The detection of gravitational waves from mergers of tens of Solar mass black hole binaries has led to a surge in interest in primordial black holes (PBHs) as a dark matter candidate. We aim to provide a (relatively) concise overview of the status of PBHs as a dark matter candidate, circa Summer 2020. First we review the formation of PBHs in the early Universe, focussing mainly on PBHs formed via the collapse of large density perturbations generated by inflation. Then we review the various current and future constraints on the present day abundance of PBHs. We conclude with a discussion of the key open questions in this field.

Ground-based gamma-ray astronomy has had a major breakthrough with the impressive results obtained using systems of imaging atmospheric Cherenkov telescopes. Ground-based gamma-ray astronomy has a huge potential in astrophysics, particle physics and cosmology. CTA is an international initiative to build the next generation instrument, with a factor of 5–10 improvement in sensitivity in the 100 GeV–10 TeV range and the extension to energies well below 100 GeV and above 100 TeV. CTA will consist of two arrays (one in the north, one in the south) for full sky coverage and will be operated as open observatory. The design of CTA is based on currently available technology. This document reports on the status and presents the major design concepts of CTA.

Primordial black holes (PBHs) can form in the early Universe from the collapse of large density fluctuations. Tight observational limits on their abundance constrain the amplitude of the primordial fluctuations on very small scales which cannot otherwise be constrained, with PBHs only forming from the extremely rare large fluctuations. The number of PBHs formed is therefore sensitive to small changes in the shape of the tail of the fluctuation distribution, which itself depends on the amount of non-Gaussianity present. We study, for the first time, how quadratic and cubic local non-Gaussianity of arbitrary size (parametrized by fNL and gNL respectively) affects the PBH abundance and the resulting constraints on the amplitude of the fluctuations on very small scales. Intriguingly we find that even nonlinearity parameters of order unity have a significant impact on the PBH abundance. The sign of the non-Gaussianity is particularly important, with the constraint on the allowed fluctuation amplitude tightening by an order of magnitude as fNL changes from just -0.5 to 0.5. We find that if PBHs are observed in the future, then regardless of the amplitude of the fluctuations, non-negligible negative fNL would be ruled out. Finally we show that gNL can have an even larger effect on the number of PBHs formed than fNL.

We revisit the calculation of the abundance of primordial black holes (PBHs) formed from primordial density perturbations, using a formation criterion derived by Shibata and Sasaki which refers to a metric perturbation variable rather than the usual density contrast. We implement a derivation of the PBH abundance which uses peaks theory, and compare it to the standard calculation based on a Press-Schechter-like approach. We find that the two are in reasonable agreement if the Press-Schechter threshold is in the range ${\Delta }_{\mathrm{th}}\simeq 0.3$ to 0.5, but advocate use of the peaks theory expression which is based on a sounder theoretical footing.