Slow–roll inflation in the power-law scalar model - Ratbay, Aisara (BULLETIN OF THE L.N. GUMILYOV EURASIAN NATIONAL UNIVERSITY. PHYSICS. ASTRONOMY SERIES, 2025)
In this work, we examine an inflationary model driven by a scalar field that evolves according to a power–law dependence on cosmological time. This assumption allows the Einstein–Klein–Gordon equations to be solved analytically within a flat FLRW metric and makes it possible to obtain closed-form expressions for the key dynamical quantities of the early Universe. Based on the chosen scalar field profile, the Hubble function and the scale factor are computed, enabling a detailed analysis of the emergence of accelerated expansion. The potential of the field and its derivatives are reconstructed directly from the equation of motion, which in turn allows us to derive analytical formulas for the Hubble and potential slow-roll parameters. The time evolution of these parameters is analyzed in order to determine the regime of validity of the slow-roll approximation and to identify the natural endpoint of the inflationary phase. The obtained results demonstrate that a power-law configuration of the scalar field can sustain a prolonged stage of inflation and accurately reproduce the main features of slow-roll dynamics within the framework of General Relativity.