Construction of Chiral Cosmological Models Unifying Inflation and Primordial Black Hole Formation

We propose the method for construction of $F(R,\xi )$ gravity model, unifying inflation and primordial black hole formation. The proposed models are based on the Starobinsky $R+R^2$ inflationary model, so, the function $F(R,\xi )$ is a quadratic polynomial of the Ricci scalar $R$. We show that the potential of the corresponding two-field chiral cosmological model in the Einstein frame can be always found in terms of the elementary functions. The special choice of the function $F(R,\xi )$ allows us to get such a generalization of the hybrid inflation that can describe both inflation, and the primordial black hole formation.