxies induced by gravitational lensing as their light travels ‘haloes' grow by the collapse and hierarchical aggregation of ever more through the intervening cosmic web53. The distortions depend only on massive systems, a process described surprisingly well by the phenom- the gravitational field in intergalactic space and so lensing data test pre- enological model of Press and Schechter and its extensions40,41. Galaxies dictions for the mass distribution in a way that is almost independent of form at the centres of these dark haloes by the cooling and condensation the complex astrophysics that determines the observable properties of of gas which fragments into stars once it becomes sufficiently dense42. galaxies. The lensing effect is very weak, but can be measured statistically Groups and clusters of galaxies form as haloes aggregate into larger sys- to high precision with large enough galaxy samples.
tems. They are arranged in the ‘cosmic web', the larger-scale pattern of As an example, Fig. 3 shows a measure of the mean square coherent filaments and sheets which is a nonlinear gravitational ‘sharpening' of distortion of distant galaxy images within randomly placed circles on the Figure 2 The Lyman α forest as a probe of
large-scale structure. The panel on the top
shows a typical high-resolution spectrum
of a quasar at redshift z = 3.62. Shortward
of the redshifted Lyman α emission line at
1216(1 + z) Å, the spectrum shows a ‘forest'
of absorption lines of different strength
produced by intervening neutral hydrogen

gas along the line-of-sight from the quasar
Observed wavelength [Å] to the Earth. Hydrodynamical simulations
reproduce the observed absorption spectra

with remarkable fidelity, as illustrated by
the simulated spectrum in the bottom panel,
corresponding to intervening large-scale
structure at z ≈ 3. The sketch in the middle
panel shows an example of the gas distribution
in a simulated ΛCDM model.
2006 Nature Publishing Group
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NATURE Vol 440 27 April 2006 attempted to describe the relation between the galaxy and mass distribu-tions by a bias function. Recent data suggest that this concept is of lim-ited value, except, perhaps, on the largest scales; bias estimates depend not only on scale, redshift and galaxy properties, but also on the particu-lar measure of clustering studied. Understanding the link between the mass and galaxy distributions requires realistic simulations of the galaxy formation process throughout large and representative regions of the Universe. Given the complexity of galaxy formation, such simulations must be tuned ‘by hand' to match as many of the observed properties of galaxies as possible. Only if clustering turns out to be insensitive to such tuning can we consider the portrayal of large-scale structure to be robust and realistic.
In Fig. 4, we show the time evolution of the mass and galaxy distribu- tions in a small subregion of the largest simulation of this type yet5. The emergence of the cosmic web can be followed in stunning detail, produc-ing a tight network of filaments and walls surrounding a foam of voids. This characteristic morphology was seen in the first generation of cold dark matter simulations carried out over 20 years ago16, but the match was not perfect; the recipe adopted to relate the galaxy and mass distri- butions was too crude to reproduce in detail the clustering of galaxies. It has taken models like those of Fig. 4 to explain why the observed galaxy autocorrelation function is close to a power law whereas the simulated Figure 3 Variance of the weak lensing shear as a function of top-hat
dark matter autocorrelation function shows significant features5,57. smoothing scale. The data points show recent measurements from the
Simulated autocorrelation functions for dark matter and for galaxies VIRMOS survey54. The solid line gives the predicted signal for the nonlinear
are shown in Fig. 5 for the same times imaged in Fig. 4. The shape differ- mass distribution in the standard ΛCDM model (normalized so that the
linear mass overdensity in spheres of radius 8 h
–1 Mpc is σ = 0.84), and the
ence between the two is very evident, and it is remarkable that at z = 0 the dashed line shows a linear extrapolation based on the structure present
power-law behaviour of the galaxy correlations extends all the way down at early times. Because the weak lensing shear depends sensitively on the
to 10 kpc, the observed size of galaxies. Similar behaviour has recently nonlinear clustering of the total mass distribution, it provides a particularly
been found for luminous red galaxies in the Sloan Digital Sky Survey58. powerful probe of cosmology. Figure courtesy of Ludo van Waerbeke.
The galaxy distribution in this simulation also reproduces the observed dependence of present-day clustering on luminosity and colour5 as well sky as a function of the radius of those circles54. Clearly, the distortion is as the observed galaxy luminosity functions, the observationally inferred detected with very high significance. The two curves show the predicted formation histories of elliptical galaxies, and the bimodal colour-mag- signal in the standard ΛCDM model based on (i) detailed simulations nitude distribution observed for galaxies59,60.
of the growth of structure in the dark matter distribution, and (ii) a A striking feature of Fig. 4 is the fact that while the growth of large- simple linear extrapolation from the structure present at early times. scale structure is very clear in the mass distribution, the galaxy distri- Nonlinear effects are strong because the distortions are dominated by butions appear strongly clustered at all times. This difference shows up the gravity of individual dark matter haloes. Meaningful comparison dramatically in the autocorrelation functions plotted in Fig. 5 and has between theory and observation thus requires high-precision large-scale been a prediction of CDM theories since the first simulations including structure simulations, and generating these constitutes a great numerical crude bias recipes16. A decade later when direct measurements of gal- challenge. Similar lensing measurements, but now within circles centred axy clustering at redshifts as high as z ≈ 3–4 found "surprisingly" large on observed galaxies (rather than random points), can be used to deter- amplitudes, comparable to those found in the present-day Universe61,62, mine the average total mass surrounding galaxies as a function of radius, the results turned out to be in good agreement with estimates based on redshift and galaxy properties55. This wealth of information can only be more detailed modelling of galaxy formation in a CDM universe63,64. interpreted by simulations that follow both the dark matter distribution In effect, the galaxies already outline the pattern of the cosmic web at and the formation and evolution of the galaxy population.
early times, and this pattern changes relatively little with the growth of The Lyman α forest and gravitational lensing thus provide windows structure in the underlying dark matter distribution.
onto the large-scale structure of the Universe that complement those obtained from galaxy surveys by extending the accessible redshift range Could the standard model be wrong?
and, more importantly, by measuring the structure in the diffuse gas Given the broad success of the ΛCDM model, is it conceivable that it and in the total mass distribution rather than in the distribution of gal- might be wrong in a significant way requiring a fundamental revision? axies. In principle, these measures should have different (and perhaps The concordance of experimental results relying on a variety of physi- weaker) sensitivity to the many uncertain aspects of how galaxies form. cal effects and observed over a wide range of cosmic epochs suggests Remarkably, all three measures are consistent both with each other and that this is unlikely. Nevertheless, it is clear that some of the most fun- with the standard model at the level that quantitative comparison is damental questions of cosmology (what is the dark matter? the dark energy?) remain unanswered. In addition, some of the key observational Galaxy surveys such as those illustrated in Fig. 1 contain an enor- underpinnings of the model still carry worrying uncertainties. Can we mous amount of information about large-scale structure. The strength use our ever-improving measurements of large-scale structure to carry of clustering is known to depend not only on galaxy luminosity, colour, out critical tests? morphology, gas content, star-formation activity, type and strength of Perhaps the deepest reason to be suspicious of the paradigm is the nuclear activity and halo mass, but also on the spatial scale considered apparent presence of a dark energy field that contributes 70% of the and on redshift. Such dependences reflect relations between the forma- Universe's content and has, for the past 5 billion years or so, driven tion histories of galaxies and their larger-scale environment. Some (for an accelerated cosmic expansion. Dark energy is problematic from a example, the dependence on halo or galaxy mass) are best thought of as field theoretical point of view65. The simplest scenario would ascribe a deriving from the statistics of the initial conditions. Others (for example vacuum energy to quantum loop corrections at the Planck scale, hc5/G, the dependence on nuclear or star-formation activity) seem more natu- which is of the order of 1019 GeV, where gravity should unify with the rally associated with late-time environmental influences. Early studies other fundamental forces. This is more than 120 orders of magnitude 2006 Nature Publishing Group
Springel pagesrc.indd 1140 19/4/06 10:25:43 am 2006 Nature Publishing Group
NATURE Vol 440 27 April 2006 Figure 4 Time evolution of the cosmic large-
scale structure in dark matter and galaxies,
obtained from cosmological simulations of the
Λ
CDM model. The panels on the left show the
projected dark matter distribution in slices
of thickness 15 h
–1 Mpc, extracted at redshifts
z
= 8.55, z = 5.72, z = 1.39 and z = 0 from the
Millennium N
-body simulation of structure
formation5. These epochs correspond to times of
600 million, 1 billion, 4.7 billion and 13.6 billion
years after the Big Bang, respectively. The colour
hue from blue to red encodes the local velocity

T = 0.6 Gyr T = 0.6 Gyr dispersion in the dark matter, and the brightness
of each pixel is a logarithmic measure of the

projected density. The panels on the right show
the predicted distribution of galaxies in the same
region at the corresponding times obtained by
applying semi-analytic techniques to simulate
galaxy formation in the Millennium simulation5.
Each galaxy is weighted by its stellar mass, and
the colour scale of the images is proportional to
the logarithm of the projected total stellar mass.
The dark matter evolves from a smooth, nearly
uniform distribution into a highly clustered state,
quite unlike the galaxies, which are strongly

T = 1.0 Gyr clustered from the start.
T = 1.0 Gyr T = 4.7 Gyr T = 4.7 Gyr 150 h–1 Mpc T = 13.6 Gyr 150 h–1 Mpc T = 13.6 Gyr larger than the value required by cosmology. Postulating instead a con- Interestingly, it has also been pointed out that without the evidence nection to the energy scale of quantum chromodynamics would still for accelerated expansion from type Ia supernovae, a critical density leave a discrepancy of some 40 orders of magnitude. A cosmological Einstein–de Sitter universe can give a good account of observations of dark energy field that is so unnaturally small compared with these par- large-scale structure provided the assumption of a single power law for ticle physics scales is a profound mystery. the initial inflationary fluctuation spectrum is dropped, a small amount The evidence for an accelerating universe provided by type Ia super- of hot dark matter is added, and the Hubble parameter is dropped to the novae relies on a purely phenomenological calibration of the relation perhaps implausibly low value h ≈ 0.45 (ref. 70).
between the peak luminosity and the shape of the light curve. It is this The CMB temperature measurements provide particularly compelling that lets these supernovae be used as an accurate standard candle. Yet support for the paradigm. The WMAP temperature maps do, however, this relation is not at all understood theoretically. Modern simulations show puzzling anomalies that are not expected from gaussian fluctua- of thermonuclear explosions of white dwarfs suggest that the peak lumi- tions71–73, as well as large-scale asymmetries that are equally unexpected nosity should depend on the metallicity of the progenitor star66,67. This in an isotropic and homogeneous space74,75. Although these signals could could, in principle, introduce redshift-dependent systematic effects, perhaps originate from foregrounds or residual systematics, it is curious which are not well constrained at present. Perhaps of equal concern is the that the anomalies seem well matched by anisotropic Bianchi cosmologi- observation that the decline rate of type Ia supernovae correlates with cal models, although the models examined so far require unacceptable host galaxy type68,69, in the sense that the more luminous supernovae cosmological parameter values76. Further data releases from WMAP (which decline more slowly) are preferentially found in spiral galaxies. and future CMB missions such as PLANCK will shed light on these 2006 Nature Publishing Group
Springel pagesrc.indd 1141 19/4/06 10:25:46 am 2006 Nature Publishing Group
NATURE Vol 440 27 April 2006 peculiarities of the current datasets. Perhaps the anomalous effects will subhaloes invisible86,87. Gravitational lensing measurements may offer go away; or they could be the first signs that the standard model needs a test of this explanation88. Lensing also allows independent determina- tions of halo density profiles, a method that has in fact led to new chal- The unknown nature of the dark matter is another source of concern. lenges for ΛCDM. Recent results on cluster scales favour steeper inner Is the dark matter really ‘cold' and non-interacting, and is it really dark? mass profiles than expected, but the significance of this discrepancy Does it exist at all? Until the posited elementary particles are discovered, is unclear because of uncertainties originating in halo triaxiality and we will not have definitive answers to these questions. Already there are hints of more complicated possibilities. It has been suggested, for instance, that the γ-ray excess flux recently detected in the direction Future tests of large-scale structure and cosmology
of the Galactic Centre77 might be due to self-annihilating dark matter Very few of the important questions in cosmology and large-scale particles78, an idea that is, in principle, plausible for a range of dark mat- structure can be regarded as closed. The recent history of the subject ter candidates in supersymmetric field theories. Alternative theories of provides a vivid reminder of how new theoretical insights and/or new gravity, most notably modified newtonian dynamics (MOND)79 have observational datasets can quickly overturn conventional wisdom in been proposed to do away with the need for dark matter altogether. rapidly advancing fields of science. At the present time, the two out- Although MOND can explain the rotation curves of galaxies, on other standing questions are the identity of the dark matter and the nature scales the theory does not seem to fare so well. For example, although of the dark energy.
it can account for the total mass in galaxy clusters, MOND requires the There is every reason to be optimistic about the prospects of detecting presence of large amounts of unseen material within the central few cold dark matter particles from the halo of our Galaxy, either directly in kiloparsecs of the cluster cores80. It has yet to be demonstrated convinc- laboratory searches or indirectly through particle annihilation radiation. ingly that MOND can reproduce observed large-scale structure start- Additionally, if cold dark matter is indeed a supersymmetric particle, ing from the initial conditions imaged in the CMB and so pass the test evidence for its existence may be forthcoming from experiments at illustrated in Fig. 1.
CERN's large-hadron collider90.
At present the strongest challenge to ΛCDM arises not from large- Unravelling the nature of the dark energy is a much more daunting scale structure, but from the small-scale structure within individual task. A strategy that has gained momentum in recent years is to set galaxies. It is a real possibility that the model could be falsified by meas- tighter empirical constraints on the amount of dark energy and on its urements of the distribution and kinematics of matter within galaxies, possible time evolution. Large projects such as the Joint Dark Energy and some astronomers argue that this has, in fact, already happened. The Mission, currently at an early design phase by NASA, are being planned internal structure of dark matter haloes predicted by the ΛCDM model to measure the equation of state parameter, w = P/(ρc2), of the dark can be calculated quite precisely from high-resolution simulations. energy, where P is the ‘dark pressure' of the vacuum, and its time evolu- These predict the survival of a large number of self-bound substruc- tion, w' = dw/dz. The hope is that such empirical constraints will clarify tures which orbit within haloes81,82, as well as a universal halo density the nature of the dark energy and perhaps point to a field-theoretical profile which is cusped in the middle, corresponding to a steeply rising explanation. The range of possibilities is large. We might find that the rotation curve83. Unfortunately, the effects of galaxy formation within dark energy interacts with the dark matter, or that the dark energy is not a dark matter halo are difficult to calculate, accounting, in part, for the a field at all but rather a manifestation of some nonlinear effect within lively debate that continues to rage over whether the measured rotation general relativity or one of its extensions. curves of dwarf and low surface brightness galaxies are in conflict with Progress towards constraining dark energy is likely to come both from the theory84,85. The second contentious issue on galaxy scales, the small refinements of classical cosmological probes and from entirely new ways number of observed satellites, may have been resolved by identifying to study large-scale structure. Examples in the first category include astrophysical processes that could have rendered most of the surviving measuring the abundance of galaxy clusters as a function of cosmic time. This probes the growth of the mass fluctuation spectrum and the variation of the cosmological volume element91. Extending such meas- urements to redshifts z ≥ 1 may set useful constraints on the dark energy equation of state, provided systematic effects can be kept under control. Also promising are observations of high-redshift type Ia supernovae for much larger samples than have been accumulated so far. Again, it will be crucial to control systematic effects. The PLANCK satellite mission and subsequent polarization-optimized experiments will make definitive measurements of the CMB and perhaps unlock some of its last secrets.
Examples of new tests of the large-scale structure include weak lensing tomography and the study of baryon oscillations in the matter distribu-tion at late times. The physical mechanism that generated acoustic peaks in the CMB temperature power spectrum also imprinted an oscillatory r (h–1 Mpc) r (h–1 Mpc) feature in the linear power spectrum of the dark matter92. The Virgo consortium's Millennium simulation, illustrated in Fig. 1 and Fig. 4, Figure 5 Two-point correlation function of galaxies and dark matter at
demonstrated that the oscillations survive the destructive influence of different epochs, in the Millennium simulation of structure formation5. The
panel on the left gives the I-band galaxy correlation function ξ
(selected
nonlinear gravitational evolution even to the present day, albeit in dis- according to M – 5 log h < –20 in the rest-frame) at redshifts z = 8.55,
torted form5. Most importantly, this simulation also demonstrated that z = 5.72, z = 1.39 and z = 0 (corresponding to the epochs depicted in Fig. 4).
these ‘baryon wiggles' should be visible in suitably selected galaxy sam- The panel on the right shows the dark matter correlation functions at the
ples. Early indications suggest that the baryon oscillations in the galaxy same epochs. For comparison, the present-day dark matter correlation
distribution have, in fact, been detected in the 2dFGRS and SDSS93–95, function is also drawn as a dashed line in the left panel. At z = 8.55, only
although at comparatively low statistical significance.
data for r > 200 h–1 kpc are shown because the finite numerical resolution of
A recent study using Virgo's earlier Hubble volume simulations the simulation precludes an accurate representation of the mass distribution
showed that the baryon wiggles should also be detectable in galaxy on smaller scales than this at early times. The galaxy correlation function
cluster samples96. The length scale of the wiggles is a ‘standard ruler' has a near power-law behaviour over several orders of magnitude and has
almost equal strength at z
= 8.55 and z = 0. By contrast, the dark matter
which, when observed at different redshifts, constrains the geometry correlation function grows by a large factor over this time span, and has a
and expansion history of the Universe and thus the dark energy equation different shape from the galaxy correlation function.
of state. An example of what may be possible in the future is illustrated 2006 Nature Publishing Group
Springel pagesrc.indd 1142 19/4/06 10:26:15 am 2006 Nature Publishing Group
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Acknowledgements We thank L. van Waerbeke for providing the data of Fig. 3, and
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Author Information Reprints and permissions information is available at
75. Land, K. & Magueijo, J. Examination of evidence for a preferred axis in the cosmic radiation npg.nature.com/reprintsandpermissions. The authors declare no competing anisotropy. Phys. Rev. Lett. 95, 071301 (2005).
financial interests. Correspondence should be addressed to V.S. 76. Jaffe, T. R., Banday, A. J., Eriksen, H. K., Górski, K. M. & Hansen, F. K. Evidence of vorticity 2006 Nature Publishing Group
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