On the present status of inflationary cosmology

We give a brief review of the basic principles of inflationary theory and discuss the present status of the simplest inflationary models which can describe Planck/BICEP/Keck observational data by choice of a single model parameter. In particular, we discuss the Starobinsky model, Higgs inflation, and \(\alpha \)-attractors, including the recently developed\(\alpha \)-attractor models with \(SL(2,\mathbb {Z})\) invariant potentials. We also describe inflationary models providing a good fit to the recent ACT data, as well as the polynomial chaotic inflation models with three parameters, which can account for any values of the three main CMB-related inflationary parameters \(A_{s}\), \(n_{s}\) and r.