Primordial black hole formation in k-inflation models

The local primordial density fluctuations caused by quantum vacuum fluctuations during inflation grow into stars and galaxies in the late universe and, if they are large enough, also produce primordial black holes. We study the formation of the primordial black holes in $k$-essence inflation models with a potential characterized by an inflection point. The background and perturbation equations are integrated numerically for two specific models. Using the critical collapse and peaks formalism, we calculate the abundance of primordial black holes today.