https://biblio.ugent.be/publication/685594/file/1130605.pdf

Review of Particle Physics

Topological insulators are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi2Te3 and Bi2Se3 crystals. Theoretical models, materials properties, and experimental results on two-dimensional and three-dimensional topological insulators are reviewed, and both the topological band theory and the topological field theory are discussed. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.

/pdf/topological-insulators-and-superconductors-2nf6p2217g.pdf

Topological insulators and superconductors

We review in detail a number of approaches that have been adopted to try and explain the remarkable observation of our accelerating universe. In particular we discuss the arguments for and recent progress made towards understanding the nature of dark energy. We review the observational evidence for the current accelerated expansion of the universe and present a number of dark energy models in addition to the conventional cosmological constant, paying particular attention to scalar field models such as quintessence, K-essence, tachyon, phantom and dilatonic models. The importance of cosmological scaling solutions is emphasized when studying the dynamical system of scalar fields including coupled dark energy. We study the evolution of cosmological perturbations allowing us to confront them with the observation of the Cosmic Microwave Background and Large Scale Structure and demonstrate how it is possible in principle to reconstruct the equation of state of dark energy by also using Supernovae Ia observational data. We also discuss in detail the nature of tracking solutions in cosmology, particle physics and braneworld models of dark energy, the nature of possible future singularities, the effect of higher order curvature terms to avoid a Big Rip singularity, and approaches to modifying gravity which leads to a late-time accelerated expansion without recourse to a new form of dark energy.

Dynamics of dark energy

We report on the implications for cosmic inflation of the 2018 Release of the Planck CMB anisotropy measurements. The results are fully consistent with the two previous Planck cosmological releases, but have smaller uncertainties thanks to improvements in the characterization of polarization at low and high multipoles. Planck temperature, polarization, and lensing data determine the spectral index of scalar perturbations to be $n_\mathrm{s}=0.9649\pm 0.0042$ at 68% CL and show no evidence for a scale dependence of $n_\mathrm{s}.$ Spatial flatness is confirmed at a precision of 0.4% at 95% CL with the combination with BAO data. The Planck 95% CL upper limit on the tensor-to-scalar ratio, $r_{0.002}<0.10$, is further tightened by combining with the BICEP2/Keck Array BK15 data to obtain $r_{0.002}<0.056$. In the framework of single-field inflationary models with Einstein gravity, these results imply that: (a) slow-roll models with a concave potential, $V" (\phi) < 0,$ are increasingly favoured by the data; and (b) two different methods for reconstructing the inflaton potential find no evidence for dynamics beyond slow roll. Non-parametric reconstructions of the primordial power spectrum consistently confirm a pure power law. A complementary analysis also finds no evidence for theoretically motivated parameterized features in the Planck power spectrum, a result further strengthened for certain oscillatory models by a new combined analysis that includes Planck bispectrum data. The new Planck polarization data provide a stringent test of the adiabaticity of the initial conditions. The polarization data also provide improved constraints on inflationary models that predict a small statistically anisotropic quadrupolar modulation of the primordial fluctuations. However, the polarization data do not confirm physical models for a scale-dependent dipolar modulation.

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Planck 2015 results. XX. Constraints on inflation

Supersymmetry, Supergravity and Particle Physics

We give an explanation of the $\mathrm{CP}$ conservation of strong interactions which includes the effects of pseudoparticles. We find it is a natural result for any theory where at least one flavor of fermion acquires its mass through a Yukawa coupling to a scalar field which has nonvanishing vacuum expectation value.

CP Conservation in the Presence of Pseudoparticles

We elaborate on an earlier discussion of CP conservation of strong interactions which includes the effect of pseudoparticles. We discuss what happens in theories of the quantum-chromodynamics type when we include weak and electromagnetic interactions. We find that strong CP conservation remains a natural symmetry if the full Lagrangian possesses a chiral U(1) invariance. We illustrate our results by considering in detail a recent model of (weak) CP nonconservation.

Constraints imposed by CP conservation in the presence of pseudoparticles

I describe how the QCD vacuum structure, necessary to resolve the U(1)_A problem, predicts the presence of a PabbrevPparity transformation, TabbrevTtime reversal transformation, and CPabbrevCPcharge conjugation transformation followed by party transformation violating term proportional to the vacuum angle θ. To agree with experimental bounds, however, this parameter must be very small (θ < 10-9). After briefly discussing some other possible solutions to this, so-called, strong CP problem, I concentrate on the chiral solution proposed by Peccei and Quinn which has associated with it a light pseudoscalar particle, the axion. I discuss in detail the properties and dynamics of axions, focusing particularly on invisible axion models where axions are very light, very weakly coupled, and very long-lived. Astrophysical and cosmological bounds on invisible axions are also briefly touched upon.

The Strong CP Problem and Axions

I consider a scenario proposed by Fardon, Nelson, and Weiner where dark energy and neutrinos are connected. As a result, neutrino masses are not constant but depend on the neutrino number density. By examining the full equation of state for the dark sector, I show that in this scenario the dark energy is equivalent to having a cosmological constant, but one that 'runs' as the neutrino mass changes with temperature. Two examples are examined that illustrate the principal features of the dark sector of this scenario. In particular, the cosmological constant is seen to be negligible for most of the evolution of the Universe, becoming important only when neutrinos become nonrelativistic. Some speculations on features of this scenario which might be present in a more realistic theory are also presented.

R.D. Peccei

Papers

CP Conservation in the Presence of Pseudoparticles

Constraints imposed by CP conservation in the presence of pseudoparticles

The Strong CP Problem and Axions

Neutrino models of dark energy

Constraints on variant axion models