Exact analytical solution of the dynamic equations of the scalar field model

Abstract

The article considers a scalar cosmological model that satisfies the field equations of general relativity to study
the role of the scalar field as a source of the accelerated expansion of the Universe at an early stage of its development. The authors have presented a point Lagrangian. There was obtained a system of equations of motion. A scalar field in the form of a power function was chosen to investigate the model and find a solution. There were calculated the Hubble parameter, scale factor, density, and pressure of dark energy using the form of the scalar field function. There were built graphs to verify obtained solutions. There were investigated parameters of a slow roll describing the inflation process. Energy conditions were
used in terms of the scale factor and the deceleration parameter to explain the evolution of the Universe. These conditions impose model-independent constraints on the behavior of the energy density and pressure.