Methods for constructing and verifying inflationary models of the early universe

The paper considers methods for analyzing inflationary models of the early universe with scalar fields based on Einstein gravity and its modifications. Definitions of the main background parameters of cosmological inflationary models and parameters of cosmological perturbations are given. Methods for constructing inflationary models of the early universe that satisfy modern observational constraints on the values of the parameters of cosmological perturbations are considered.