What is dark matter, what is dark energy, and which high-energy framework completes the Standard Model? The open core of Wilczek's 'The Universe is a Strange Place'

Frank Wilczek's essay 'The Universe is a Strange Place' (Int. J. Mod. Phys. A 21, 2011-2025 (2006)), the published form of his July 2005 public lecture at Lepton-Photon 2005 in Uppsala (accessible full text: arXiv:physics/0511067), which surveys the standard models of particle physics and of cosmology and lists the major issues they leave unresolved. The essay's composite question is: (1) the nature of dark matter — whether it is made of particles, what its mass is, whether it interacts with ordinary matter only gravitationally or also weakly, and whether it self-interacts or annihilates; (2) the nature of dark energy — the component that does not clump, appears equally dense everywhere, and exerts the negative pressure driving the accelerating expansion, about which the essay states that even less is known than about dark matter: what it is, and whether it is an intrinsic property of space-time itself or something else; and (3) which high-energy framework — low-energy supersymmetry, grand unification, or another extension — completes the Standard Model, given that their predicted new particles and phenomena remain unobserved. Because the source is a survey lecture, the question is a conjunctive composite of three logically independent major open problems.

Background

By the early 2000s, physics rested on two 'standard models'. The Standard Model of particle physics is the quantum field theory of the known elementary particles and their non-gravitational interactions: the strong force is described by quantum chromodynamics (QCD), the gauge theory of quarks and gluons, while the electromagnetic and weak forces are unified in the electroweak interaction, whose symmetry is broken by the Higgs field. The standard model of cosmology, called 'ΛCDM' (Λ for the cosmological constant, CDM for cold dark matter), describes a spatially flat, expanding universe whose content is summarized by a few density parameters: about 5% ordinary (baryonic) matter, about 27% 'cold dark matter', and about 68% 'dark energy'. Frank Wilczek's 2006 essay 'The Universe is a Strange Place' — the published form of his July 2005 public lecture at Lepton-Photon 2005 in Uppsala (arXiv:physics/0511067; a different, earlier talk of the same title, the December 2003 SpacePart03 keynote, was published separately as astro-ph/0401347) — surveys both models and lists the unresolved questions they share. Dark matter is matter that neither emits nor absorbs light. It has been inferred since the 1930s-1970s from the motions of galaxies in clusters and the flat rotation curves of spiral galaxies, and since the 1990s it has been mapped precisely by gravitational lensing and by the acoustic peaks of the cosmic microwave background (CMB, the relic radiation of the hot early universe; the Planck satellite's 2018 analysis pins the non-baryonic matter density to about 27% of the total). It is 'cold' (non-relativistic when structure forms) and effectively collisionless. Its gravitational phenomenology is nailed down, but its microscopic identity is not: candidates span primordial black holes, the QCD axion (a very light, feebly interacting particle predicted by the Peccei-Quinn mechanism, which removes an unobserved time-reversal-violating term from QCD), and weakly interacting massive particles (WIMPs), the classic example being the lightest supersymmetric particle (LSP), such as the neutralino (the lightest neutral fermionic superpartner). Supersymmetry (SUSY) is the proposal that every known fermion has a bosonic partner and vice versa; when softly broken at the TeV scale, the virtual effects of the superpartners change the 'running' (energy-dependence due to vacuum polarization) of the three Standard Model gauge couplings so that they meet accurately at a common scale of order $10^{16}$ GeV — the quantitative success of grand unification, the embedding of the gauge group $SU(3)\times SU(2)\times U(1)$ into a simple group such as $SU(5)$ or $SO(10)$, which predicts interconversion of quarks and leptons and hence proton decay. In R-parity-conserving supersymmetric models (R-parity being a multiplicative quantum number forbidding the decay of the lightest superpartner into ordinary particles) the LSP is stable and, for standard thermal freeze-out in the early universe (thermally produced particles annihilating until the annihilation rate falls below the cosmic expansion rate, at which point their residual abundance is fixed), is produced with roughly the observed relic abundance — the reason it is the textbook dark matter candidate. Wilczek's essay leans on these unification and relic-abundance successes — it notes that if a predicted new particle is stable, its big-bang abundance can be calculated, and 'if we're lucky' one such particle may 'supply the astronomers' dark matter' — and looks to the Large Hadron Collider (LHC), which 'will achieve the energies necessary to access the new world of heavy particles, if it exists', as the decisive test; none of the essay's proposed new particles had been observed when it was written. Dark energy is the component driving the accelerating expansion discovered with Type Ia supernovae in 1998; its equation-of-state ratio of pressure to density, $w$, is observed to be close to $-1$, the value of a cosmological constant. In quantum field theory, empty space carries energy: zero-point fluctuations plus condensates associated with electroweak symmetry breaking and with the spontaneous chiral symmetry breaking of QCD. A straightforward estimate of this vacuum energy exceeds the observed dark-energy density by dozens to over a hundred orders of magnitude (commonly quoted as $10^{56}$ to $10^{120}$, depending on the assumed ultraviolet cutoff, the highest energy up to which the quantum-field-theory estimate of the vacuum energy is carried). This is the 'old' cosmological-constant problem, canonically formulated by Weinberg (1989): if dark energy is the energy of empty space, the positive contributions and any negative contribution must cancel to within dozens to over a hundred orders of magnitude of their natural scale. Two broad families of explanation of a small vacuum energy exist in the literature: anthropic selection — the observation, due to Steven Weinberg, that a much larger Λ would prevent galaxy formation, so that observers in a multiverse where Λ varies must find it small (Weinberg, 1989) — and dynamical mechanisms, including modifications of gravity. Neither family is established. The essay's composite question — what the dark matter and dark energy that together make up about 95% of the universe are, and which proposed extension of the Standard Model (if any) is realized — is the problem posed here.

Problem Statement

The problem, as posed by Wilczek's essay, is a composite of three unresolved questions about the universe's dark sector and the completion of the Standard Model. (1) Nature of dark matter: establish what the non-baryonic matter component of the universe (about 27% of its energy density, about 85% of its matter) consists of — whether it is made of particles, what its mass is, whether it interacts with ordinary matter only gravitationally or also through weak non-gravitational couplings, and whether it self-interacts or annihilates. Among the candidates the essay discusses are the QCD axion and the lightest supersymmetric particle; a new stable particle arising from an improved framework carries a calculable big-bang abundance, and any identification must be assessed against the existing observational and experimental constraints. (2) Nature of dark energy: establish what the component driving the late-time accelerating expansion (about 68% of the total) is — the essay notes that even less is known about dark energy than about dark matter: it does not clump, appears equally dense everywhere, exerts negative pressure, and behaves 'as if it is an intrinsic property of space-time itself'. A resolution must account for these observed properties; if dark energy is identified with vacuum energy, this includes the smallness of the effective vacuum-energy density relative to the natural contributions of known condensates and zero-point energies (the cosmological-constant problem of the background literature). (3) The high-energy completion of the Standard Model: establish which specific framework — low-energy supersymmetry, grand unification, or another extension — actually completes the Standard Model, given that these are attractive because they improve gauge-coupling unification and supply dark matter candidates, while their predicted new particles and phenomena (superpartners, proton decay, axions) have not been decisively observed. The common objective uniting the three components is the essay's stated program of 'improving, rather than merely complicating, our description of the world' in response to the discovery that ordinary matter is only about 5% of the universe: the identification of the dark matter and of the dark energy should follow from, or cohere with, the high-energy framework that extends the Standard Model — the essay explicitly links the two by noting that a new stable particle from the improved equations might 'supply the astronomers' dark matter'. The three components are, respectively: (i) the leading candidate(s) for the identity of dark matter and the evidence for and against each; (ii) whether dark energy is consistent with a pure cosmological constant or requires something else, and the status of the leading explanations of a small effective vacuum-energy density; and (iii) which specific framework, if any, completes the Standard Model, together with the decisive tests that would confirm or refute it.

References

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