The dark side of the universe

Abstract

One of the greatest mysteries in the cosmos is that it is mostly dark. Not only is the observed night-sky dark, but so is most of the matter in the universe. For every atom currently visible in planets, stars and galaxies, there exists at least five or six times as much “dark matter” in the universe. Astronomers are seeking to unravel the nature of this mysterious but pervasive dark matter, and determine whether it can be detected. There is also a dark force, dubbed “dark energy” and originally postulated by Einstein in the form of the cosmological constant, that is systematically accelerating the universe and accounts for two-thirds of its mass-energy density. Understanding the nature of dark matter and dark energy present two of the greatest challenges in physics.

Modern cosmology began in the 1920s when Alexander Friedmann (1888–1925) and Georges Lemaitre (1894–1966) independently discovered the expanding solution equation to Einstein's equations of general relativity. Friedmann had a career as a meteorologist, a military pilot in the First World War, and professor of mathematics and physics. In 1922, he published his new solution, which Einstein promptly criticized as being erroneous. But Einstein retracted the following year and Friedmann became famous, at least in Russia. He died of typhoid in 1925 within a month of setting the world altitude record for a balloon flight at 7400 m. Lemaitre, who spent time in Pasadena and was much closer to the data than Friedmann, not only independently discovered the expanding universe solution in 1927, but also realized that Edwin Hubble's new law (1929) was in fact a prediction of, and evidence for, the expanding universe theory. Hubble was a lawyer and a heavyweight boxer before becoming converted to astronomy.

Modern observations centre on the implications of a space–time diagram of the universe (figure 1). Here one views relics of the Big Bang in the form of the cosmic microwave background and the uneven distribution of galaxies. The universal expansion began about 13.7 billion years ago, the universe became transparent about 300 000 years after the Big Bang, and galaxies formed over the past billion years or so.

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A space-time diagram.

Most scientists subscribe to this view, although a substantial subset of the population prefer a more traditional interpretation of the universe, ultimately deriving from a literal reading of the Bible. In fact, dating from Pius XII and the intervention of Abbe Lemaitre onward, there has been an enlightened theological, ecclesiastically led, approach to modern cosmology. This view holds that science is paramount, but presents no challenge to a creed that rests on faith-based belief. Indeed the converse applies: the beauty of science and the nature of scientific relevations constitute part of the modern theologian's perspective and toolbox. Sadly, the wheel has turned full circle, with many physicists appealing to the Anthropic Principle, an unabashedly self-based egocentric worldview, to account for the initial conditions of the Big Bang. Whether this is physics or philosophy is another story.

The case for the Big Bang

Four predictions of the Big Bang Theory have now been verified — surely enough to quench even the most biased critics. First was the expansion of the universe, predicted by Friedmann and Lemaitre and measured by Hubble. Next came the abundances of the light elements. This was largely the insight of George Gamow, but interpreted in more modern terms by Fowler, Hoyle, Wagoner and Peebles (figure 2). A corollary of the light element interpretation was the prediction of the cosmic microwave background as a blackbody spectrum. The first predictions of the temperature of the universe were by Gamow's student Alpher and colleague Herman, although the connection with microwave astronomy was only made later by Dicke and collaborators, culminating in the detection by Penzias and Wilson in 1964 and the blackbody spectral measurement by the FIRAS instrument on COBE (figure 2). The spectrum is indistinguishable from that of a blackbody with remarkable precision.

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Predictions of the abundances of ⁴He, D, ³He and ⁶L as a function of the baryon density and the baryon-to-photon ratio. Observed abundances are shown as statistical errors (white boxes) and systemic errors (yellow boxes) (from B Fields and S Sarkar). (b): CMB spectrum from the FIRAS on the COBE satellite (J Mather et al., NASA).

The final and most recent success of the Big Bang was confirmation of the fluctuations in the cosmic microwave background, a corollary of the theory of structure formation from gravitational instability. These measurements have garnered increasing accuracy over the past decade. No significant inconsistencies have been found, but there has been at least one unanticipated result: the universe is accelerating, driven by a cosmological constant or dark energy term. This leads to what is now the standard model of cosmology, in which the universe is at the critical density required to just be spatially flat, but with two-thirds of its mass-energy density in the form of dark energy. Dark matter constitutes about one-third of the critical density and only 15% of the dark matter is baryonic.

Inflation

The missing link in cosmological modelling has always been the strength of the initial fluctuations. Theory does not provide an answer. Inflationary cosmology first emerged in 1980. The idea was driven by a phase transition in the very early universe, associated with the breaking of symmetry as the universe cooled down. This led to a temporarily exponential rate of expansion and an associated flattening of spatial curvature. Quantum fluctuations were amplified onto macroscopic scales, and the resulting amplitude distribution was approximately scale invariant. However, inflation failed to specify the fluctuation strength, and this consequently motivated developments of a huge number of variations on the early models of single field inflation.

One consequence is that it is difficult today to describe inflation as a predictive theory. Any observations can be accommodated, including, for example, data that a decade ago favoured an open universe. Nevertheless, the elegance of inflationary cosmology makes it a compelling explanation for several observational phenomena. These include the observed near flatness of the universe, its size and homogeneity, and near scale-invariance of the inferred primordial fluctuation spectrum.

From inflation to galaxy formation

Inflation-generated fluctuations provide the density fluctuations that grow via gravitational instability to eventually form galaxies. Growth only occurs on subhorizon scales and only effectively in the matter-dominated era. The net effect is growth stagnation on scales below the horizon scales at matter-radiation equality, with the radiation epoch power spectrum being preserved during the matter-dominated phase via subhorizon growth. On larger scales, growth occurs systematically later as the horizon grows, so that by today the initial fluctuation amplitude is seen only on the current epoch horizon scale.

The net effect is a distribution of seed density fluctuations with larger amplitudes on smaller scales. The fluctuations grow by gravitational instability in the matter-dominated epoch. Bottom-up galaxy formation commences once dark matter clumps form that are sufficiently massive for the baryons to be able to cool. This corresponds to a minimum mass of about 10⁶M_⊙ at a redshift of about 30. The normalization of the fluctuation spectrum, which determines the epoch of galaxy formation, is set observationally by the strength of the observed fluctuations in the cosmic microwave background radiation.

In the radiation-dominated era, the fluctuations are like sound waves, travelling at the speed of sound. The nonbaryonic dark matter has similar fluctuations, but does not interact with radiation. Once the universe becomes matter-dominated, the dark matter fluctuations strengthen. The baryons remain coupled to the photons and still oscillate as sound waves.

A dramatic event occurs when the radiation temperature drops below 1000 K. There are no longer enough energetic photons to keep the hydrogen ionized. The hydrogen becomes predominantly atomic. There are very few free electrons left behind. The photons no longer are scattered, and the radiation is decoupled from the matter. The baryons fall into the gravity potential wells of the dark matter fluctuations. In this way, the growth of fluctuations is boosted due to the presence of dark matter.

Gravitational instability continues and eventually the fluctuations are dense enough to separate from the average density field. They are no longer fluctuations, but rather assemblies of self-gravitating dark matter and baryons. Larger and larger systems condense out as the universe expands. The dark halos of galaxies have formed. The baryons condense into dense clouds embedded in the dark halos, retaining much of their initial angular momentum to form a disc. These discs are themselves gravitationally unstable and stars form. The epoch of galaxy formation has begun, a billion years after the Big Bang.

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Early symmetry breaking at grand unification, left. Centre, inflation resolves the flatness problem. Inflation, right, resolves the horizon problem.

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From primordial curvature fluctuations to galaxy formation.

Detection of the elusive fluctuations

The year 1967 marked a breakthrough in our understanding of the initial conditions for galaxy formation. The goal was to incorporate the newly discovered cosmic fossil radiation into galaxy formation theory. To form the galaxies, the initial density fluctuations must have had a finite amplitude, that left a potentially observable trace in the CMB via the acoustic imprint in the temperature fluctuations on sub-degree angular scales.

In 1967 Sachs and Wolfe had already predicted the large-angular-scale fluctuations based on the observed large-scale irregularity of the universe. This was an observation with no accompanying theoretical explanation. The irregularity was seen in the observed large-scale structure of the galaxy distribution, but did not have to be there. By studying the coupling and growth of primordial density irregularities, the temperature fluctuation strength could be qualitatively predicted. There is a minimum scale of surviving adiabatic density fluctuations due to the coupling with the radiation field. There is a corresponding minimum angular scale above which the temperature fluctuations could survive and be detectable. It was a phenomenological prediction but fundamental to our understanding of the Big Bang as a cosmological model of the observed universe.

How was one to test such a theory, in the era before the advent of the very large telescopes and the space telescopes? The prediction of small-angular-scale temperature fluctuations provided a crucial missing link in the connection between the initial conditions and the formation of the galaxies. The irregularities arose from a fundamental theoretical argument. The fluctuation strength was quantitatively predicted (Silk 1967) via the requirement that galaxies must have formed by the gravitational instability of tiny density fluctuations whose amplitude was calculated from the theory laid down in a pioneering paper in 1946 by E Lifschitz. Fluctuations grew in strength via the effects of gravity in the expanding universe. Without them there would be no galaxies.

There were several generations of cosmic microwave background radiation experiments. A prolonged period followed when the improved experimental limits were above the progressively refined theory. Each time there was a major experimental improvement, as happened with the pioneering attempts of Bruce Partridge in the 1970s, then of Juan Uson and David Wilkinson in 1981, the theoretical hurdle was raised with the advent of more precise calculations.

The final theoretical refinements came in 1984 with the introduction of cold dark matter, in papers published independently by myself and Nicola Vittorio at Berkeley and by Dick Bond and George Efstathiou at Cambridge (Vittorio and Silk 1984, Bond and Efstathiou 1984). Nor was it long before the cosmological constant was probed via these predictions (Vittorio and Silk 1985). The weakly interacting cold dark matter allowed fluctuations to grow despite the tight baryon–photon coupling once the universe was matter-dominated. The prediction of temperature fluctuations arising from structure formation was now an order of magnitude or so lower than the early predictions, three parts in 100 000 at the first acoustic peak at an angular scale of about 30 arcminutes, and substantially lower on smaller angular scales where the damping played a role.

There was a major breakthrough in 1992 when the Cosmic Background Explorer satellite (COBE) verified, to within a factor of two, the Sachs–Wolfe prediction on angular scales over 7°. It was to take almost another decade before the angular scale anisotropy predictions on sub-degree scales were confirmed. A ground-based experiment (TOCO) and the balloon-borne experiments (BOOMERANG, MAXIMA) provided strong confirmation of the elusive signal.

Flatness of space

Refined data was needed for the next step. This was the prediction that one could measure the curvature of the universe (Sugiyama and Silk 1994) in the sky. It turns out that in the cosmic microwave background alone, there are significant parameter degeneracies (Bond and Efstathiou 1999). Indeed, the simple addition of a Hubble constant as measured by the Hubble Space Telescope key project (72 km s⁻¹ Mpc⁻¹) leads to the highly significant inference that the universe is flat. The spatial curvature is close to zero.

Dark matter

Rotation curves of galaxies provide the best studied and most robust evidence for dark matter. The luminous components — stars — fall short of accounting for the circular velocity in the outer parts of almost every disc galaxy studied, and imply a mass shortfall of an order of magnitude out to several disc scale lengths. There is a similar shortfall for elliptical galaxies, whose mass distribution is traced by X-ray emitting halo gas pressure gradients, the radial run of stellar velocity dispersion, or gravitational lensing. Rotation curves demonstrate the dominant presence of dark matter on comoving scales up to 1 Mpc.

On larger scales, the dark matter fraction rises, until it reaches a universal value amounting to about 23% of the critical density on the comoving scale of galaxy clusters, about 10 Mpc. The relevant measurements include virial mass determinations of galaxy clusters from the velocity dispersion of the member galaxies and the thermal pressure of the hot intergalactic gas, as well as gravitational lensing. The total dark matter content of rich clusters is unambiguously measured by gravitational lensing of background galaxies. Image distortions trace the dark matter content. With a combination of weak and strong lensing, one can trace the dark matter density profile out to several optical scale lengths.

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(a): Primordial acoustic waves seed galaxy formation and leave an imprint on the CMB. (b) COBE: the CMB at 5° angular resolution. (c) WMAP: the CMB at 0.25° angular resolution, with polarization due mostly to galactic foregrounds.

Global dark matter density

The resolution of the dark matter content of the universe, and in particular its asymptotic value on large scales, is via the presence of a dominant contribution of nonbaryonic dark matter. Independent evidence of a substantial nonbaryonic contribution to the matter budget comes from primordial nucleosynthesis of the light elements. The successful interpretation of the baryon density from the abundances of He, ²H, and ⁷Li yields a baryon density that is only 0.04 of the critical density. Essentially all of these baryons are needed to account for the baryons observed in stars and in intergalactic gas. The nonbaryonic content of the universe amounts to about six times the baryonic content. Precisely this ratio is measured in massive clusters of galaxies, where the intergalactic gas content is about three times the mass of the stellar content.

Lensing of individual galaxies allows one to compare the baryonic content, inferred by near-infrared observations, with the dark matter content on galactic scales. Here one encounters an important clue that has implications for galaxy evolution and the intergalactic medium. Only about half of the primordial baryons are present in massive early-type galaxies. Where are the baryons? The observed repository is in the intergalactic medium. Vast intergalactic clouds of enriched gas are measured in absorption against distant quasars. Most likely the gas has been ejected after being enriched in early star formation. Energetic winds are indeed observed from massive galaxies in the early universe as well as from nearby starbursting galaxies. There is no mystery about the baryon budget. Most baryons are dark, that is not in stars, but are present as diffuse gas in the intergalactic medium which is probed, outside of galaxy clusters, by absorption line studies.

Fluctuations in galaxy distribution

The definitive measurements of the global dark matter density come from studying the dark matter distribution on scales even larger than those of galaxy clusters. Galaxy redshift surveys of up to a million galaxies probe the three-dimensional density distribution of the universe out to a redshift of 0.2 for the 2DF and Sloan galaxy redshift surveys, or even 0.5 for the luminous red galaxy sample from the SDSS. The redshift space distortions allow a direct measurement of the dark matter density, subject to correction by an unknown bias factor. Bias is the ratio of light to dark matter, which on sufficiently large scales corresponds to the initial baryon fraction.

Fluctuations in matter distribution

When the measured three-dimensional galaxy distribution is smoothed over scales that average over the largest bound structures — clusters of galaxies — the matter distribution is found to be clumpy. The fluctuations in the galaxy distribution match those in the CMB, scale for scale, once account is taken of the very different redshifts at which the two measurements are made, as well as of the contribution of the velocity fluctuation mode. One can detect the wiggles or acoustic oscillations both in the background radiation and in the galaxy counts. The amplitude of the wiggles measures the baryon density, but the separation measures the particle horizon at last scattering. In effect, this scale specifies the curvature of the universe. The flatness of space has been confirmed both in the radiation and in the matter oscillations.

Unexpected discovery: dark energy

The universe is measured to be at the critical density. Yet the total matter component is found to be only a third of the critical density. The preferred candidate for the shortfall is Einstein's cosmological constant. Einstein originally used this to counteract gravity in the long-since discarded Einstein static universe. But its introduction in the expanding universe was advocated by Lemaitre and Eddington.

The acceleration is manifest in the Friedmann–Lemaitre theory of the Big Bang by adding a term that counteracts the effects of gravity, which of course tends to deaccelerate the expansion. The modern interpretation of the cosmological constant is as a constant contribution to the energy density of the universe. If dark energy accounts for two-thirds of the critical density, the flatness of the universe is explained.

There is a remarkable consequence. At late epochs, as the dark energy dominates over the redshifting matter density, the universe enters into a phase of acceleration. This effect has been detected, thereby confirming the dominance of the dark energy.

The modern Hubble diagram revealed a phenomenon that would have astonished Hubble. The most distant galaxies, detected via their supernovae, are found to be unexpectedly dim. The best explanation advanced to date is that the expansion of the universe is accelerating.

The dark energy equation of state

There is no explanation for the low value of the dark energy density. Any particle physics explanation prefers a value higher by 10¹²⁰ to yield the Planck value, considered the most natural scale for dark energy. This discrepancy has led to theories in which dark energy increases in density towards earlier epochs, scaling as a power of the radiation density. In general, one can introduce a new parameter, the ratio of the pressure to density of the dark energy (w) which, if Einstein's cosmological constant is the explanation, would be –1. However, acceleration requires only that w < –1/3 , and much observational effort is going into determining its value and redshift dependence. So far, all results point to Einstein's cosmological constant as the dark energy. Current measures show that w=−1.08 ± 0.12 , equal to the cosmological constant value of –1±10%.

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(a): The 2DF galaxy redshift survey, coloured to show distortions from galaxy peculiar velocities. (b): WMAP3 power spectrum for temperature-temperature (TT) and temperature-polarization (TE) angular corrections. (c): Distribution of luminous red galaxies from the SDSS compared (above) with the temperature fluctuation power spectrum (Percival et al. 2007 Astrophysical J.).

Observing w

Ongoing and proposed experiments, over the next five years or so, focus on refining independent probes of dark energy. Primary among these is improvement of the measurements of baryon oscillations. This involves surveys of thousands of square degrees to obtain photometric redshifts of millions of galaxies out to redshifts ˜1. Complementary probes include more supernova light curves, studies of weak lensing and surveys of the redshift distribution of galaxy clusters. All of these have systematic limitations, and only a modest decrease in limits on the uncertainties in w is expected. A significant reduction requires a major (and expensive) effort. This is projected, for example, for the Square Kilometre Array, which will obtain spectroscopic (21 cm) redshifts of every galaxy over tens of thousands of square degrees to a redshift of 1 by 2020. Complementary experiments include galaxy spectroscopic surveys with 8 m class telescopes (WFMOS) and a space-based survey telescope (JDEM) dedicated to supernovae and weak lensing.

Observing dark matter

There are many candidates for dark matter. Fortunately, the most popular class of candidate particles is observable. The lightest supersymmetric particle is expected to be stable, and can account for the dark matter density. Supersymmetry is motivated both by theory and by empirical arguments. The candidate particle must be neutral and weakly interacting. It is referred to as the neutralino, and is the heavy counterpart of a known particle such as the photon. Neutralinos are in thermal equilibrium in the very early universe. As the temperature drops, a relic density of particles survives. The weak nature of neutralino self-interactions results in a large relic density, in contrast to that from strongly interacting particles. Remarkably, the relic density generically gives an approximately critical density of dark matter for a weak-like cross-section.

Moreover, the fact that decoupling of the particles from the radiation occurred very early means that recently, the particles were completely cold — they had negligible random velocities associated with their thermal origin. Cold dark matter provides a highly plausible explanation for the large-scale structure of the universe. The detailed clustering properties can be reproduced, if simple models for galaxy formation are introduced. However, the cold dark matter candidate has not yet been detected: it remains a hypothesis.

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(a): Apparent magnitude vs recession velocity for near and far galaxies (Clocchiatti et al. 2006 AJ 642 1). (b): Limits on dark energy if constant (above) or a function of redshift (below) (Seljak et al. 2005 Phys. Rev. D71 3515).

Annihilations

Self-annihilations of the dark matter particles are very rare today, but may still lead to a detectable signal. The debris from annihilations of particles, with typical masses of order the SUSY-braking scale of around 100 GeV, includes high-energy gamma rays, antiprotons, neutrinos and positrons. The predicted flux depends on the density of dark matter. The local density in the solar neighbourhood is 0.3 GeV cm⁻³. The positron flux is controlled by the local dark matter density but the gamma rays are sensitive to the density profile of dark matter in the inner galaxy.

There are hints of possible detections in positrons and diffuse gamma rays (reviewed by Bertone 2004). The HEAT balloon experiments reported an anomalous spectral bump in the positron flux near 20 GeV that is not explained by the featureless secondary spectrum of positrons from cosmic-ray interactions with interstellar matter. Neutralino annihilations naturally yield a positron feature centred on m_χ. Similarly, the COMPTON/EGRET gamma-ray experiment found a diffuse flux from the inner galaxy that was spectrally harder than that predicted from cosmic-ray/ISM interactions due to χ⁰ decays. More exotic decay channels may be indicated. The massive quark decay channels available in neutralino annihilation (for m_χ≳ 100 GeV) provide the required spectral hardening. However, in both instances, the data needs to be confirmed.

If the HEAT/EGRET results were, however, interpreted as due to annihilations, a serious issue remains over the normalization of the predicted neutralino signal. A uniform halo falls short by up to two orders of magnitude in accounting for the observed fluxes with plausible annihilation cross-sections. The halos may be clumpy.

Clumpiness

One uncertainty in computing the flux is the degree of clumpiness of the dark matter. The annihilation rate is proportional to the square of the density. Simulations show that halos are clumpy, with ˜10% of the dark matter being in clumps. This can result in a large boost factor for the annihilation flux. The flux is sensitive to the minimum clump size. This is of order an Earth mass for 100 GeV neutralinos. However, interactions with stars will tidally disrupt many clumps, effectively depending on their orbits. Clumps with orbits highly inclined to the disc should survive. Low-mass clumps are visible only via their annihilation signal.

Direct detection

There is no substitute for direct detection of the dark matter particles. The flux of such particles at the Earth is relatively large. Of course the interactions are weak, but elastic recoils leave potentially detectable signals in sufficiently large masses of target materials. Signatures include ionization and phonons from nuclear recoils. Hitherto detectors in underground laboratories have been kilogramme-scale, with sensitivities to elastic scattering cross-sections down to 10⁻³⁷ cm². However, the SUSY model parameter space allows a significant density of dark matter for cross-sections up to three orders of magnitude lower than current limits. Ton-scale detector masses are required to probe the full range, and this is the goal of the new generation of experiments that use detector materials as varied as liquid Xe or crystalline Ge.

An intriguing development has come from the realization that the dark matter may possess fine-scale structure on the scale of the solar system, leading to an annual modulation of the elusive signal (Savage 2006). Streams of dark matter in the solar neighbourhood result from the incomplete tidal disruption of dark matter clumps in galactic orbits. One experiment, DAMA, uses this signature for a detection disputed by other groups (notably CDMS2, Edelweiss and Zeplin) with more sensitive experiments. A window remains, however, if neutralino interactions are spin-dependent for a mass below about 5 GeV. This is allowed in certain models for neutralinos, such as the NMSSM.

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Predicted distribution of IMBHs in the galactic halo and estimated neutrino detection rates (from Bertonne et al. 2006 Phys. Rev. D73 103519).

Indirect detection

A complementary approach utilizes the property that the SUSY LSP dark matter candidate is a majorana particle and self-annihilates. For typical heavy masses, in the 100 GeV to 1 TeV range, the annihilation products include energetic gamma rays, neutrinos, positrons and antiprotons, and have potentially observable signatures relative to the known backgrounds (Silk and Srednicki 1984). Despite the multiplicity of candidates for the LSP, its annihilation cross-section is known from the requirement that it accounts for the density of nonbaryonic dark matter. Of course the particle being undetected means that its mass is unknown. However, SUSY modelling specifies a range of cross-sections at a given mass. This range spans some three orders of magnitude, but the allowable mass range in the minimally supersymmetric model extends from only 50 GeV to 1 TeV.

As mentioned, there are hints of anomalous signals in both high-energy cosmic-ray positron and gamma-ray experiments. However, it is far too premature to make much of any possible annihilation signal. New experiments are underway. The PAMELA satellite, launched in 2006, is currently taking data on cosmic-ray positrons, and the GLAST satellite, to be launched in 2007, will provide an order of magnitude improvement in sensitivity over EGRET. These experiments will greatly improve on the existing data and could confirm (or reject) the reality of the possible signal from annihilating WIMPs.

Relic spikes of dark matter

The annihilation flux may be greatly boosted near a massive black hole that forms in the nucleus of a forming galaxy. These black holes are expected to form via accretion of baryons onto a seed black hole from a massive star. This is not the only possibility, but the phase of black hole growth is observed indirectly via the fuelling of the SMBHs that power quasars and AGN.

Another compelling argument comes from the correlation between SMBHs and galactic spheroids. We will return to this but it suffices here to note that this apparently universal correlation applies over all spheroid masses. In particular, if the SMBH grows adiabatically by accreting baryons, it will also concentrate cold dark matter. The weakly interacting dark matter responds adiabatically to the deepening potential well around the black hole by developing a density cusp within the gravitational sphere of influence of the black hole. Since the accretion occurs initially within dark matter mini-halos, rather than in massive halos, dark matter spikes develop around the central black holes in the mini-halos. Black-hole merging destroys such a cusp, hence it is unclear whether the million solar mass at the centre of the Milky Way possesses such a feature. If this were the case, the annihilation rate would be greater near the central black hole. A more promising prospect is to search for the ubiquitous intermediate-mass black holes (IMBHs) without a complex merging history.

IMBHs are relics of the initial clouds within which the first stars formed. The most massive of these clouds would have cooled via Lyman-α emission, and the efficient cooling associated with this cooling channel would have facilitated high core accretion rates and the likely formation of 10³–10⁴M_⊙ black holes. Such precursors are required in order to explain the presence of the black holes as massive as 3 × 10⁹M_⊙ at z= 6–7 that are associated with the most luminous of the quasars. The IMBHs, considered to be the missing link between primordial clouds and quasars, should populate our halo, as the efficiency of build-up by merging is low, and many would be ejected by recoil as binaries form and dissolve during the hierarchical merging whereby the larger systems grow. The isolated IMBHs, which are expected to cumulatively account for as much mass as the central SMBH in a galaxy, should populate the inner halo and retain their initial dark matter spikes. They are prime candidates for gamma ray and neutrino detection.

Galaxy formation

The cold dark matter paradigm has had considerable success in accounting for the large-scale structure of the universe. The postulated collisionless nature of the dominant dark matter, in combination with a primordial power spectrum of density fluctuations that naturally peaks at the ˜20 Mpc scale corresponding to the horizon at matter–radiation equality, means that structure develops a filamentary structure on larger scales. This is a consequence of caustic formation on the largest nonlinear scales, and was first recognized as an ingredient of large-scale structure by Ya B Zeld'ovich (1970). Modern observations of the three-dimensional structure of the galaxy distribution, most notably the 2DF and SDSS galaxy redshift surveys, have eloquently confirmed the filamentary pattern of the so-called cosmic web, wherein massive galaxy clusters are situated at the intersections of filaments. Accretion of matter and cluster, as well as galaxy halo, growth mostly occurs along the filaments. Numerical simulations, such as the 2006 Millennium survey, are able to reproduce the web-like structure of the galaxy distribution, galaxies serving as markers of large-scale structure. The key assumptions underpinning this successful comparison, apart from the fluctuation power spectrum, are that the dark matter is cold and weakly interacting.

Baryons account for 15% of the matter content of the universe and, unlike the weakly interacting cold dark matter, are able to dissipate energy, cool and condense into galaxy-mass clouds. Theory can account for the minimum and maximum masses of the luminous stellar components of the observed galaxies by the simple requirement that the baryons must be able to cool within a dynamical timescale. Cooling is a necessary condition for star formation. Remarkably, simple arguments yield a minimum baryonic mass of ˜10⁶M_⊙ and a maximum mass of ˜10¹²M_⊙ that accord well with observations. There are problems, however, with the predicted number densities of small and massive baryonic objects.

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Predicted distribution of clumps in the galactic halo for two different escape velocity cuts, compared to observed satellites (from J Taylor).

The dwarf problem

The minimum mass of a dark-mass clump within which baryons are able to cool is of order a million solar masses. Such clumps may be visible as the gas can form stars. These clumps are candidates for dwarf galaxies and are the building blocks for more massive galaxies.

One of the strongest objections to the cold dark matter hypothesis for structure formation is that the bottom-up scenario motivated by inflation and by the measured density fluctuations results in a huge number of small satellite galaxies. These greatly exceed the observed satellite frequency.

Two possible solutions have been proposed. One involves supernova explosions in the first dwarf galaxies. So much gas is expelled that little gas remains, and the number of stars is greatly reduced relative to the stellar fraction in a massive galaxy. Expulsion of gas is observed in starburst galaxies. The well-studied nearby examples of starbursts typically have energetic galactic winds and are associated with low-mass galaxies. The outflow rate is observed to be comparable to the star formation rate. The outflows are driven by supernovae whose hot ejecta mix with interstellar gas and drive a wind. The same phenomenon in more massive galaxies results in a fountain, where gas is ejected from the disc, cools in the halo and falls back into the disc after some hundreds of millions of years. However, for the small dwarfs predicted by CDM theory, the galactic potentials are so shallow that after even the first supernova one plausibly expects most of the baryons to be ejected (Dekel and Silk 1986).

There are restrictions on the surviving dark-matter halo clumps. There is a risk that many surviving clumps may dynamically heat the disc. Discs are observed to be thin and their stellar components must be dynamically cold.

The second possibility for resolving the dwarf problem circumvents any issues of overheating the disc by appealing to tidal disruption of the dwarfs. Many clumps are completely disrupted by tidal heating. Simulations suggest that surviving clumps have trajectories that are predominantly normal to the discs, and so over-heating of the discs may not be an issue. The dark matter should consist of many tidal streams of debris, that would be merged into a quasi-homogeneous soup in the inner galaxy. Stellar tidal streams are indeed observed to form as relics of orbiting dwarfs in the Milky Way and in the M31 halos.

The massive galaxy problem

The galaxy luminosity function is observed to have an approximately exponential cut-off (at least for normal galaxies) at the bright end. Baryons, however, continue to accrete into massive galaxies, and there is no compelling reason for star formation to stop after a dynamical time. Theory suggests that the baryons should accumulate, cool and continue to form stars. Massive galaxies are expected to still be forming stars and hence still growing in total stellar mass. Yet the most massive galaxies are ellipticals, galaxies which are almost completely devoid of ongoing star formation and whose space density is fit by an exponentially decreasing luminosity function. Growth ceased long ago, apart from the occasional merger. It is necessary to quench recent star formation in massive early-type galaxies.

The resolution of the dilemma of the massive-galaxy problem has come with recognition of the connection between supermassive black holes and galaxy formation. The story begins with the empirical correlation between the masses of supermassive black holes, universally found at the centres of galactic spheroids, and the stellar masses of the spheroids. The correlation applies to spheroids similar to the bulges of the Milky Way galaxy and of M31, up to the most massive galactic spheroids of elliptical galaxies such as M87. The ellipticals are pure spheroid, whereas disc galaxies are a hybrid of disc plus spheroid, yet the empirical correlation applies generally to all spheroids. Spheroids contain only old stars, and we infer that virtually the entire phase of supermassive black hole formation and growth must have coincided with spheroid assembly.

Supermassive black holes are associated with an intensely active but short-lived phase at the centres of galaxies. These active galactic nuclei, powered by SMBHs, are observed at high redshift as quasars, among the most luminous objects in the universe. Vigorous outflows are observed from the core emission line regions, amounting to of order a solar mass per year at a substantial fraction of c. The transported momentum has a substantial impact on the surrounding interstellar medium. Detailed interactions need to be simulated, but simple momentum balance arguments suggest that the input is sufficient to drive out the bulk of the diffuse interstellar medium from the galaxy. Global winds are indeed observed from ultra-luminous star-forming galaxies, with an outflow rate that is a significant fraction of the star formation rate, up to 1000 M_⊙/yr. It is likely that the outflows are enhanced by triggered star formation. The massive dense interstellar clouds overtaken by the outflows will be overpressured and collapse to form stars. The resulting supernovae will further drive the outflow. Less massive clouds will be shredded by Kelvin–Helmholtz and Rayleigh–Taylor instabilities. The most luminous infrared galaxies indeed have both strong AGN activity and star formation, suggesting that the two phenomena are closely connected.

There are several studies of SMBH masses at high redshift, along with the corresponding mass of the associated stellar component, that is, the host galaxy stellar mass. The conclusions are discrepant. Some studies maintain that the supermassive black holes are correspondingly more massive than the stellar components in the early universe relative to the present-day observations, while others obtain the opposite result. Hence one cannot say whether SMBH formation and growth precedes that of the spheroid, or is a sequel. Most likely, SMBH growth and spheroid growth occur contemporaneously. The details of whether AGN feeding and outflows drive star formation or vice versa remain unclear, and remain to be elucidated by future observations, especially at FIR and X-ray frequencies.

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10: Simulation of tidal disruption of satellites and generation of tidal tails. (Courtesy Paul Harding)

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11: Galaxy luminosity function, (from Benson et al. 2003 Astrophysical Journal 599 38).

Cosmology today

While one can always find inflationary models to explain whatever phenomenon is represented by the flavour of the month, it is true that the generic predictions, associated with the vast majority of the models of inflation on the market, have had two immense successes. One of these is the verification of the flatness of space. Another stems from an achievement of the three-year data from WMAP, which has succeeded in eliminating one of the rival hypotheses to inflation, the Harrison–Zel'dovich prediction of the scale-invariant nature of the primordial density fluctuations. This asserts that the spectral index of the scalar fluctuation power spectrum n_s= 1.0 , on the basis of simple but compelling scaling arguments. However, this is one situation where simplicity has to be abandoned when confronted with reality. The result from the WMAP satellite (in 2006) is that n_s= 0.96 ± 0.02 – expected as a consequence of the finite duration of inflation. Smaller and smaller fluctuations exit the horizon later and later as inflation peters out and the fluctuation distribution gradually rolls over in power.

Nowadays, cosmology seems rather unexciting. All measurements converge on the standard cosmological model with hypothesized ingredients of dark matter and dark energy that are themselves poorly understood. Future experiments concentrate on reducing error bars, with the possibility always lurking of finding new physics. It requires immense hubris to be confident that we have found the final solution, given our woefully inadequate mastery of the first instants of the Big Bang. Whatever the ultimate theory of cosmology, it will surely include our standard cosmological model as a component.

The George Darwin Lecture

This lecture is given annually on a topic in astronomy, cosmology, astroparticle physics, etc by a speaker distinguished not only by their understanding and insight, but also by their special skills as a speaker. The lecture is given at an A&G Meeting of the Royal Astronomical Society, open to all.