Introduction

In the late 1940s and throughout the 1950s a number of visionary scientists including Alpher, Fermi, Follin, Gamow, Hayashi, Herman and Turkevich attempted to explain nuclear abundance patterns observed in the nearby Universe, such as the peculiar high helium mass fraction YP ≈ 0.25. This initially speculative work on an era of nucleosynthesis (element formation) in an expanding Universe at very high temperature T ∼ 109 K developed slowly but steadily over the coming decades into what is now known as the Standard Model of Big Bang nucleosynthesis (BBN). The idea that the Universe may have undergone a very hot and dense early phase was triggered by the observations of Hubble, in the 1920s, of the recession velocity of galaxies being proportional to their inferred distance from the Milky Way, which were most elegantly explained by a Universe in expansion. The ‘expanding hot Big Bang’ idea received further support from the observation by Penzias and Wilson in 1965 of the cosmic microwave background radiation (CMBR), believed to be the left-over radiation of the early Universe. Detailed observational and theoretical studies of BBN as well as the CMBR and the Hubble flow have developed into the main pillars on which present-day cosmology rests.

BBN takes place between eras with (CMBR) temperatures T ≠ 3 MeV and T ≠ 10 keV, in the cosmic time window t ≠ 0.1–104s, and may be characterized as a freeze-out from nuclear statistical equilibrium of a cosmic plasma at very low (∼10−9) baryon-to-photon number ratio (cf. Section 28.2), conditions which are not encountered in stars.

Introduction

Gravitational lensing effects arise from the modification of space-time metric produced by mass concentrations. Following an early prediction of General Relativity, gravitational fields deflect the light path of photons and modify the apparent flux and shape of astronomical sources. By observing gravitationally lensed images, cosmologists can probe dark matter almost ‘directly’. They can in principle examine it without the need to speculate on the distribution of matter inside the gravitational potential responsible for the light deflection, nor on its dynamical state and on its thermodynamical properties.

A most attractive application of gravitational lensing concerns the quest for dark matter candidates and for the properties of dark matter particles. Successful examples are the microlensing experiments (see [798] and references therein) carried out over the past decade to detect sub-stellar dark compact objects in the Galaxy. Similar searches for invisible cosmologically distributed compact objects have been carried out using microlensing on quasars [609]. These experiments set limits on compact dark objects (CDO) in the mass range 10−6M⊙ < m < 106M⊙ [1918] and prove they represent a fraction ΩM(CDO) < 0.1 of invisible mass in the Universe, if any.

Beside microlensing, other extragalactic gravitational lensing effects on quasars and extended sources (galaxies) can also probe dark matter. Although they are less frequent and more complex phenomena than microlensing, these lensing configurations provide much more detail on the lens and on the amount and distribution of matter inside.

In this chapter we discuss the prospects for detecting dark matter (DM) by means of the model-independent annual modulation signature, using large-mass highly radiopure NaI(Tl) detectors at the Gran Sasso National Laboratory of the INFN.

The annual modulation signature and the target material

A model-independent approach is necessary in order to find the presence of DM particles in the Galactic halo. In principle, two main possibilities exist; they are based on the correlation between the distribution of the events, detected in a suitable underground set-up, and the Galactic motion of the Earth.

The first one (which mainly applies just to WIMP or WIMP-like DM candidates) correlates the direction of WIMP-induced nuclear recoils with that of the Earth's velocity. This directionality signature is, however, difficult to exploit in practice, mainly because of technical difficulties in reliably and efficiently detecting the short recoil track and in realizing suitably large mass detectors; this will be discussed elsewhere in this volume.

Another possibility is the DM annual modulation signature, which is the only feasible one at present; it is sensitive to wide ranges both of DM candidates and of interactions, and it is also able to test a large interval of cross-sections and of halo densities. This was originally suggested in the 1980s in refs. Such a signature exploits the effect of the Earth's revolution around the Sun on the number of events induced by the DM particles in a suitable low-background set-up placed deep underground.

Introduction

We consider here as cryogenic detectors the solid state or superfluid He detectors operated at temperature lower than 77 K. The principle of operation of these detectors is presented in Section 20.2. Liquid xenon, argon and neon detectors operated respectively at 165 K, 87 K and 20 K are described in the following chapter.

The first searches for dark matter particles were performed with ultrapure semiconductors, operated at liquid nitrogen temperature and installed in pure lead and copper shields in underground environments. Combining a-priori excellent energy resolutions (low energy thresholds) and very pure detector material, they produced the first limits on WIMP searches in the 1980s. It turns out that about 20 years later, such germanium detectors, reaching sub-keV thresholds, have produced the best limits at very low WIMP masses, i.e. lower than 10 GeV. Performances and results of these detectors are described in Section 20.3.1.

In the 1980s, the idea was also put forward in the United States, Europe and Japan of using very low temperature detectors to achieve the required excellent energy resolution and low threshold characteristic of semiconductors, but with different materials and then different nuclei. The idea was to detect particles in a crystal by measuring the increase of temperature induced by the energy deposition. As the heat capacity approximately follows a Debye law with a T3 dependence, it is possible to consider real calorimetric measurements down to very small energy deposition, by using the proper absorber and low enough temperature.

At the time the Peccei–Quinn (PQ) solution [1555] to the strong CP problem [1553] was proposed it seemed perfectly reasonable to identify the PQ symmetry breaking scale with the electroweak scale. As the mass and the couplings scale inversely with the symmetry breaking scale, the expectation was that the mass of the axion would be hundreds of keV with couplings strong enough to be seen in accelerator and reactor experiments. The experimental situation quickly began to disfavour a massive axion as null results began to be amassed from a variety of particle and nuclear physics experiments. Tacitly acknowledging that there was no strong theoretical guidance for such a choice, new models soon appeared with arbitrarily large fa, resulting in couplings so extraordinarily weak as to render the axion effectively invisible. Frustrating as this might have been to experimentalists, an unintended consequence of such a small coupling would be the prospect for the axion to be the dark matter pervading the Universe (since) [1600].

Still, it was unsatisfying that axion dark matter could, in principle, completely escape detection. Fortunately, in 1983 Pierre Sikivie made a proposal that could make ‘invisible’ axions ‘visible’ again [1277; 1754; 1755]. To overcome the dreadfully small couplings and excessively long decay natural lifetimes, a technique was borrowed from the gravitational wave community. Specifically, Sikivie proposed that axion decay into two photons could be stimulated with a high-Q oscillator.

Direct dark matter detection technologies and directionality

The direct detection technologies described in Chapters 18, 20 and 21 are motivated mainly by a desire actively to distinguish hypothesized WIMP-induced nuclear recoil events from backgrounds such as electron recoils. In each case this is achieved by attempting to measure a quantity, or ratio of quantities, such as heat to light, that depends on the dE/dx of the particle. This raises the question, why not measure the dE/dx directly itself, that is, measure the energy loss distribution along the recoil tracks? Achieving this in a suitable medium, for instance by imaging the tracks in some way, could provide the maximum possible information on events, not just the dE/dx and Bragg curve but also the range and perhaps the absolute direction of the recoiling nucleus.

This is the objective of directional WIMP detectors discussed here. However, the advantage of directional sensitivity is not just the prospect of reaching the best feasible discrimination and particle identification, possible because there is no doubt that different species with the same recoil energy will have different ranges for instance, but more importantly the prospect of linking the direction of those recoils to our motion through the Galaxy. This would provide a clear route towards a signature based on the non-terrestrial nature of WIMPs, a potentially definitive signature for WIMPs as dark matter, with maximum model-independency from particle physics and cosmology assumptions.

Searching for dark matter with neutrinos

As the Solar System moves through the halo of the Milky Way, WIMPs become swept up by the Sun. Although dark matter particles interact only weakly, they occasionally scatter elastically with nuclei in the Sun and lose enough momentum to become gravitationally bound. Over the lifetime of the Sun, a sufficient density of WIMPs can accumulate in its centre so that an equilibrium is established between their capture and annihilation rates. The annihilation products of these WIMPs include neutrinos, which escape the Sun with minimal absorption, and thus potentially constitute an indirect signature of dark matter. Such neutrinos can be generated through the decays of heavy quarks, gauge bosons and other products of WIMP annihilation, and then proceed to travel to Earth where they can be efficiently identified using large volume neutrino detectors.

Compared with other dark matter detection techniques, indirect dark matter searches using neutrinos involve minimal astrophysical uncertainties. Although the capture rate of WIMPs onto the Sun depends on the local density and velocity distribution of dark matter (as do direct detection rates), the rate at which WIMPs annihilate is determined by the total number of WIMPs in the core of the Sun, which have accumulated over billions of years. As a consequence, any structure or other variations in the local dark matter density (subhaloes, streams, etc.) become averaged out.

Satellite galaxies

Historical review

Since Hubble first resolved stars in external galaxies and confirmed that these ‘island universes’ were beyond the realm of our own MilkyWay Galaxy, astronomers have sought to understand the properties of galaxies over many orders of magnitude in luminosity and distance from the Milky Way. To deal with the various morphologies of observed galaxies, Hubble proposed a classification in which galaxies are broadly identified as variations of spirals, ellipticals and irregulars. Although galaxies are observed with widely varying morphologies, the mass of most of them appears to be dominated by an unseen dark matter component, as was shown by Vera Rubin, Ken Freeman and others using measurements of gas clouds in spiral galaxies in the 1970s. Since these early studies, observations of the mass distributions of many galaxies have been studied, with results showing that the ratio of dark matter to luminous matter varies from galaxy to galaxy; the largest clusters of galaxies and the smallest known dwarf galaxies have the highest ratio of dark to luminous matter.

It is now known that even though galaxies with brightness similar to that of the Milky Way dominate the luminosity distribution of galaxies, by far the most numerous galaxies in the Universe are dwarf galaxies, which fall under Hubble's irregular category. The first recorded discovery of a dwarf galaxy came perhaps as early as the tenth century in the Persian astronomer Al-Sufi's Book of Fixed Stars.

Motivations

Supersymmetry is one of the best-motivated proposals for physics beyond the Standard Model. There are many idealistic motivations for believing in supersymmetry, such as its intrinsic elegance, its ability to link matter particles and force carriers, its ability to link gravity to the other fundamental interactions, and its essential role in string theory. However, none of these aesthetic motivations gives any hint as to the energy scale at which supersymmetry might appear. The following are the principal utilitarian reasons to think that supersymmetry might appear at some energy accessible to forthcoming experiments.

The first and primary of these was the observation that supersymmetry could help stabilize the mass scale of electroweak symmetry breaking, by cancelling the quadratic divergences in the radiative corrections to the mass-squared of the Higgs boson [1374; 1829; 1940], and by extension to the masses of other Standard Model particles. This motivation suggests that sparticles weigh less than about 1 TeV, but the exact mass scale depends on the amount of fine-tuning that one is prepared to tolerate.

Historically, the second motivation for low-scale supersymmetry, and the one that interests us most here, was the observation that the lightest supersymmetric particle (LSP) in models with conserved R-parity, being heavy and naturally neutral and stable, would be an excellent candidate for dark matter [760; 973]. This motivation requires that the lightest supersymmetric particle should weigh less than about 1 TeV, if it had once been in thermal equilibrium in the early Universe.

Dark matter haloes formed in ∧CDM cosmologies exhibit a characteristic dependence of density on distance from the centre (Chapter 2). Early studies [721; 1501] established ρDM ∼ r−3 or r−4 at large radii and ρDM ∼ r−1 inside the virial radius. On still smaller scales, the form of ρDM(r) was little more than an ansatz since the relevant scales were barely resolved in the N-body simulations. A debate ensued as to whether the profiles were indeed universal and, if so, what power of the radius described the dark matter density in the limit r → 0. Subsequent studies found central profiles both steeper [666; 940; 1247; 1471] and shallower [1431; 1503; 1504] than r−1.

The focus of this chapter is the dark matter distribution on sub-parsec scales. At these radii, the gravitational force in many galaxies is known to be dominated by the observed baryonic components (stellar bulge, nuclear star cluster) and by the supermassive black hole. Dark matter densities at these radii are barely constrained observationally; however, they could plausibly be orders of magnitude higher than the local value at the solar circle (∼10−2M⊙ pc−3), owing both to the special location at the centre of the halo and to interactions between dark matter and baryons during and after formation of the galaxy. High dark matter densities make the centres of galaxies preferred targets for indirect detection studies, in which secondary particles and photons from the annihilation or decay of supersymmetric dark matter particles are detected on the Earth (Chapter 24).

Introduction

The study of the interactions of elementary particles at high-energy accelerators over the past 40 years has led us to a paradoxical situation. On one hand, these studies have apparently solved the problem of the nature of the strong and weak nuclear interactions. The precision data from LEP, SLC, the Tevatron and the B-factories has confirmed the leading theory of the strong interactions – QCD – to per cent accuracy and the leading theory of the electroweak interactions SU(2) × U(1) Yang–Mills theory to the accuracy of parts per mil. On the other hand, there are important phenomena in Nature that are completely outside the scope of this ‘Standard Model’. Dark matter, which makes up 80% of the matter in the Universe and cannot be composed of any Standard Model particle, provides the most striking example.

Most of the information that we have now on dark matter relates to the properties we can learn from gravitational measurements. We know the overall cosmic density of dark matter, and the local density of dark matter on the scale of galaxies and clusters. Soon we can hope to have measurements of dark matter at the particle level, of the rates of dark matter annihilation in the Galaxy and of dark matter scattering in underground detectors. To learn what the dark matter particle is and how it fits into a more general theory of Nature, it will be important to interpret these measurements in terms of data obtained from particle physics experiments.

The LHC is a proton–proton collider with centre of mass energy of 14 TeV, which started data-taking at CERN in 2009. Its purpose is to understand the nature of electroweak symmetry breaking and search for physics beyond the Standard Model. Two large general-purpose experiments are installed on the LHC, ATLAS [1] and CMS [22]. In these two experiments, much effort has been devoted to designing detectors sensitive to the broadest possible range of signatures of new physics, and to developing general and efficient search strategies.

While the Standard Model from a theory point of view is a complete renormalizable quantum field theory which does not require an ultraviolet completion, it is clearly experimentally incomplete: adding new stable particles at the weak scale with a typical weak coupling can, for example, explain the observed dark matter density in the Universe. Going up in energy, flavour physics in the quark sector is merely parameterized in the Standard Model, without any hint of what the underlying structure might be. Lepton flavour and in particular neutrino masses can be described by a see-saw mechanism that requires a heavy right-handed neutrino and an effective dimension-five operator at high energy scales. The measured almost-perfect gauge coupling unification in the Standard Model is in contradiction with proton decay searches, but it could easily be rescued by new physics at the weak scale.

Dark matter (DM) is one of the pillars of the Standard Cosmological Model, but the nature of this elusive component of the matter budget of the Universe remains unknown, despite the compelling evidence at all astrophysical scales. The possible connection with theories beyond the Standard Model of particle physics makes DM one of the most important open problems in modern cosmology and particle physics, as witnessed by the enormous theoretical and experimental effort that is being put towards its identification.

Many different strategies have been devised to achieve this goal. First, the Large Hadron Collider, which is just starting operations, is expected to provide insights of paramount importance into possible extensions of the Standard Model of particle physics. Whether or not a specific candidate is “observed” at the LHC, any evidence for new physics (or lack thereof) will inevitably change our understanding of physics, and in particular our understanding of DM. If DM candidates are actually found, the question will arise of whether they actually are the DM in the Universe.

A convincing identification can probably be obtained only by combining the results of accelerator searches with astrophysical searches, based on the direct or indirect detection of DM particles in the local Universe. Direct DM searches are based on the measurement of the recoil energy of nuclei struck by DM particles in large detectors. This field has evolved dramatically in the past decade, and the different experimental strategies (cryogenic, liquid noble gases, superheated) developed over the years have led to a spectacular improvement of the constraints on DM–nucleon interactions.