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 that 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 $r$.