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.

Dark matter direct and indirect detection signals depend crucially on the dark matter distribution. While the formation of large scale structure is independent of the nature of the cold dark matter (CDM), the fate of inhomogeneities on sub-galactic scales, and hence the present day CDM distribution on these scales, depends on the micro-physics of the CDM particles. We study the density contrast of Weakly Interacting Massive Particles (WIMPs) on sub-galactic scales. We calculate the damping of the primordial power spectrum due to collisional damping and freestreaming of WIMPy CDM and show that free-streaming leads to a CDM power spectrum with a sharp cut-off at about 10 −6 M ⊙ . We also calculate the transfer function for the growth of the inhomogeneities in the linear regime, taking into account the suppression in the growth of the CDM density contrast after matter-radiation equality due to baryons and show that our analytic results are in good agreement with numerical calculations. Combining the transfer function with the damping of the primordial fluctuations we produce a WMAP normalized primordial CDM power spectrum, which can serve as an input for high resolution CDM simulations. We find that the smallest inhomogeneities typically have co-moving radius of about 1 pc and enter the non-linear regime at a redshift of 60±20. We study the effect of scale dependence of the primordial power spectrum on these numbers and also use the spherical collapse model to make simple estimates of the properties of the first generation of WIMP halos to form. We find that the very first WIMPy halos may have a significant impact on indirect dark matter searches.

We reexamine the constraints on the density perturbation spectrum, including its spectral index n, from the production of primordial black holes. The standard cosmology, where the Universe is radiation dominated from the end of inflation up until the recent past, was studied by Carr, Gilbert, and Lidsey; we correct two errors in their derivation and find a significantly stronger constraint than they did: nՇ1.25 rather than their 1.5. We then consider an alternative cosmology in which a second period of inflation, known as thermal inflation and designed to solve additional relic overdensity problems, occurs at a lower-energy scale than the main inflationary period. In that case, the constraint weakens to nՇ1.3, and thermal inflation also leads to a ''missing mass'' range 10 18 gՇM Շ10 26 g in which primordial black holes cannot form. Finally, we discuss the effect of allowing for the expected non-Gaussianity in the density perturbations predicted by Bullock and Primack, which can weaken the constraints further by up to 0.05. ͓S0556-2821͑97͒04022-8͔PACS number͑s͒: 98.80.Cq